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AP Statistics > DECK 11 BEFORE INFERENCE MIXED > Flashcards

DECK 11 BEFORE INFERENCE MIXED Flashcards

1
Q

<p>Compare population to sample</p>

A

<p>populations are generally large, and samples are small subsets of these population. We take samples to make inferences about populations. We use statistics to estimate parameters.</p>

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2
Q

How are we manipulating the environment differently in experiments and studies?

A

No manipulation or treatments in an observational study. You only manipulate environment in an experminet.

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3
Q

<p>How can you check for "straight enough?"</p>

A

<p>Residuals plot fool!</p>

<p>check the resids</p>

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4
Q

<p>What are random variables?</p>

A

<p>If you randomly choose people from a list, then their hair color, height, weight and any other data collected from them can be considered random variables.</p>

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5
Q

How to find P(at least 1)?

A

1-P(none)

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6
Q

If we use a NORMAL model to approx a BINOMIAL.. What are mean and SD?

A

mean= np and sd= root(npq). So N (np, root(npq))

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7
Q

<p>What percentile is Q1?</p>

A

<p>25th</p>

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8
Q

<p>How do you find outliers in regression?</p>

A

<p>they don'tfollow the "flow"</p>

<p>(pinky trick, cover with you pinky.. Then uncover.. Does it follow the flow?)</p>

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9
Q

<p>What do you call things that are not independent?</p>

A

<p>associated. Or not independent. We generally don't say DEPENDENT (unless talking about y variable on a scatterplot).</p>

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10
Q

<p>What point is on every regression line?</p>

A

<p>the mean-mean point. (x bar, y bar).</p>

<p>This point is generally not one of the points on the scatterplot.</p>

<p>Usually none of the scatterplot points are on the regression line.</p>

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11
Q

<p>is r sensitive to outliers?</p>

A

<p>yes. A single outlier can make it seem like there is a relationship ( if way out in x direction), or even seem like there is no relationship.</p>

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12
Q

<p>Interpret residual: Points above the line/positive resid</p>

A

<p>"the model underpredicted" or "actual performance was above the expected performance</p>

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13
Q

give an Example of a MULTISTAGE sample

A

Suppose you want to poll urban, suburban and rural citizens, you can divide a map into those strata, and then randomly choose neighborhoods or streets in each and ask everyone on those streets. Here you stratified by community type and then clustered by street.

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14
Q

<p>Q: How can you get a parameter? A: By taking a \_\_\_\_\_\_\_\_\_\_\_</p>

A

<p>Census</p>

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15
Q

What’s the difference between a prospective and a retrospective study?

A

A retrospective study takes a group and looks back at its history while a prospective study watches a group for a period of time and records the data along the way into the future.

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16
Q

<p>Does a high r value mean anything?</p>

<p>(can it look strong, but not be?)</p>

A

<p>Sure. It can. It tells you strength of LINEAR relationship.</p>

<p>BUT</p>

<p>CHECK THE SCATTER. One outlier or typo can make it look STRONG.</p>

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17
Q

<p>How do you describe CENTER for bimodal or multimodal?</p>

A

<p>talk about the modes (the lumps, the clusters)</p>

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18
Q

<p>What is a sample?</p>

A

<p>A subset of a population, often taken to make inferences about the population. We calculate statistics from samples.</p>

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19
Q

<p>How is r calculated?</p>

A

<p>r = sum(ZxZy) / (n-1)</p>

<p>it is the sum of rectangle areas on the standardizes Zaxes</p>

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20
Q

<p>Why do we plug 999 into normcdf?</p>

A

<p>It needs a z score, but we can't plug in infinity. So we go down or up 999 standard deviations and that pretty much gets everything</p>

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21
Q

Why do you have to Stratify?

A

You don’t have to.. But you might want to if you feel that a simple random sample might not be representative of the population . You want your sample to be like the population. a representative sample (it represents the population well).

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22
Q

what is independent?

A

when P(A)=P(A|B)… When the probability of A is the same even when B is also true… Knowing B does not affect the probability of A. (can also be checked by P(A)*P(B)=P(AandB))

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23
Q

<p>Interpret r squared</p>

A

<p>r squared % of variability in y can be explained by the model with x. The rest is in residuals…</p>

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24
Q

<p>What is meant by relative frequency?</p>

A

<p>The PERCENT of time something comes up (frequency/total)</p>

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25
Q

<p>How can you think about the mean and median to remember the difference when looking at a histogram?</p>

A

<p>mean is balancing point of histogram, median splits the area of the histogram in half.</p>

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26
Q

How is Blocking in an Experiment Similar to Stratefying in a Sample?

A

The two are similar because they divide the subjects into homogenous groups where the subjects are all similar (these traits were already present in the population)

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27
Q

<p>Why is it called the"least squares regression line?"</p>

<p>the LSRL?</p>

A

<p>Because, after you find the mean-mean point, you fix the line so that it minimizes the squared vertical distancesto that line from each point.</p>

<p>Itminimizes the squared residuals, the least squares....</p>

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28
Q

using calculator: suppose 30% of dogs have fleas. WTPT first dog with fleas was the fifth you checked?

A

not, not, not, not, yes… .7x.7x.7x.7x.3orgeopdf (.30, 5

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29
Q

<p>are there any normal samples?</p>

A

<p>no, nothing is normal, just normalish. The only normal thing is the model we use.</p>

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30
Q

<p>What is the difference between a sample and a census?</p>

A

<p>With a sample, you get information from a small part of the population. In a census, you get info from the entire population. You can get a parameter from a census, but only a statistic from a sample.</p>

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31
Q

In the fertilizer experiment, how could you plan to eliminate the confounding variable?

A

USING RANDOMIZED BLOCK DESIGN. Make each table a block, and then randomly assign fertilzer A and B to the plants at each table. Compare the fertilizers for table 1, then compare the fertilizers on table 2.

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32
Q

<p>Give example of correlation without causation and explain the lurking variable.</p>

A

<p>Ski accidents are higher on days with more hot chocolate sales, therefore, hot chocolate must cause ske accidents. (lurking variable: the number of people on the mountain). What is happening is that on days when the mountain is crowded, there are more hot chocolate sales and more ski accidents. So the population on the mountain is causing both to rise and fall together.</p>

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33
Q

<p>Interpret residual: Points below the line/negative resid</p>

A

<p>"the model overpredicted"</p>

<p>or</p>

<p>"Actual value was below the the expected (or predicted)"</p>

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34
Q

What is area under ANY probability curve?

A

1 (or 100%)

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35
Q

Systematic, how do you find the N for every nth subject, and then how do you proceed?

A

TOTAL POP/SAMPLE SIZE= your n (round down). Then use RAND INT to Randomly choose first. RANDINT(1, n). And then take every nTH.

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36
Q

<p>Compare Descriptive and Inferential STATS</p>

A

<p>Descriptive tells youabout the data that you have, inference uses that data you have to try to say something about an entire population?.</p>

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37
Q

How can you use random numbers to sample?

A

Number the subjects 00-99 (if less than 100) or 000-999 (if less than 1000) or 0000 to 9999 etc.. then use a random number table taking one, two, three or four numbers at a time. Throw out repeats.

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38
Q

<p>How do youinterpret slope EQUATION?</p>

<p>rSy/Sx</p>

A

<p>for each increase of 1 st dev in x direction,</p>

<p>you go r st dev in y direction.</p>

<p>2st dev in x, you go 2r st. devin y.</p>

<p>3st dev in x, you go 3r st. dev in y.</p>

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39
Q

<p>What is homoscedasticity?</p>

A

<p>equal scatter along the regression line</p>

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40
Q

<p>Compare data to statistics</p>

A

<p>Data is each little bit of information collected from the subjects?. They are the INDIVIDUAL little things we collect? we summarize them by, for example, finding the mean of a group of data. If it is a sample, then we call that mean a "statistic" if we have data from each member of population, then that mean is called a "parameter"</p>

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41
Q

What are the differences between the subjects in strata and the subjects in clusters?

A

the “strata” are homogeneous, or have similar traits. The clusters are heterogeneous, or mixed traits.

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42
Q

What is response bias? How do you avoid it?

A

Response bias is any influence that may sway the respondent e.g wording of the question, interviewer’s behavior/background. Therefore, in a survey, ask questions that allow respondents to answer comfortably and honestly. Keep the wording “indifferent” or neutral in some way in order to unduly favor one response over another.

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43
Q

Do we add or subtract st dev when combining models?

A

neither… you always just add variances. Square the st devs, add them, then take sqrt.

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44
Q

<p>If I take a random sample of 20 hamburgers from FIVE GUYS and count the number of pickles on a bunch of them? and one of them had 9 pickles, then the number 9 from that burger would be calle</p>

A

<p>a datum, or a data value.</p>

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45
Q

<p>If something is correlated is it associated?</p>

A

<p>Yes.</p>

<p>If it is correlated then it must be associated.</p>

<p>However, if it is associated,it may not be correlated.</p>

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46
Q

A 4 year high school of 2000 students, sampling 40 high students: Describe a convenience sample

A

Ask the first 40 students coming to the locker rooms after school. This is problematic because athletes may not have the same preferences as non athletes.

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47
Q

using calculator: suppose 30% of dogs have fleas. WTPT exactly 7 or less out of 20 have fleas?

A

binocdf (20, .30, 7)

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48
Q

<p>If a distribution is skewed right, what will be greater, the mean or median? WHY?</p>

A

<p>Mean. The mean moves further to the right to keep balance.</p>

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49
Q

When we say “statistics vary” or the “variablility of statistics” are we talking about data from an individual?

A

NO… we are stating that summaries of samples (statistics) will vary from sample to sample. Statistics from one sample will differ from statistics from another sample and they will also differ from the parameters. The distance your statistic is from the parameter is called the ERROR.

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50
Q

What is the expected value?

A

The mean… What you’d AVERAGE if you played the game A LOT!!!!!!!!!

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51
Q

using calculator: suppose 30% of dogs have fleas. WTPT less than 4 out of 10 have fleas?

A

less than 4 is the same as 3 or less.binocdf (10, .30, 3)

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52
Q

<p>What's up with extrapolation? Is it OK?</p>

A

<p>Notideal. Sometimes it's all you can do, but state CAUTION.</p>

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53
Q

A 4 year high school of 2000 students, sampling 40 high students: Describe a cluster sample

A

Imagine that all of art classes have 10 students and they are mixed with fr, so, jr and srs… You would randomly choose 4 classes and survey everyone in each of the 4 classes.

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54
Q

What is difference between non response bias and undercoverage?

A

You may ask someone to take a survey, they may say no. They may feel differently than the people who decide to take the survey. In this case, that is non-response bias. Undercoverage happens when you didn’t even ask some people to take the survey. The people you didn’t even ask might feel different.

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55
Q

<p>Which is more sensitive to outliers and skewed? Mean, median. Sd or IQR?</p>

A

<p>Mean and SD are most influenced by outliers. median and IQR are RESISTANT, RESILIENT, ROBUST!!</p>

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56
Q

How do you find mean and sd of probability model?

A

put values in L1, probabilities in L2, and run “1-var stats L1,L2” and you get it!

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57
Q

<p>First step in interpreting slope</p>

A

<p>Write "slope units y over 1 unit x" and look at it. </p>

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58
Q

binocdf

A

(n,p,x)….. Probability of X OR LESS successes in N trials. (CUMULATIVE probability)

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59
Q

<p>How do you match OGIVES to histograms?</p>

A

<p>RECTANGLE DROP!!</p>

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60
Q

what does geometric model tell us about

A

it is about FIRST SUCCESS… What is likelihood first success is on 5th trial?

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61
Q

What’s a useful alternative when you can’t run an experiment? What are they useful forms of this, and how do you preform them respectively?

A

An alternative of an experiments could be an observational study. t.

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62
Q

<p>When drawing a graph or chart, what do you have to remember to do?</p>

A

<p>LABEL AXES, make a KEY(if needed ) AND GIVE IT A NAME!!! "Figure 1: Age and Food Preference"</p>

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63
Q

<p>What does normcdf do?</p>

A

<p>It gives you the area under the normal curve between any two z scores</p>

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64
Q

How is undercoverage different from non response

A

undercoverage you don’t even ask people, non-response you ask, but they don’t answer.

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65
Q

<p>what is the shortcut invnorm?</p>

A

<p>gives data value from percentile, skips Z score. Invnorm (percentile, mean, sd)</p>

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66
Q

<p>how do you describe form of a scatterplot?</p>

A

<p>straight orcurved?</p>

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67
Q

<p>How do you undo squares or cubes?</p>

<p>like if you have x2= stuff</p>

<p>or x3= stuff</p>

A

<p>^ 1/2 or ^ 1/3</p>

<p>(raise stuff to these powers to get x)</p>

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68
Q

<p>if you mult or divide the x's or y's (shift/scale) does r change?</p>

A

<p>no. the strength remains the same. (If you log or square it, it will change, but just adding or multiplying won't change it)</p>

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69
Q

<p>Does a census make sense?</p>

A

<p>A census is ok for small populations (like Mr. Nystrom's students) but impossible if you want to survey "all US teens"</p>

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70
Q

What is a level in an experiment? give example

A

Example. For the Factor “SLEEP” the, level(s) would be how many hours the subjects were alowed to sleep.. 4 hours, 6 hours, 8 hours.. 3 levels

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71
Q

<p>Think of the minimum value, the median and the IQR, which is</p>

A

<p>If you multiply a data set by a number, then the min, median and the IQR will multiply by that number.</p>

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72
Q

<p>What percent of the data is above Q3?</p>

A

<p>25%</p>

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73
Q

Example of undercoverage

A

You only ask people who go to Home Depot about their views on school lunches.

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74
Q

What is difference between completely randomized and random block design?

A

Completely randomized takes all units and puts them in a hat and randomly chooses treatments, blocked puts them all in different hats first (blocks) and then chooses

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75
Q

A bag has 3 red chips and 4 blue chips.. WTPT you reach in and grab 2 reds?

A

3/7 * 2/6 = 6/42 or 3/21 (notice the denominator changed)

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76
Q

using calculator: suppose 30% of dogs have fleas. WTPT first dog with fleas was ON OR BEFORE the fifth you checked?

A

geocdf (.30, 5)

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77
Q

<p>What is a "percentile?"</p>

A

<p>It tells you the percent of data BELOW a certain value</p>

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78
Q

What is probability first success is on 7th try?

A

qqqqqq p (q^6*p). (this is a GEO prob)

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79
Q

<p>What percentile is the median (aka Q2)?</p>

A

<p>50th</p>

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80
Q

<p>What do we sometimes call a categorical variable?</p>

A

<p>qualitative</p>

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81
Q

<p>Does the regression line (LSRL) go through a lot of points?</p>

A

<p>No, usually it goes through NONE!</p>

<p>It just goes through the center of the cloud of points.</p>

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82
Q

<p>What is Statistics?</p>

A

<p>The study of variability</p>

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83
Q

When can we use a NORMAL model to approx a binomial?

A

when np and nq are over 10

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84
Q

<p>what is leverage?</p>

A

<p>Far right or left from the middle.</p>

<p>leverage just means it is far away from x-bar</p>

<p>Some leverage points are not influential if they go along with the flow of the scatter.</p>

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85
Q

<p>How can you match boxplots to histograms?</p>

A

<p>USE THE FISH TANK METHOD!</p>

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86
Q

<p>What is a Z score?</p>

A

<p>The number of standard deviaiton away from the mean</p>

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87
Q

What’s the difference between stratified and cluster sampling?

A

Stratified- you divide the population up into groups with similar traits, called strata (homogeneous groups) and randomly choose a few from each strata.

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88
Q

Why is it called “binomial”

A

These numbers come from the coefficients of expanded binomials.. (x+y)^1, (x+y)^2, (x+y)^3….

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89
Q

How to make TREES with screening tests????

A

SPLIT UP POPULATION FIRST&raquo_space;»» then split the groups by outcomes of the test

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90
Q

What is the difference between single-blind and double blind?

A

Single blinding is when all individuals in either one of the classes are blinded; double-blinded is when everyone in BOTH classes are blinded. Classes are: subjects and the other is treatment givers + evaluators…

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91
Q

How do you write “A BINOMIAL MODEL WITH p=.35 and n=12?”

A

B(12, .35) B(N, P)

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92
Q

What is BIAS in sampling?

A

A systematic FLAW in your method.

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93
Q

<p>Lurking variable: Why are there more ice cream sales on days that there are more surfing accidents? Is the ice cream putting surfers at risk?</p>

A

<p>The WEATHER is the lurking variable.</p>

<p>When it is a nice day, more surfers and more ice creams are sold.</p>

<p>So, the WEATHER causes both to go up and down together.</p>

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94
Q

How are we proving causation in experiments and obs studies?

A

No causation in a study, maybe association or correlation. ONLY IN EXPERIMENTS TO YOU TALK ABOUT CAUSALITY.

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95
Q

How are we using random numbers in experiments vs studies?

A

In a study, we randomly choose subjects to survey from the population as a whole. In an expermint we

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96
Q

<p>How do you find Q1 and Q3?</p>

A

<p>Q1 is the median of the bottom half and Q3 is the median of the upper half (they are the 25th and 75th percentiles)</p>

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97
Q

<p>the output for normcdf(Zleft, Zright) is\_\_\_\_\_\_\_</p>

A

<p>the area under the normal curve between the given z scores</p>

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98
Q

what is representative?

A

It means that the sample statistics will be kind of like the population parameters.. The sample “looks like” the population.

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99
Q

<p>How do you descrive SPREAD for unimodal and symmetric distributions?</p>

A

<p>use the standard deviation</p>

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100
Q

what is a complement?

A

the probability that it doesn’t happen. 1-P(it happens). (together they add to 100%) (P and Q are complements)

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101
Q

<p>How do you find percentiles and make a boxplot from OGIVE?</p>

A

<p>Go across till you hit the curve and then STRAIGHT DOWN!</p>

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102
Q

<p>How does multiplying by a constant impact the summary statistics of a data set? (or random variable)</p>

A

<p>It is SCALED. Both center and spread are effected. They all (mean, median, IQR, SD, range) get multiplied by three. (BE CAREFUL, remember the variance is the SD squared, so the variance gets multiplied by 9).</p>

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103
Q

A bag has 3 red chips and 4blue chips.. WTPT you grab a blue?

A

7-Apr

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104
Q

how do you combine probability models?

A

add or subtract the means, and then ADD THE VARIANCES ALWAYS…

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105
Q

Why randomize in an experiment?

A

To reduce confounding variables (and bias).

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106
Q

What is a continuous probability function or curve?

A

A line or curve (like the normal model) that has an area of exactly one. The probability is found by finding the area between the boundaries given.

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107
Q

<p>What percent of the data is below the median?</p>

A

<p>50%</p>

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108
Q

<p>If you want to find % below a value, what do put into normcdf (? ?)</p>

A

<p>find z score for value, and then normcdf (-999, Zright)</p>

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109
Q

What are the “good” sampling methods?

A

SRS (simple random sample), stratified, clustered, systematic, multistage

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110
Q

<p>What is the difference between a population mean and a sample mean?</p>

A

<p>population mean is the mean of a population, it is a parameter, sample mean is a mean of a sample, so it is a statistic. We use sample statistics to make inferences about population parameters.</p>

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111
Q

What is a weakness of a SRS?

A

Suppose you want a sample of 50 high school students, with an SRS, although unlikely you could get “all freshmen” which wouldn’t be representative.

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112
Q

What is the “hot hand” view of probability?

A

Misrepresentation of the law of large numbers. If someone flipped a coin and it landed on heads 4 times in a row… you’d expect it to be heads again because “heads is hot”.. NOT TRUE..

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113
Q

4 ingredients: What is “replication?”

A

Having enough subjects. You don’t want to test fertilizer on just one plant.

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114
Q

<p>What is the total area under the normal curve?</p>

A

<p>1 or 1.000</p>

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115
Q

How do you find the mean of a random variable if it is in a table?

A

values in L1, percents in L2, run 1-VAR STATS L1, L2.

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116
Q

<p>if you switch x and y does r change?</p>

A

<p>NO. The strength stays the same.</p>

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117
Q

<p>What is the difference between quantitative and categorical data?</p>

A

<p>The data is the actual gathered measurements. So, if it is eye color, then the data would look like this "blue, brown, brown, brown, blue, green, blue, brown? etc." The data from categorical variables are usually words, often it is simpy "YES, YES, YES, NO, YES, NO" If it was weight, then the data would be quantitative like "125, 155, 223, 178, 222, etc.." The data from quantitative variables are numbers.</p>

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118
Q

<p>what happens if you multiply all of a data set by a constant? Think of an example</p>

A

<p>it is scaled Both center and spread are impacted. Mean/ median/ stand dev/ iqr/ quartiles all multiplied by that constant. Center, spread and all individual values are changed. Consider 1,2,3,4,5 mean of 3 and range of 4. Now multiply by 3: 3,6,9,12,15 and you get a mean of 9 and a range of 12... both multiplied by three.</p>

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119
Q

<p>What does invnorm do?</p>

A

<p>It gives you the Z SCORE from a percentile</p>

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120
Q

<p>which calculator function gives you a percent?</p>

A

<p>normcdf(Z left, Z right)</p>

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121
Q

using calculator: suppose 30% of dogs have fleas. WTPT more than 10 out of 40 have fleas?

A

1 - 10 or less1-binocdf(40, .30, 10)

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122
Q

<p>Give a simple example showing that adding a constant doesn't change the spread, but changes the center. (this always happens)</p>

A

<p>Data set: 1,2,3,4,5 Spread (range):4, Center: 3 add three and get new data set: 3,4,5,6,7 spread:4 Center: 5 (center went up, spread stayed the same). The IQR and SD will stay the same, but median and mean go up 3. Called shifting, or sliding the data.</p>

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123
Q

A 4 year high school of 2000 students, sampling 40 high students: Since ALL GROUPS (samples) are possible and equally likely, show some groups that you could get randomly from and SRS that would not be representative of the entire school.

A

all female, all freshmen, all seniors, all athletes.. these could happen in an SRS (but they are not likely to)

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124
Q

<p>How do you undo an ln (natural log) when solving?</p>

<p>ex: ln x = stuff</p>

<p>or: ln x = m</p>

A

<p>estuff</p>

<p>or</p>

<p>em</p>

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125
Q

<p>Does the IQR capture 68% of the data?</p>

A

<p>NO. it catches the middle 50%.</p>

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126
Q

<p>How can you describe spread?</p>

A

<p>range, IQR, stand dev, variance, or simply say: From here, to about here</p>

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127
Q

<p>What is a random sample?</p>

A

<p>When you choose a sample by rolling dice, choosing names from a hat, or other REAL RANDOMLY generated sample. Humans can't really do this well without the help of a calculator, cards, dice, or slips of paper.</p>

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128
Q

<p>mean/SD/median/IQR. How do I know which ones to use?</p>

A

<p>when unimodal and symmetric, mean and sd. If skewed or outliers? Median and IQR. If bimodal? Talk about the MODES</p>

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129
Q

In which sampling methods do the subjects have equal chances of being selected?

A

SRS, Stratified, Clustered, Systematic, and multistage. In all of these, the subjects have an equal chance (but groups have different chances)

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130
Q

<p>What are DESCRIPTIVE STATS?</p>

A

<p>Tell me what you got! Describe to me the data that you collected, use pictures or summaries like mean, median, range, etc?</p>

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131
Q

What is the main purpose of a placebo ?

A

To blind the subject that is being experimented on to avoid influence to the given variable therefore altering the response variable . When people think they’re getting help, they often improve anyway..

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132
Q

<p>What percent of the data is above Q3?</p>

A

<p>25%</p>

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133
Q

How is a sampling frame different from the population?

A

Suppose you are wondering how elderly people on the cape feel about a new medicare law. If you go to nursing homes and randomly sample residents, then the frame is “elderly people at those nursing homes.” Your population is still elderly people on cape cod.

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134
Q

<p>What is a population?</p>

A

<p>the group you're interested in. Sometimes it?s big, like "all teenagers in the US" other times it is small, like "all AP Stats students in my school"</p>

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135
Q

<p>Think of the minimum value, the median and the IQR, which is impacted by shifting (adding a constant?)</p>

A

<p>adding a value shifts the entire histogram to the right, so the min and the median will increase by that amount, BUT THE IQR WILL NOT CHANGE.</p>

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136
Q

What is a factor? give example

A

DIET PLAN would be a factor and levels could be: low carb, low fat, and no diet

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137
Q

what is disjoint?

A

can’t be joined…. They can’t both happen at the same time! (being over 5 feet and under 4 feet)

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138
Q

<p>What percentile is Q3?</p>

A

<p>75th</p>

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139
Q

<p>What are 2 branches of AP STATS?</p>

A

<p>Inferential and Descriptive</p>

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140
Q

<p>How do you get equation from computer output?</p>

<p>variable coeff indep: doc</p>

<p>constant 0.005</p>

<p>genet - 0.233</p>

A

<p>doc = 0.005 - 0.233 (genet)</p>

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141
Q

what is probability?

A

THE LONG RUN RELATIVE FREQUENCY!!

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142
Q

Give example of factors and levels

A

Factor: medication. Levels: 50mg, 100mg and 200mg.

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143
Q

What is the problem with convenience sampling?

A

The sample may not be representative as it is not randomized to include every type of person. Friends and family are convenient but they likely share similar opinions and thus the sample is not representative of a population.

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144
Q

A 4 year high school of 2000 students, sampling 40 high students: Explain how clustering has “impossible groups”

A

You couldn’t get 2 people from each classroom, because you would be randomly choosing classrooms and asking everyone in those classes.

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145
Q

What are the two types of observational studies?

A

Retrospective, and Prospective

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146
Q

How many ways can I arrange M N W Z ?

A

4! 432*1 = 24 ways

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147
Q

<p>How do you describe distributions (histograms)?</p>

A

<p>Shape-Cener-Spread- and STRANGE (Outliers and gaps) some say GSOCS. where's yo GSOCS?</p>

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148
Q

What is a sampling frame?

A

It is the frame from which you get your sample. For instance, if you call people the frame would be “people with phones”

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149
Q

Give example of randomized block design for a new anxiety med vs placebo with 100 volunteers (60m and 40f)

A

Block by gender. Randomly assign 30m to new and rest placebo. Randomly assign 20w new and rest placebo.

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150
Q

<p>Computer ouput:</p>

<p>What does "constant" mean?</p>

A

<p>It is the y intercept</p>

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151
Q

<p>How can you describe the center of a distribution?</p>

A

<p>OPTIONS: give the mean (balance), median (splits area in half), mode (peaks, if bimodal talk about both modes) or say "centered around \_\_\_\_"</p>

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152
Q

How are voluntary and convenience samples similar…

A

With voluntary, people choose them selves, with covenience, the people are just chosen by researcher, neither uses randomness and both are prone to BIAS.

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153
Q

<p>How do you describe CENTER for skewed or distributions with outliers?</p>

A

<p>use the MEDIAN</p>

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154
Q

<p>How do you undo and exponent?</p>

<p>Example</p>

<p>stuffx= other</p>

<p>ax=b</p>

A

<p>log other / log stuff</p>

<p>that gives you x</p>

<p>or</p>

<p>x = (log b) / (log a)</p>

<p></p>

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155
Q

What is the purpose of matching?

A

it isolates the differences between subjects so help see the impact of the treatment.

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156
Q

What is the law of averages?

A

a misinterpretation of the law of large numbers. Using this law, if you flipped 4 heads in a row, you’d expect the next one to be a tails because it should even out in the long run, as if the coin remembers that it “owes you” something… NOT TRUE

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157
Q

What is a control group?

A

The group that doesn’t get a treatment (or gets the old treatment). It helps us see the impact of the environment. It gets the placebo or standard care but goes through all of the motions

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158
Q

<p>For information purposes, which gives LEAST… stem-leaf, histogram or box-whisker?</p>

A

<p>Box/Whisker, BE CAREFUL. you really don't know how things are distributed. The box and whisker and fish tank give a very GENERAL look.</p>

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159
Q

When sampling, what kind of sample are we striving to get?

A

A representative sample, we want our sample to have similar charactaristics as the population

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160
Q

A bag has 3 red chips and 4blue chips.. WTPT you grab a blue then a red? (without replacing)

A

4/7 * 3/6 (notice that there were only 6 in the bag)

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161
Q

<p>What is the line that you plot?</p>

A

<p>IT IS A MODEL!</p>

<p>It is the LSRL and it is the model we are talking about</p>

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162
Q

<p>What are the percentiles for Q1, med, and Q3?</p>

A

<p>25, 50 and 75</p>

163
Q

<p>Another name for "skewed right" is</p>

A

<p>positively skewed</p>

164
Q

<p>Can numbers be CATEGORICAL?</p>

A

<p>sure. Zip codes, sports jersey numbers, telephone numbers, social security nunmbers, area codes… these are categorical.</p>

165
Q

What is the difference between a completely randomized and a randomized block?

A

In a completely randomized experiment, all of the subjects names go into ONE HAT and you pick for treatment groups. In a randomized block design you have more hats (a hat for males, a hat for females etc) and pick for treatments from each.

166
Q

<p>What symbols do we use for population mean and sample mean?</p>

A

<p>Mu for population mean, xbar for sample mean.</p>

167
Q

A bag has 3 red chips and 4 blue chips.. WTPT you reach in and first grab a blue and then grab a red?

A

4/7 * 3/6 = 12/42 or 6/21

168
Q

What is stratified sampling?

A

When you break the population into groups with similar attributes and randomly select from each strata.

169
Q

<p>Year in school (F,S,J,S) and Pizza Preference (pepperoni or cheese) are \_\_\_\_\_\_\_\_\_\_ because \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_</p>

A

<p>independent because all grades have similar preference distributions.. 40% cheese, 30%pepperoni, 20% veggie 10% other</p>

170
Q

<p>How do you make a residuals plot? (find RESID?)</p>

A

<p>stat>plot make a scatterplot, but instead of L1 vs L2, change L2 by putting cursor on it and going to 2nd>lists down to RESID.</p>

<p>You can plot L1 vs RESID</p>

<p>or you can plot L2 vs RESID</p>

171
Q

4 ingredients: What is “compare?”

A

Having something to compare your treatment with helps you see its effectiveness.

172
Q

To make a survey to tell of a restaurant is good, would you ask the people coming out of the restaurant?

A

People at the restaurant are probably there because they already like it. If you asked the question “Is this your first time dining here?” and if they say “yes” you survey them, that would be a better method. But then again.. the people wouldn’t go into an Italian restaurant if they didn’t like that type of food.

173
Q

<p>How do you find the median from an OGIVE?</p>

A

<p>go halfway up the y axis, then shoot across to the curve, then straight down. It's at the 50th percentile (halfway up)</p>

174
Q

<p>What is the mode?</p>

A

<p>the most common, or the peaks of a histogram. We often use mode with categorical data</p>

175
Q

<p>If you want to find percentile for a value, what do you put into normcdf (? ?)</p>

A

<p>find z score for value, and then normcdf (-999, Zright) like going from negative infinity up to the z score</p>

176
Q

<p>How are mean, median and mode positioned in a skewed left histogram?</p>

A

<p>goes in that order, mean median mode</p>

177
Q

<p>What is Q2 also known as?</p>

A

<p>the median</p>

178
Q

<p>What symbols do we use for population standard deviation and sample standard deviation?</p>

A

<p>Sigma for population and s for sample.</p>

179
Q

what is the best way to reduce bias?

A

randomness and good sampling methods.

180
Q

<p>If the distribution is bimodal or multimodal, what would you use for center and spread statistics?</p>

A

<p>Talk about each mode (center) and maybe use the range or IQR. You could also say "one group seems to go from \_\_ to \_\_ and the other from about \_\_ to \_\_"</p>

181
Q

<p>When can you round?</p>

A

<p>AT THE VERY END!!! (keep at least 3 digits until end!)</p>

182
Q

<p>independent is the same as \_\_\_\_\_\_\_\_\_\_</p>

A

<p>not associated</p>

183
Q

<p>What is the mode?</p>

A

<p>the peaks of a histogram (the humps). or with categorical data, the most popular category</p>

184
Q

What is wording bias

A

A type of response bias, When the wording of the question impacts response to it. (type of response bias)

185
Q

Things that cause nonresponse bias ?

A

(remember non response is that the people you ask, or try to ask don’t respond) Lazy researcher, shy survey takers, who is the questioner, environment,

186
Q

<p>Can there be a correlation between grade and music preference?</p>

A

<p>No, music preference is categorical.</p>

<p>There is an association, however.</p>

187
Q

<p>What if a scatterplot goes straight across horizontally?</p>

A

<p>NO ASSOCIATION.</p>

<p>That would be like height and IQ, they are independent so each height has about the same IQ.</p>

188
Q

What is wrong with using volunteers in a survey?

A

(Volunteers are often upset or emotionally attached) Those who volunteer may not be like the rest of the population. An example may be, if you’re trying to find our how often people volunteer for things. So you ask for volunteers to take the survey. A question may be “when was the last time you volunteered for something?” Well. they all just volunteered for the survey!

189
Q

What is the difference between response bias and nonresponse bias?

A

Response is when the person’s response is influenced by the question or questioning method (like if a parent asks if you use drugs, as opposed to a friend… there is only one answer to this, but one might respond differently to them), non response is is when the people who don’t respond might have different opinions/views than the people who did.

190
Q

What is a mistake that people make with the law of large numbers?

A

they make short term predictions. The law of large numbers talks about the LOOOOOOONG run relative frequency.

191
Q

<p>What percent of the data is between Q1 and Q3?</p>

A

<p>the middle 50%. That is the IQR</p>

192
Q

<p>What is a frequency distribution?</p>

A

<p>A table, or a chart, that shows how often certain values or categories occur in a data set.</p>

193
Q

<p>what does influential mean?</p>

A

<p>It impacts the SLOPE.</p>

<p>It means that the point, when added or removed to data, will influence the SLOPE.</p>

<p>Generally these are outliers in the x direction. Far left or right.</p>

194
Q

Can you eliminate sampling error?

A

Only if you take a census. Larger samples have less error.

195
Q

<p>If the distribution is skewed (or outliers/not symmetric) what would you use for center and spread statistics?</p>

A

<p>Median (center) and IQR (spread)</p>

196
Q

<p>What is the difference between quantitative and categorical variables?</p>

A

<p>Quantitative variables are numerical measures, like height and IQ. Categorical are categories, like eye color and music preference</p>

197
Q

What is the standard sampling method? (the gold standard)

A

A Simple Random Sample (SRS) is our standard. Every possible group of n individuals has an equal chance of being our sample. That’s what makes it simple. Put the names in a hat.

198
Q

What is sampling error?

A

How far your statistic is from the parameter (how far your calculation from your sample was from the population parameter)

199
Q

What is a quality of SRS that is not a quality of Systematic, Stratified or Clustering?

A

In an SRS, all groups are possible, and ALL POSSIBLE GROUPS have the same chance of being picked (like all senior male students.).The other methods have lots of impossible groups. SRS has no impossible groups. Example: -Stratified- an impossible group would be all girls (you’re taking some boys and girls)-Clustered- an impossible group would be all girls (each cluster has boys and girls)-systematic- an impossible group would be first 10 people that are right next to each other (you are taking every nth person, so you will skip)

200
Q

Example of wording bias

A

Do you support food assistance and nutrition programs for children living in poverty? VS. Do you approve of supporting lazy people on welfare?

201
Q

<p>where are the "outlier fences?"</p>

A

<p>1.5 IQR above Q3 and 1.5 IQR below Q1. Just a rule of thumb.</p>

202
Q

<p>describe a scatterplot's strength?</p>

A

<p>give the r value (if straight),</p>

<p>or say…</p>

<p>"tightly packed… loosely packed"</p>

203
Q

<p>How can you straighten data?</p>

A

<p>Do stuff to the y (square it, root it, log it, etc) and recheck the plot. Remember to put the transformation into your equation. Example Sqrt y = 4.33 - 2.03 x</p>

204
Q

<p>When drawing a normal model, what are the PERCENTILES from left to right?</p>

A

<p>2.5, 16, 50, 84, 97.5</p>

205
Q

In which sampling methods do all subjects have the same probability of being chosen?

A

SRS, cluster, systematic and stratified all give subjects equal likelihood of being chosen.

206
Q

<p>Which calculator function gives you a z score?</p>

A

<p>invnorm(%ile)</p>

207
Q

<p>not associated is the same as being \_\_\_\_\_\_\_\_\_\_\_\_</p>

A

<p>independent</p>

208
Q

What is wrong with using voluteers in an experiment?

A

Not much. In an experiment, we are not looking for a sample that is like the population. We just want to see the effectiveness of a treatment. It is fine if the subjects are all similar. In fact it is best sometimes when they are!

209
Q

<p>How do you describe CENTER for unimodal and symetric distributions?</p>

A

<p>use the MEAN</p>

210
Q

using calculator: suppose 30% of dogs have fleas. WTPT AT LEAST ONE OUT OF 10 has fleas?

A

1-none= 1-.7^10or1-binopdf( 10, .30, 0)or1-binocdf( 10, .30, 0)

211
Q

<p>What if the scatterplot is curved?</p>

A

<p>Either straighten the scatterand fit a line,</p>

<p>or keep it and fit a curve</p>

<p>Try quadreg, cubicreg, lnreg, logreg and check the graph and the r.</p>

212
Q

<p>How do you undo sqrt when solving?</p>

<p>like</p>

<p>sqrt(x) = stuff</p>

A

<p>^2</p>

<p>(raise stuff to power of 2 to get x)</p>

213
Q

How do we use representative samples in experiments and studies?

A

You don’t need a representative sample in an experiment. You are not making inferences about a population, just about a treatment.

214
Q

How is BIAS different from SAMLING error

A

Bias is a systematic flaw in your sampling method. Sampling error is always present even with the best methodology.

215
Q

<p>How do you describe SPREAD for bimodal or multimodal?</p>

A

<p>talk about the outer edges of the clusters "from here to here" or use the IQR.</p>

216
Q

What is “probability of at least one” the same as?

A

1-probability of NONE.

217
Q

can independent events be disjoint? EXPLAIN

A

NO, if they are independent, then knowing one doesn’t change the probability of the other, but if they are disjoint, knowing one makes the other impossible, so it does change the probability to 0

218
Q

How can you decrease sampling error?

A

Get a larger sample

219
Q

<p>What does GSOCS stand for?</p>

A

<p>Gaps Shape Outliers Center Spread (put on your gsocs when comparing distributions) be sure to talk about each one clearly (make a list)</p>

220
Q

<p>If there is a crazy outlier, what can you do?</p>

A

<p>Run the analysis with and without the outlier and write about both.</p>

221
Q

geopdf

A

(p,x)… probability of FIRST SUCCESS being ON the Xth trial

222
Q

How are statistics and parameters different?

A

A statistics is a numerical description of a sample, and a parameter is a description of a population. The difference between these is called ERROR (sampling error).

223
Q

What is the sure way to assign treatments correctly?

A

throw names in hat and first half in group 1 and the rest group 2. . Or number subjects from 1-n and use randint until you get half for group 1.

224
Q

<p>What is a residual?</p>

A

<p>Vertical distance to the LSRL.</p>

<p>ACTUAL-PREDICTED,</p>

<p>A-P, like this class AP (get it?)</p>

<p>Take y data found and from that, subtract the y you get from plugging the x into the model (equation).</p>

225
Q

<p>How do you undo a log when solving?</p>

<p>log x = stuff</p>

<p>or</p>

<p>log x = m</p>

A

<p>10^ stuff</p>

<p>10stuff</p>

<p>that will get you x</p>

<p>or</p>

<p>x= 10m</p>

226
Q

<p>What values can r be?</p>

A

<p>from -1 to +1</p>

<p>(r near 0 is WEAK)</p>

227
Q

<p>How do you interpret slope?</p>

A

<p>For an increase of 1 [unit of x] there is an (increase/decrease) of [SLOPE] [units of y].</p>

<p>You can write "SLOPE UNITS Y/ ONE UNITS X" to help</p>

228
Q

<p>are any populations actually normal?</p>

A

<p>no, nothing is normal, just normalish. The only normal thing is the model we use.</p>

229
Q

<p>What is a contingency table?</p>

A

<p>shows distributions across 2 variables like gender and music pref. AKA 2-way table</p>

230
Q

<p>How do you find a certain percentile on an OGIVE?</p>

A

<p>Start at the % on the Y axis.. travel horizontally to the right until you hit the line, then straight down to the X axis. That data value is the percentile.</p>

231
Q

<p>what is a clear example of the medians resiliance and when you would use the median instead of the mean?</p>

A

<p>(change just the top value). Imagine if we asked eight people how much money they had in their wallet. We found they had {1, 2, 2, 5, 5, 8, 8, 9}. The mean of this set is 5, and the median is also 5. You might say "the average person in this group had 5 bucks." But imagine the same group the next week, but one of them just got back from the casino and the dist was (1, 2, 2, 5, 5, 8, 8, 9000}, in this case, the median would still be 5, but the mean goes up to over 1000. Which number better describes the amount of money the average person in the group this time? 5 bucks or 1000 bucks? I think 5 is a better description of the average person in this group and the 9000 is simply an outlier.</p>

232
Q

when can you expect the first success? (mean of GEO)

A

1/p……… this tells you, on average, when the first success will occur….

233
Q

<p>what is a conditional distribution?</p>

A

<p>A distribution with a condition (within the table), along only one row or one column… NOT IN THE MARGINS. You are given a condition.. Then read along that row or column.</p>

234
Q

the (n over k) thing has a (5 over 2), how would you do it? What is it called?

A

Also known as “5 choose 2” or “5 C 2”.. 5! / 3!2! (notice the bottom two add to the top)

235
Q

<p>When are box plots used most often?</p>

A

<p>When comparing a bunch of different sets of data.</p>

236
Q

What is systematic sampling?

A

collecting data from every nth subject.

237
Q

<p>What is the difference between categorical VARIABLES and categorical DATA?</p>

A

<p>The Variable is the overall category. Like "EYE COLOR". The data is the actual measurement from the subjects. Like "blue, brown, blue"</p>

238
Q

WHAT ARE THE TWO INDEPENDENCE EQUATIONS USED FOR CHECKING?

A

P(A)=P(A|B) or P(A)*P(B)= P(A and B)

239
Q

<p>What is categorical data?</p>

A

<p>The actual individual category from a subject, like "blue" or "female" or "sophomore"</p>

240
Q

<p>What is a categorical variable?</p>

A

<p>Qualitative variables are like categories: Blonde, Listens to Hip Hop, Female, yes, no? etc.</p>

241
Q

How are we making inferences differently in experiments vs studies?

A

In observaional studies, you make and inference about the population, in an experiment you make an inference about a treatment.

242
Q

What is prospective study?

A

Prospective study is when you study the experimental unit’s present and future.

243
Q

<p>When there is no relationship between two variables, we say they are</p>

A

<p>independent (or not associated)</p>

244
Q

What “designs” are there for experiments?

A

completely randomized, random block, and matched pair design(type of block)

245
Q

<p>what happens if you ADD a constant to each value in a data set?</p>

A

<p>it is SHIFTED only. Does not impact spread. This effects all of the data values and measures of center (mean, med) and quartiles, deciles, etc, IT DOES NOT CHANGE THE SPREAD! (IQR, St Dev, Range all stay the SAME).</p>

246
Q

<p>Why don't we always use the mean, we've been calculating it all of our life ?</p>

A

<p>It is not RESILIENT, it is impacted by skewness and outliers</p>

247
Q

<p>If the mean is above the median, the distribution may be</p>

A

<p>skewed right... the mean follows the tail</p>

248
Q

What type of study would find relationship beween Verbal and Math SAT?

A

You could take all of the SAT Math and Verbal scores and run a regression and find the r-quared value and linear model. This would be a Retrospective Study.

249
Q

<p>What is frequency?</p>

A

<p>How often something comes up</p>

250
Q

What are the two (three) types of experiments?

A
  1. Completely randomized 2. Randomized block (matched pairs)
251
Q

<p>Can you predict an X by using a Y?</p>

A

<p>NOT WITH THE SAME EQUATION!</p>

<p>BE CAREFUL!! Don't just solve for x...</p>

<p>You have to change the entire equation and start from scratch.</p>

<p>(run LinReg L2, L1)</p>

252
Q

<p>If you want to calculate the probability (%) something falls between two values in a normal model, what do you do?</p>

A

<p>find z scores for both value, and then normcdf (Z LOW, Z HIGH )</p>

253
Q

<p>What do we look for in a residuals plot?</p>

A

<p>To proceed, it should look random.</p>

<p>if there is a pattern, then find a new model or proceed with caution.</p>

254
Q

Example of response bias

A

A teenager goes to the doctor’s office with their parents. The doctor asks the teen if they vape. The teen may say “no” because their parent’s are there, even though they do vape.

255
Q

What is the difference between confounding and lurking?

A

Confounding is in experiments, like sunlight confounding a fertilizer experiment. Lurking is when you think hot chocolate causes ski accidents. “lurking”is actually a word not even used in AP STATS.

256
Q

<p>Does r2 tell direction?</p>

A

<p>NO</p>

<p>r2 is always positive, so you can't use it to see if the relationship is negative.</p>

257
Q

<p>Give a quick example of associated variables</p>

A

<p>A higher percentage of boys play video games than girls so we say "gender and video game playing are associated" or "gender and video game playing are not independent"</p>

258
Q

Does sample size matter, or percent of population?

A

Sample size. A sample of 150 will say as much about a population of 2,000 as it will about a population of 2,000,000. The sample size determines level of confidence and interval widths..

259
Q

You own a bike shop and order your tires from 2 companies (A and B). You order 80% from A and 20% from B. 1% of the tires from A are defective, while 4% from B are defective… What is the probability that a defective tire is from company A? How would you do this?

A

Tree diagram. Split up by company first, then use conditionals. A BAD (.8)(.01)= .008A GOOD (.8)(.99)= .792B BAD (.2)(.04)= .008B GOOD (.2)(.96)= . 192It seems that .008/(.008+.008) or 50% are bad

260
Q

When your sampling frame is different from the population, then you risk ____

A

undercoverage

261
Q

<p>does correlation mean causation?</p>

A

<p>NO WAY DUDE</p>

262
Q

What is “mutually exclusive?”

A

disjoint. Can’t happen at the same time.

263
Q

<p>How can you tell if variables in a contingency table are independent?</p>

A

<p>If the distributions are the same across the variables.. Then it doesn't DEPEND… so INDEPENDENT. Ex: 30% of freshman and 30% of seniors like cabbage.</p>

264
Q

what is pythagorean theorem of stats?

A

st dev of combined model is: sqrt(st dev squared + st dev squared) or more if you combine more…

265
Q

A 4 year high school of 2000 students, sampling 40 high students : Describe a systematic sample

A

Get an alphabetical list of all of the students, 2000/40=50. Randomly choose one of the first 50 students and then every 50th student after that.

266
Q

<p>What is meant by cumulative frequency?</p>

A

<p>ADD up the frequencies as you go. Suppose you are selling 25 pieces of candy. You sell 10 the first hour, 5 the second, 3 the third and 7 in the last hour, the cumulative frequency would be 10, 15, 18, 25</p>

267
Q

<p>Computer Output:</p>

<p>What is "S"</p>

A

<p>The average, or typical residual..</p>

<p>Standard deviation of the residuals</p>

<p>typical distance from actual value to the model's prediction.</p>

<p>About how far off your prediction is likely to be.</p>

268
Q

<p>What is quantitative data?</p>

A

<p>The actual numbers gathered from each subject. 211 pounds. 67 beats per minute.</p>

269
Q

<p>How can you describe shape?</p>

A

<p>TWO THINGS: modes and symmetry.unimodal, bimodal, multimodal AND uniform, symmetric, skewed</p>

270
Q

What is a simple random sample?

A

put all of the names in a hat. every group is possible. pull the numbers

271
Q

what is the law of large numbers?

A

guarantees that in the long run.. The relative frequency settles down to true probability.. (you’ll have 50% heads after an infinite number of coin flips with a fair coin)

272
Q

<p>Association and Independence. How are they related?</p>

A

<p>Variables are either independent or associated. Meaning: if one impacts the other then we say there is an association. If not, Then they are independent.</p>

273
Q

A bag has 3 red chips and 4 blue chips.. WTPT you grab a red first, then put it back in and then grab a red again?

A

3/7 * 3/7 = 9/49 (indep events)

274
Q

Suppose you want to see the relationship between gender and candy preference in squirrels. How may you do a stratified vs cluster sample

A

STRATIFIED: You can split the list of all of the squirrels in your neihborhood by gender and randomly select 20 males from th list of all of the males, and then 20 females (strata) from all of the females. CLUSTER: you can randomly choose to 5 different trees and survey all of the squirrels in those trees, assuming that there are 4 squirrels living in each tree (clusters, the trees have both M and F).

275
Q

<p>What other regressions does your calculator do?</p>

A

<p>Quadreg, cubicreg, lnreg, etc.</p>

<p>just be careful when substituting while writing the equation given.</p>

276
Q

<p>what is a linear model?</p>

A

<p>It is an equation you can useor a line of a graph,</p>

<p>but it is just a model that says what kind of happens,</p>

<p>and can be used to ESTIMATE WHAT MIGHT HAPPEN</p>

277
Q

What are the “bad” sampling methods.

A

convenience samples, voluntary samples

278
Q

<p>What do OGIVES look like?</p>

A

<p>They all start at the bottom left (0%) and go to top right (100%)</p>

279
Q

<p>associated is the same as \_\_\_\_\_\_\_\_\_\_</p>

A

<p>not independent</p>

280
Q

What is retrospective study?

A

A retrospective study is a study that looks backwards in time (or at the present moment).

281
Q

<p>When we say the average teenager are we talking about mean</p>

A

<p>It depends, if we are talking height, it might be the mean, if we are talking about parental income, we'd probably use the median, if we were talking about music preference, we'd probably use the mode to talk about the average teenager.</p>

282
Q

<p>What symbols do we use for population proportion (%) and sample proportion (%)?</p>

A

<p>p for population and p-hat for sample</p>

283
Q

<p>what is the LSRL</p>

A

<p>the "least squares regression line"</p>

<p>that line you plot</p>

<p>OR</p>

<p>That equation</p>

284
Q

Why does it make sense to double-blind an experiment?

A

It reduces bias in an experiment. If subjects don’t know what treatment they’re receiving, they won’t change their habits based on that knowledge. If evaluators don’t know which treatment each subject is receiving, they won’t bias the true results based on the results they expect to see

285
Q

<p>What is the IQR?</p>

A

<p>Interquartile range… a measure of spread. Q3-Q1. The distance from Q1 to Q3. The regular range is Hi-Lo, this is the inner range, the interquartile range.</p>

286
Q

<p>What does SHIFT and SCALE mean?</p>

A

<p>Shift is when you add or subtract, scale is when you multiply</p>

287
Q

Suppose you are doing a weight loss experiment with 2 diets (A. low carb and B. low fat), and three medications (1. NUTRI LOSS, 2. POUND DROPPER and 3. SLIMMERLY). What is the response variable?

A

weight loss (pounds)

288
Q

what is a probability model?

A

a list of all possible values of random variable with respective probabilities. The probabilities should add to 1! Normal model is one…

289
Q

<p>What is the variance?</p>

A

<p>The average squared distance to the mean. Or the SD2 (It is the SD before you take the square root, so it is the stuff under the radical in the formula)</p>

290
Q

<p>what is b1 and bo ?</p>

A

<p>b1 is the SLOPE,</p>

<p>bo is the intercept.</p>

291
Q

<p>What is the five number summary?</p>

A

<p>min, Q1 , Q2(median), Q3 and max</p>

292
Q

<p>If asked to compare distributions, what should you write about?</p>

A

<p>A sentence comparing the SHAPES. A sentence comparing the CENTERS. A center comparing the SPREADS. and a sentence comparing the STRANGE STUFF. (GSOCS)</p>

293
Q

geocdf

A

(p,x)…. Probability of the FIRST SUCCESS being ON OR BEFORE the Xth trial.

294
Q

<p>If I take a random sample of 20 hamburgers from FIVE GUYS and count the number of pickles on a bunch of them? and I do this because I want to know the true average number of pickles on a bur</p>

A

<p>parameter, a one number summary of the population. The truth. AKA the parameter of interest.</p>

295
Q

<p>How do you get equation from computer output?</p>

<p>variable coeff indep: age</p>

<p>constant 7.2</p>

<p>Height 3.5</p>

A

<p>For this case:</p>

<p>age = 7.2 + 3.5 (height)</p>

296
Q

what does binomial model tell us about?

A

exactly x successes in K trials. What is likelihood of exactly 3 heads out of 13 flips?

297
Q

Is sampling error a mistake?

A

IT IS NOT A MISTAKE!!! Because the data in samples are generally different, the statistics calculated from one sample to another vary and are generally not equal to the parameter. This variablilty of STATISTICS is called sampling error.

298
Q

4 ingredients: What is “randomization?”

A

You want to randomly assign subjects to treatment groups.

299
Q

<p>Does high r squared mean a good model?</p>

A

<p>CHECK SCATTERFIRST..</p>

<p>Make sure model "FITS" the data.</p>

<p>You should check your scatterplot and residuals plot to make sure model is appropriate and no outliers present… then it means something</p>

<p>So YES, but after you check the resids.</p>

300
Q

<p>What is a standard deviation?</p>

A

<p>average (typical) distance to the mean (about). It is how far you expect a random value to be away from the middle.</p>

301
Q

What is a probability distribution?

A

A table or graph showing all of the probabilites of certain occurances. THE PROBABILITIES HAVE TO ADD TO ONE!

302
Q

<p>data or datum?</p>

A

<p>datum is singular.. Like "hey dude, come see this datum I got from this rat!" data is the plural.. "hey look at all that data Edgar got from those chipmunks over there!!"</p>

303
Q

<p>Compare data to parameters</p>

A

<p>Data is each little bit of information collected from the subjects?. They are the INDIVIDUAL little things we collect? we summarize them by, for example, finding the mean of a group of data. If it is a sample, then we call that mean a "statistic" if we have data from each member of population, then that mean is called a "parameter"</p>

304
Q

<p>Height and weight has an r value of 0.7. You would expect a person with a height that is 2 st. dev above the mean in height to have a weight that is only\_\_\_St. Dev above the mean weight.</p>

A

<p>only 1.4S.D above the mean for weight.</p>

<p>(for each SD in the x direction you change r SD in the y direction)</p>

305
Q

<p>If you want to calculate % above a value, what do you put into normcdf(? ?)</p>

A

<p>find z score for value, and then normcdf (Z left, 999)</p>

306
Q

4 ingredients: What is “BLOCKING?”

A

If you think different groups of subjects may respond differently to treatments because of location, gender, age, then you make BLOCKS, and make sure to compare the treatments within each block.

307
Q

Is it always better to do a census or to sample?

A

depends on the availablility of the data. If the you want to look at SAT vs GPA, you may easily be able to get all of the school’s data and do that study (a census). If you have to go out and get the info, you may want to take a sample to save time and energy.

308
Q

<p>Gender and Video Game playing are\_\_\_\_\_\_\_\_\_\_\_ because\_\_\_\_\_\_\_</p>

A

<p>associated (or not independent) because a higher percentage of males play video games. (think.. It depends on gender)</p>

309
Q

<p>what is the shortcut normcdf?</p>

A

<p>gives % from raw data, skips Z score. normcdf (low VALUE, high VALUE, mean, sd)</p>

310
Q

How can the WORDING of the question lead to response bias

A

Words or phrases that impact your feelings tend to influence responses. Look for “devastating, horrific, wonderful… etc.” Sometimes there is a background story like “Many americans lose jobs to illegal aliens every year, do you feel this is fair”

311
Q

<p>If r= 0.8.</p>

<p>An x value that is 2 standard deviations above the mean will have a predicted y value that is \_\_\_\_\_\_\_</p>

A

<p>1.6 standard deviations above the mean in the Y direction</p>

312
Q

<p>What percent of the data is between Q1 and Q3?</p>

A

<p>50%</p>

313
Q

<p>How do you describe a scatterplot?</p>

A

<p>DIRECTION</p>

<p>FORM</p>

<p>STRENGTH</p>

<p>and STRANGE</p>

314
Q

<p>How do students often mix up IQR and St. Dev</p>

A

<p>They INCORRECTLY think that Q1 is 1sd below the mean and Q3 is 1sd above the mean. THIS IS NOT TRUE!!! Q1 is only .67 sd above the mean and Q2 is .67 below</p>

315
Q

<p>How do you describe SPREAD for skewed distributions (or distributions with outliers?)</p>

A

<p>Use the IQR</p>

316
Q

<p>Use the following words in one sentence: population, parameter, census, sample, data, statistics, inference, population of interest.</p>

A

<p>I was curious about a population parameter, but a census was too costly so I decided to choose a sample, collect some data, calculate a statistic and use that statistic to make an inference about the population parameter (aka the parameter of interest).</p>

317
Q

What is the “mean of a random variable?”

A

The expected value… sum of probs times values

318
Q

In which sampling methods do all GROUPS have the same probability of being chosen?

A

Only in SRS do all GROUPS have the same probability of being chosen, all of the other methods have IMPOSSIBLE GROUPS.

319
Q

using calculator: suppose 30% of dogs have fleas. WTPT no more than 8 out of 15 have fleas?

A

not more than 8 is the same as 8 or less.binocdf(15, .30, 8)

320
Q

<p>If something is associatied is it correlated?</p>

A

<p>Not necessarily.</p>

<p>It can be associated and have a zero correlation</p>

<p>( parabolic scatterplot)</p>

<p>or categorical variables.</p>

321
Q

binopdf

A

(n,p,x)….. Probability of exactly X successes in N trials. (PARTICULAR probability)

322
Q

<p>What is variability?</p>

A

<p>Differences? how things differ. There is variability everywhere.. We all look different, act different, have different preferences? Statisticians look at these differences.</p>

323
Q

<p>Compare DATA-STATISTIC-PARAMETER using quantitative example</p>

A

<p>Data are individual measures, like how long a person can hold their breath: ?45 sec, 64 sec, 32 sec, 68 sec.? That is the raw data. Statistics and parameters are summaries like ?the average breath holding time in the sample was 52.4 seconds? and a parameter would be ?the average breath holding time in the population was 52.4 seconds?</p>

324
Q

name 2 differences between observational studies and experiments

A
  1. Experiments can prove causation (studies can’t) . 2. In experiments, you assign treatments (studies you just watch)
325
Q

What is difference between subject and experimental unit?

A

Humans who are experimented on are commonly called subjects in an experiment. Subjects like dogs, days, plants and anything not human are called Experimental Units

326
Q

<p>Think of the minimum value, the mean and the standard deviation, what is impacted by shifting (adding a constant)</p>

A

<p>adding a value shifts the entire histogram to the right, so the min and the mean will increase by that amount, BUT THE SD WILL NOT CHANGE.</p>

327
Q

A 4 year high school of 2000 students, sampling 40 high students: Explain how stratifying has “impossible groups”

A

You couldn’t get all freshmen in your sample

328
Q

What is undercoverage?

A

Undercoverage is when a group of the population is not represented in the sample. When the sampling frame isn’t representative.

329
Q

<p>What are some strong r values and some weak r values</p>

A

<p>Strong r values are close to 1 or -1, like -0.83 or 0.94. Weak r values are close to zero like 0.10 or -0.06</p>

330
Q

<p>What does r2 tell us?</p>

<p>(r-squared)</p>

A

<p>It tells us the percent of variablility of y that is explained by the model with x.</p>

331
Q

<p>What is extrapolation?</p>

A

<p>Making predictions outside of the x values you have.</p>

332
Q

4 ingredients: What is “control?”

A

You want to control the environment as best as you can so that the only difference between groups is the treatment, and the treatment only. Everything else should be similar.

333
Q

<p>how do you describe direction?</p>

A

<p>positive or negative</p>

334
Q

<p>What are INFERENTIAL STATS?</p>

A

<p>Look at your data, and use that to say stuff about the BIG PICTURE? like tasting soup? a little sample can tell you a lot about the big pot of soup (the population)</p>

335
Q

<p>What's wrong: Age and height havea correlation of 2.7</p>

A

<p>WRONG.</p>

<p>Correlation must bebetween 1 and -1</p>

336
Q

Give an example of matched pair design for comparing a new blood pressure medication to an older version?

A

Have subjects use the new medication for a month and the old one for a month and compare. Be sure to randomize which month and blind.

337
Q

<p>We are curious about the average wait time at a Dunkin Donuts drive through in your neighborhood. You randomly sample cars one afternoon and find the average wait time is 3.2 minutes. What i</p>

A

<p>The parameter is the true average wait time at that Dunkin Donuts. This is a number you don't have and will never know. The statistic is "3.2 minutes." It is the average of the data you collected. The parameter of interest is the same thing as the population parameter. In this case, it is the true average wait time of all cars. The data is the wait time of each individual car, so that would be like "3.8 min, 2.2 min, .8 min, 3 min". You take that data and find the average, that average is called a "statistic," and you use that to make an inference about the true parameter.</p>

338
Q

<p>How do you find 5 number summary from OGIVE?</p>

A

<p>Split the y axis into quarters. Shoot out to the right from 0, .25, .50, .75 and 1.00 till you hit the line in the ogive, then go straignt down. Those numbers on the x axis below correspond to the 5 numbers.</p>

339
Q

<p>not independent is the same as</p>

A

<p>associated</p>

340
Q

<p>What is the difference between discrete and continuous variables?</p>

A

<p>Discrete can be counted, like "number of cars sold" they are generally integers (you wouldn't sell 9.3 cars), while continuous would be something like weight of a mouse? 4.344 oz.</p>

341
Q

What is cluster sampling?

A

Cluster- grab clusters of the population. each cluster should be representative ( like the population) use a few clusters.

342
Q

What is random sampling?

A

When we use chance to select a sample, like rolling dice, a random number generator, or a random number table in our selection process. We use randomization in all of the “GOOD” sampling methods.

343
Q

<p>What is a census?</p>

A

<p>Like a sample of the entire population, you get information from every member of the population</p>

344
Q

<p>How can you turn OGIVES into histograms?</p>

A

<p>RECTANGLE DROP! (bin drop)</p>

345
Q

<p>What percent of the data is below Q2?</p>

A

<p>50%</p>

346
Q

<p>If you are tasting soup.. Then the flavor of each individual thing in the spoon is the \_\_\_\_\_\_\_\_, the entire spoon is a \_\_\_\_\_\_.. The flavor of all of that stuff together is like the \_\_\_\_\_ and</p>

A

<p>If you are tasting soup. Then the flavor of each individual thing in the spoon is DATA, the entire spoon is a SAMPLE. The flavor of all of that stuff together is like the STATISTIC, and you use that to MAKE AN INFERENCE about the flavor of the entire pot of soup, which would be the PARAMETER. Notice you are interested in the parameter to begin with... that is why you took a sample.</p>

347
Q

<p>What does r tell us?</p>

A

<p>The direction (+/-) and how strong a LINEAR relationship is between two QUANTITATIVE variables… (when linear)</p>

348
Q

<p>What is the difference between a bar chart and a histogram</p>

A

<p>bar charts are for categorical data (bars don't touch) and histograms are for quantitative data (bars touch)</p>

349
Q

<p>What is a CUMULATIVE FREQUENCY GRAPH?</p>

A

<p>An OGIVE. It shows the added up totals as you go left to right.</p>

350
Q

Will larger samples reduce BIAS?

A

No, bias is a systematic flaw, even large samples will still have bias. If you ask more people outside of McDonalds, you still only get answers from people who eat at McDonalds (large samples can reduce error, however)

351
Q

What is a representative sample?

A

A sample that looks like the population. It has similar characteristics.

352
Q

Give example of a matched pair design study for fuel efficiency

A

Testing fuel efficiency of different gasolines. Subjects use both fuel A for a month and fuel B for a month and compare, based on their driving habits and vehicle, which was more efficient. BE SURE TO RANDOMLY CHOOSE WHICH ONE GOES FIRST FOR EACH SUBJECT.

353
Q

<p>Which is explanatory variable?</p>

A

<p>the x</p>

<p>the horizontal axis.</p>

<p>it "explains" what happens to y</p>

354
Q

A 4 year high school of 2000 students, sampling 40 high students: Explain how systematic has “impossible groups”

A

You couldn’t get the first 40 people alphabetically (because you are taking every nth)

355
Q

<p>What is the median?</p>

A

<p>the middlest number, it splits area in half (always in the POSITION (n+1)/2 )</p>

356
Q

What do observational studies and experiments have in common?

A

In both, you are making OBSERVATIONS.. recording data… doing statistical analysis…

357
Q

<p>When there is a relationship between two variables, we say that they are</p>

A

<p>associated (or not independent)</p>

358
Q

can disjoint events be independent? EXPLAIN

A

NO.. If they are disjoint then knowing one tells you that the other couldn’t happen so they are always NOT INDEPENDENT

359
Q

using calculator: suppose 30% of dogs have fleas. WTPT exactly 5 out of 12 have fleas?

A

binopdf(12, .30, 5)

360
Q

<p>Give an example of independent variables</p>

A

<p>If 80% prefer cheese and only 20% prefer pepperoni IN EACH GRADE AT BHS…then they all have the same preference, so grade doesn't matter. We say "school year and pizza choice are independent"</p>

361
Q

what is n! ?

A

it is “n factorial” example: 5! = 54321= 120. tells you how many ways you can arrange n objects.

362
Q

<p>what is the emperical rule?</p>

A

<p>mean 68-95-99.7 yeah!</p>

363
Q

<p>How many SD wide is the IQR in a normal distribution?</p>

A

<p>NOT 2!!!! Think about it. The middle 68% is 2 sd wide, since the IQR is only the middlest 50% it must be less than 2. try [invnorm(.75)] x2. You find that it is only 1.35 SD wide if the distribution is nearly normal.</p>

364
Q

Name types of bias

A

undercoverage, non response, response, voluntary

365
Q

what is that (n over k) thing in the binomial equation?

A

n choose k it tells you how many ways you can choose k objects from a set of n things. The formula is n!/(n!(n-k)!) the two numbers on bottom add to the number up top. These are coefficients in expanded binomials and can also be found in Pascal’s Triangle

366
Q

Example of nonresponse bias

A

In a survey, a person does not answer a few questions (or a person is on your list and you can’t get a hold of them)

367
Q

<p>What is the difference between a parameter and a statistic?</p>

A

<p>BOTH ARE A SINGLE NUMBER SUMMARIZING A LARGER GROUP OF NUMBERS?. But pppp parameters come from pppp populations? sss statistics come from ssss samples.</p>

368
Q

<p>Think of the minimum value, the mean and the standard deviat</p>

A

<p>If you multiply a data set by a number, then the min, mean and the SD will multiply by that number.</p>

369
Q

Give example of confounding variable.

A

fertilizer A vs B. If you have two tables in a room with tomato plants and and one table gets A and the other gets B, but later you realize that the table with A was near the windows. You say that SUNLIGHT IS A CONFOUNDING FACTOR in that experiment.

370
Q

<p>Why are there different standard deviation formulas for population and sample? Arent they the same thing?</p>

A

<p>Both equations are actually doing the same thing. They both attempt to calculate the true population proportion. When you have all of the data from the population you just divide by n and get the actual SD. BUT If you only have a sample then you are using that to make a guess (inference) at what the population standard deviation is.. What happens is that samples tend to have less spread so their SD underestimates the population, BUT, when you divide by n-1 instead of n, It gives you a better estimate of what the population standard deviation is.</p>

371
Q

<p>Give example of incorrectly using the word "correlation"</p>

A

<p>"there is a correlation between gender and video game playing"</p>

<p>This person should say "association."</p>

<p>You can't say correlation because gender is categorical.</p>

372
Q

<p>Compare DATA-STATISTIC-PARAMETER using categorical example</p>

A

<p>Data are individual measures? like meal preference: ?taco, taco, pasta, taco, burger, burger, taco?? Statistics and Parameters are summaries. A statistic would be ?42% of sample preferred tacos? and a parameter would be ?42% of population preferred tacos.?</p>

373
Q

A 4 year high school of 2000 students, sampling 40 high students: Describe a stratified sample

A

Stratify by year. Randomly choose 10 FR, 10 SO, 10 JU and 10 SENIORS

374
Q

What is statistically significant?

A

When an observed difference is too odd for us to believe that it is likely to have occurred naturally (or just randomly). Basically it is Statistically Significant when we don’t think it happened randomly. when you think “something’s up” or “something’s fishy”

375
Q

Suppose you sample 150 people randomly from a city to make an inference about the city, and then you sample 150 people randomly from around the country to make an inference about the entire country, which will you be more confident in????

A

It will tell you just as much about both. Same reliability (if sample is representative). Sample size determines confidence. To get more confidence you need a larger sample (not a smaller population)

376
Q

<p>Diff between association or correlation?</p>

A

<p>association is talking about a relationship.</p>

<p>If you see a pattern in the scatterplot, there is an association.</p>

<p>Correlation is an actual calculated number (two quantitative variables)</p>

377
Q

<p>How do you find relative frequency?</p>

A

<p>just divide frequency by TOTAL?.</p>

378
Q

What is the placebo effect?

A

When those who get the placebo show improvements, or show the effects of the treatment. This often happens to up 20% of participants!

379
Q

<p>What symbols do we use for population mean and sample mean?</p>

A

<p>Mu for population mean, xbar for sample mean.</p>

380
Q

<p>What is a statistic?</p>

A

<p>A numerical summary of a sample. Like a mean, median, range? of a sample.</p>

381
Q

<p>When do we often use mode?</p>

A

<p>With categorical variables. For instance, to describe the average teenagers preference, we often speak of what ?most? students chose, which is the mode. It is also tells the number of bumps in a histogram for quantitative data (unimodal, bimodal, etc?).</p>

382
Q

What does mutually exclusive mean?

A

Same as disjoint.. Can’t both happen.

383
Q

<p>Make a guess as to what relative cumulative frequency is?</p>

A

<p>It is the ADDED up PERCENTAGES.. An example is selling candy, 25 pieces sold overall..., with 10 the first hour, 5 the second, 3 the third, and 7 the fourth hour, we'd take the cumulative frequencies, 10, 15, 18 and 25 and divide by the total giving cumulative percentages... .40, .60, .64, and 1.00. Relative cumulative frequencies always end at 100 percent.</p>

384
Q

4 INGREDIENTS TO EXPERIMENTS

A

Compare, control , randomization, replication (and BLOCKING when you need to)

385
Q

<p>If I take a random sample 20 hamburgers from FIVE GUYS and count the number of pickles on a bunch of them? and the average number of pickles was 9.5, then 9.5 is considered a \_\_\_\_\_\_\_?</p>

A

<p>statistic. (t is a summary of a sample.)</p>

386
Q

<p>how do you interpret y intercept?</p>

A

<p>The model predicts that if there were no [x stuff] this is how much [y stuff] you'd have</p>

387
Q

Suppose you are doing a weight loss experiment with 2 diets (A. low carb and B. low fat), and three medications (1. NUTRI LOSS, 2. POUND DROPPER and 3. SLIMMERLY). How many treatment groups would there be?

A

there would be 6: A1, A2, A3, B1, B2, B3

388
Q

<p>If the distribution is unimodal and symmetric, what would you use for center and spread statistics?</p>

A

<p>Mean (center) and Standard Deviation (spread)</p>

389
Q

<p>which is response?</p>

A

<p>y variable,</p>

<p>the Vertical axis..</p>

<p>It "responds" to the x</p>

390
Q

An unbiased sampling method will eliminate error

A

No, error is always there. Error is not a mistake.

391
Q

Who can be blinded? ( two groups)

A
  1. Subjects (and dog owners..). The poeple getting treatment and 2. administrators. Those delivering treatments and assessing effectiveness of treatments.
392
Q

<p>What is the mean?</p>

A

<p>the old average we used to calculate. It is the balancing point of the histogram</p>

393
Q

<p>will residual plots always show outliers?</p>

<p>(will outliers always have large residuals?)</p>

A

<p>Not necessarily. Some points have so much leverage, they pull the line up to it…</p>

394
Q

<p>What is data?</p>

A

<p>Any collected information. Generally each little measurement? Like, if it is a survey about liking porridge? the data might be ?yes, yes, no, yes, yes? if it is the number of saltines someone can eat in 30 seconds, the data might be ?3, 1, 2, 1, 4,3 , 3, 4?</p>

395
Q

<p>marginal distribution</p>

A

<p>distribution in the margins (outside of the table). The overall distributions of a single variable in contingency table.</p>

396
Q

<p>What should we look for in resid plot?</p>

A

<p>Curve or pattern.</p>

<p>Also, it should have equalish scatter from left to right</p>

<p>It should look RANDOM</p>

397
Q

What is matched pair design?

A

A type of blocking where you match subjects to other “like” subjects… MOST OFTEN SEEN WHEN YOU COMPARE A SUBJECT TO ITSELF!! (like pre-post tests)

398
Q

Can you stratify in an experiment?

A

NO. stratification is a sampling method, blocking is method used in experiments. They are similar ideas.

399
Q

<p>What is a parameter?</p>

A

<p>A numerical summary of a population. Like a mean, median, range? of a population</p>

400
Q

What is a multistage sample?

A

A sample that combines several sampling methods

401
Q

<p>If you switch x and y will slope change?</p>

A

<p>YES (but not just reciprocal)</p>

<p>slope is rsy/sx ,</p>

<p>to get new slope you can use shortcut:</p>

<p>r2/old slope</p>

<p>(reciprocal times r2)</p>

402
Q

<p>What is a quantitative variable?</p>

A

<p>Quantitative variables are numeric like: Height, age, number of cars sold, SAT score</p>

403
Q

How do you do the tricky reverse tree problems (like test says pregnant.. What is probability you actually are?)

A

SPLIT UP POPULATION FIRST&raquo_space;»» then split the groups by outcomes of the test.. BE SURE TO LABEL THE OUTCOMES and multiply the branches to the end… To find P(pregnant|test says pregnant), only look at the 2 branches that end with test saying pregnant.. put the actual pregnant over the sum of both pregnant and non.

404
Q

A bag has 3 red chips and 4 blue chips.. If you grab a red one on the first try and keep it, WTPT the next one is red?

A

6-Feb

AP Statistics (15 decks)

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