skills Flashcards

Question

3 how to **use the standard normal table**

Answer 1

1. draw a picture of the distribution (any area **to the right ( x ≥ ? )** are 1-area to the left) 2. Standardize. The proportion minus mean mu divided by standard deviation sigma = a number 3. find that number on the table BUT if it's an x ≥ problem, then subtract that number from 1. 4. to find sections, repeat above and do the math converting x to z or see 3.7

Answer 2

* A response variable measures an outcome of a study. An explanatory variable may explain or influence changes in a response variable.

Answer 3

SPSS 1. Analyze → Correlate → Bivariate 2. move variables into window 3. Graphs → Legacy Dialog → Scatter/Dot 4. Simple Scatter → Define 5. put explanatory on X, response on Y, OK 6. Elements → Fit Line at Total 7. Analyze → Regression → Linear 8. put explanatory in independent, response in dependent, OK

Answer 4

you describe its direction, form and strength, positive or negative association and outliers

Answer 5

when making the scatterplot, after you determine the axes, move a categorical variable into the "set markers by" box, go into chart editor and select the little legend symbols to edit shape and color

Answer 6

correlation measures the strength and direction of the linear relationship **SPSS:** look at regression cards * The values for each individual are x₁ and x₂, y₁ and y₂, etc * the mean is x̄ (or y-bar) * the standard deviation is s_x and s_y * so correlation is (([the first x individual value] minus [x's mean] divided by [x's standard deviation]) + the next and next etc) divided by x's standard deviation, then also for y, added all up ALL divided by the number of individuals *n*-1

Answer 7

1. Analyze --\> regression --\> Linear 2. Response variable --\> dependent, explanatory --\> independent 3. save... Predicted values "Unstandardized" 4. Click OK for basic linear regression output 5. "Model Summary" (2nd table): R = absolute value of small r... R Square = the square thereof and stanard error 6. Coefficients (4th (bottom) table) "1 (Constant)" at "B" is the **Y intercept** 7. "[Explanatory variable] at "B" is the **slope** 8. **back to dataset** see a new column of predicted values based on slope

Answer 8

Use SPSS to calculate (resression cards has it) * *b* is the slope, i.e. the amount by which Y changes when X increases by 1 * *a* is the y-intercept, the value of Y when X = 0 * find the slope and intercept attached

Answer 9

1. Analyze --\> regression --\> Linear 2. Response variable --\> dependent, explanatory --\> independent 3. Click OK for basic linear regression output 4. "Model Summary" (2nd table): R = absolute value of small r... R Square = the square thereof and stanard error 5. Coefficients (4th (bottom) table) "1 (Constant)" at "B" is the Y intercept 6. "[Explanatory variable] at "B" is the slope

Answer 10

1. Analyze --\> regression --\> Linear 2. Response variable --\> dependent, explanatory --\> independent 3. save... --\> unstandardized 4. Click OK for basic linear regression output 5. "Model Summary" (2nd table): R = absolute value of small r... R Square = the square thereof and stanard error 6. Coefficients (4th (bottom) table) "1 (Constant)" at "B" is the Y intercept 7. "[Explanatory variable] at "B" is the slope 8. back to dataset a new variable has been added 9. graph --\> legacy dialogue --\> scatter 10. Simple --\> explanatory on the X, **new residuals on the Y**

Answer 11

a variable that is not included as an explanatory or responsevariable in the analysis but can affect the interpretation of relationships betweenvariables

Answer 12

often due to voluntary response and other inferior sampling methods

Answer 13

SPSS 1. Data --\> Select Cases 2. select "Random Sample of cases. click Sample 3. decide whether you want a percentage of fixed number of cases, continue 4. Decide on "output" 5. makes a filter variable column with zeroes for filtered or 1's 6. go to variable view and rename filter to variable 1 or whatever

Answer 14

SPSS 1. assign a random number to each subject 2. Transform --\> compute variable 3. Function Group "Random Numbers" 4. Functions box: Rv.Uniform (creates (?,?) (create random numbers that fall between these two numbers (0,1) 5. Target variable: "random" 6. Dataset now has new variable, now sort 7. Data --\> sost cases --\> move radnom to sort by 8. make new variable "treatment group" put a 1, 2, 3 next to equal amounts of subject (i.e. first ten second ten third ten)

Answer 15

if the subjects are assigned to random groups, it's an experiment

Answer 16

An explanatory variable is one that explains changes in that variable

Answer 17

make sure that only the treatment varies across all groups

Answer 18

it should include size of groups, specific treatments and the response variable and be expressed as a flow diagram with arrows

Answer 19

SPSS 1. assign a random number to each subject 2. Transform --\> compute variable 3. Function Group "Random Numbers" 4. Functions box: Rv.Uniform (creates (?,?) (create random numbers that fall between these two numbers (0,1) 5. Target variable: "random" 6. Dataset now has new variable, now sort 7. Data --\> sost cases --\> move radnom to sort by 8. make new variable "treatment group" put a 1, 2, 3 next to equal amounts of subject (i.e. first ten second ten third ten)

Answer 20

(width x height)/2

Answer 21

1. Rule 1. The probability P(A) of any event A satisfies **0 ≤ P(A) ≤ 1.** 2. Rule 2. If S is the sample space in a probability model, then **P(S) = 1**. 3. If A and B are disjoint, then **P(A or B) = P(A) + P(B)** 4. If A and B are disjoint, then for any event A, * *P(A does not occur) = 1 − P(A)**

Answer 22

then you do the multiplication of either the probability number if it's of it *happening* or 1 - P if it's of it *NOT* happening. (prob of no calls for flat in 4 calls = 1-(.28)(.28)(.28)(.28) or .994 (see prev card))

Answer 23

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

Answer 24

if you keep drawing from the same pool, thus changing the odds, that's dependence. If P's are independent, you can multiply them. (Probability that two calls for a flat tire (72% or .72 chance each) is .72 x .72)

Answer 25

* think of it as "given the information that..." so * P (truck | imported)=0.546 would mean "“What proportion of imports are trucks?” whereas * P(imported | truck)=0.207 would mean "What proportion of trucks are imports?” * In other words, what proportion of the far one is the near one?

Answer 26

If A and B are independent, then **P(A and B) = P(A)P(B)**

Answer 27

a parameter describes a whole population and is often unknowable, a statistic describes a sample

Answer 28

* Take a large number of samples of small size 10 from the population. * Calculate the sample mean x̄ for each sample. * Make a histogram of the values of x̄ . * Examine the shape, center, and variability of the distribution displayed in the histogram.

Answer 29

the sampling distribution of x̄ has mean μ and σ/√n

Answer 30

First compute the Z-score and look it up on the table, (remember to subtract from 1 for higher thans) and then use N(μ, σ/√n)

Answer 31

1. analyze \> descriptive statistics \> explore 2. move continuous variable to dependent list 3. click on statistics button to change 95% to 99% etc 4. look at "Descriptives" output table 5.

Answer 32

The Z score is a test of statistical significance that helps you decide whether or not to reject the null hypothesis. The p-value is the probability that you have falsely rejected the null hypothesis. Z scores are measures of standard deviation. ... Both statistics are associated with the standard normal distribution.

Answer 33

Use a confidence interval

Answer 34

Small P-values are evidence against H₀ because they say that the observed result would be unlikely to occur if H₀ were true. Large P-values fail to give evidence against H₀. You might say, "an outcome that would occur so often when H₀ is true is not good evidence against H₀. The study looked for evidence against H0: μ = 0 and failed to find strong evidence. That is all we can say."

Answer 35

m=z•sigma over square root of n

Answer 36

n=(z•sigma/m)²

Answer 37

put in the value of z\* for your desired confidence level, and solve for the sample size n

Answer 38

To analyze samples from Normal populations with unknown σ, just replace the standard deviation σ/√n of x-bar by its standard error s/√n in the z procedures, then a level C confidence interval is this formula...

Answer 39

when you have to estimate the standard deviation from data, it's called the standard error. you find the standard error of a sample mean like this: s / √n

Answer 40

When you perform a t-test, you're usually trying to find evidence of a significant difference between population means (2-sample t) or between the population mean and a hypothesized value (1-sample t). The t-value measures the size of the difference relative to the variation in your sample data. Put another way, T is simply the calculated difference represented in units of standard error. The greater the magnitude of T (it can be either positive or negative), the greater the evidence against the null hypothesis that there is no significant difference. The closer T is to 0, the more likely there isn't a significant difference.

Answer 41

The hypothesis of no difference is used when investigating whether a treatment has an effect.

Answer 42

* analyze \> compare means \> one sample t test * move response variable over to the "test variable window" * enter the "test value" (or null value) * hit okay * first box is sample data * second is one sample test incl t, df, and 2 sided P value ("Sig. 2-tailed) * BEWARE the confidence interval you see is not for the mean, if you wan that, go to analyze desc stat explore

Answer 43

* analyze \> compare means \> independent sample t test * put quantitative response into "test variable" * put two, labeled data sets in grouping variable * define groups * set confidence level under options *

Answer 44

Because we don’t know the population standard deviations, we estimate them by the sample standard deviations from our two samples. The result is the standard error, or estimated standard deviation, of the difference in sample means

Answer 45

standardize the estimate by dividing it by its standard error

Answer 46

tests and confidence intervals for a **population proportion** p when the data are an SRS of size n.

Answer 47

the mean is p the standard deviation is found with this formula

Answer 48

we use this when we have to guess at a proportion, so that we can determine the sample size. .05 yields the largest sample size, we use this when trying to get the desired margin of error

Answer 49

to test the null hypothesis H₀: p = p₀...

Answer 50

where p\* is a guessed value for the sample proportion. The margin of error will always be less than or equal to m if you take the guess p\* to be 0.5.

Answer 51

To test H0, we compare the observed counts in the table with the expected counts, the counts we would expect—except for random variation—if H0 were true.

Answer 52

it's equal to its degrees of freedom

Answer 53

To test whether the observed differences among the four distributions of living arrangements given age are statistically significant, we compare the observed and expected counts. The chi-square statistic is a measure of how far the observed counts in a two-way table are from the expected counts if H0 were true. The Chi-square statistic is a sum of terms, one for each cell in the table. Think of χ2 as a measure of the distance of the observed counts from the expected counts if H0 were true. Large values of χ2 are evidence against H0 because they say that the observed counts are far from what we would expect if H0 were true.

Answer 54

The Chi-square distributions are a family of distributions that take only positive values and are skewed to the right. A specific Chi-square distribution is specified by giving its degrees of freedom. You find the degrees of freedom by: (# of rows-1)(# of columns)

Answer 55

You can safely use the Chi-square test with critical values from the chi-square distribution when no more than 20% of the expected counts are less than 5, and all individual expected counts are 1 or greater. In particular, all four expected counts in a 2 × 2 table should be 5 or greater. Note that these guidelines use EXPECTED counts.

Answer 56

* (if summarized as counts) data \> weight cases * (if summarized as counts) move variable to "weight cases by" window, click OK * analyze \> descriptive stats \> cross tabs * determine row and column, click "statistics" * check chi-square \> continue * click "cells" * check "expected" \> continue * also check "clustered bar charts" at the bottom * click OK * middle chart is table * bottom right "asymptotic" is P-value

Answer 57

I = number of populations/means N = number of total observations so I-1/N-I

Answer 58

The results of the ANOVA F test are approximately correct when the largest sample standard deviation is no more than twice as large as the smallest sample standard deviation.

Answer 59

1. Analyze \> Compare Means \> one-way ANOVA 2. plug in response/dependent and factor/explanatory 3. click options 4. check "descriptive" and "means plot" 5. click continue and ok 6. "Sig." is P-value Tukey: 7. click Post-Hoc and Tukey

Answer 60

* analyze \> compare means \> one sample t test * assign test variable * put null hypothesis into test value * options \> pick confidence interval * continue \> OK * to get one tailed value, divide sig. two tailed by 2