Midterm #3 Flashcards
(121 cards)
1
Q
Flattened middle and high, short tails. Big space between axis and curve.
A
Platykurtic
2
Q
Degree to which data values are distributed in the talks of the distribution
A
Kurtosis
3
Q
Tall, narrow, high peaked-middle. Low, long, skinny tails; little space between axis and curve
A
Leptokurtic
4
Q
Normally shaped distribution ‘bell curve’
A
Mesokurtic
5
Q
A specific form of a mesokurtic distribution having a characteristic bell-shaped curve that is mathematically defined by a quadratic equation.
A
Normal distribution
6
Q
Empirical vs Theoretical distribution
A
Empirical- based on data, distribution is based on real data
Theoretical- based on theory or hypothetical observations. Based on certain basic facts, principles or assumptions.
7
Q
Which of the following statements is false about normal distributions?
a) a mesokurtic distribution is always a mathematically defined normal distribution
b) It is unimodal
c) It is mathematically defined by a quadratic
equation
d) It is symmetrical
A
a) a mesokurtic distribution is always a mathematically defined normal distribution
8
Q
Name 4 reasons why the normal distribution is the most important distributions we will learn in this class
A
- Many DVs are commonly assumed to be normally distributed in the population
(eg. if we obtain a whole population of observations, the distribution would be clse to normal) - If we can assume that a variable is at least approximately normally distributed, then it allows us to make a number of inferences about values of that variable
- Sampling distributions of the mean can be shown to be approximately normal under a wide variety of conditions
- Most of the tests we’ll learn have in their derivations an assumption that the population of the observations is normally distributed.
9
Q
What is normal distribution? (3 points)
A
- Unimodal
- Symmetrical
- Bell Curve
10
Q
What is an example of theoretical data?
A
Height in population because we assume it is something normally distributed but there is so much data
11
Q
What are standard scores?
A
A linear transformation of raw scores to values with a universal meaning relative to the mean and SD for that set of scores.
Transformation preserves the original information in terms of each score’s quantitative distance from other scores and the shape of the distribution..
12
Q
What does a Z score describe?
A
A score in terms of how much of it is below or above the average.
Z =(X − X-M`)/SD
13
Q
What does the Z score indicate?
A
How many SD a raw score is from the mean and in what direction.
(above the mean= pos. value, negative=below)
14
Q
How are the Z scores communicated in terms of distance?
A
By the distance in terms of SD
15
Q
What does a Z score of -2 tell us?
A
The score is 2 SD below the mean.
16
Q
What does a Z score of 0 tell us?
A
The score is at the mean.
17
Q
Peter got a 45 on his spelling test. If the class mean was 57, and the SD was 6, what was Peter’s Z score?
A
-2
18
Q
Ben of Baltimore makes $45,000 a year. Tom of Toronto
makes $42,500. The mean income in the US is $28,000
with a standard deviation of $6000 and the mean
income in Canada is $30,000 with a standard
deviation of $4000 . Relatively speaking, in their
respective countries who is better off financially?
A
Tom is better off.
Convert to Z scores
Ben = 2.83 Tom= 3.13
19
Q
What does the Z score distribution apply only to?
A
Only to interval or ratio scale
Converts all raw scores to their Z score equivalents.
20
Q
Does the shape change when converting into a Z score?
A
No because we are subtracting a constant (the mean) from the raw score and then diving the difference by another constant (SD)
21
Q
Your data is negatively skewed. Transforming your raw data into a Z score distribution will
a) make it positively skewed.
b) make it a normal distribution.
c) allow you to compare your data with another
dataset that is normally distributed.
d) not change the shape of the distribution.
A
d) Not change the shape of the distribution.
22
Q
3 Advantages of standard scores
A
- Find a location of a score relative to other scores in the same dataset
- Permits comparison of scores within that distribution
- Theoretically, can compare scores from different distributions as long as both distributions have the same shape
23
Q
2 Limitations of Standard scores
A
- Can not compare scores across distributions (eg. if one distribution is positively skewed and another distribution is negatively skewed you cannot compare the scoers)
- Very unusual to find 2 identically skewed distributions that would make direct comparisons possible between different tests or datasets.
24
Q
If the mean= 6, SD= 1.5. What is the raw score if your Z score is 1.35?
A
X= 8.025
25
Your stats professor tells you that the exam mean was
78 and the SD was 9.
You then look for your mark on CourseSpaces and it’s
listed as a Z=0.8.
What mark did you get on the exam?
X= 85.2
26
What is a standard normal distribution (SND)?
If a set of scores that is already normally distributed is transformed into a Z score distribution, the distributions is referred to as a Standard Normal Distribution which has specialized properties.
27
7 properties of a Standard Normal Distribution of Z scores.
1. Symmetrical
2. Unimodal, (the mean, mode, median are equal)
3. Data are normally distributed (most follow a mathematically defined normal curve)
4. Data are measured on interval and ratio scales
5. The mean is 0
6. The SD is 1
7. The total area under the curve is 1
28
Instead of using the matematically defined formula to determine the height of X values with normal distribution what can we do?
Make it a Standard Normal Distribution. Can get the area under the curve between 2 points and thus the probability that a randomly drawn score will fall within that interval.
29
Percentage of scores that will fall within 1, 2, 3 SD.
```
1= 68%
2= 95%
3= 99.7%
```
30
What would we have to do if we just used the normal distribution (raw scores) rather than the standard normal distribution?
We would have to have many different tables for the different combinations of means and SDs.
31
How much of the total area under the curve lies between the mean and a z score of 1.05?
Area= 0.3531
| Approximately 35.31% of the total area under the curve is found between the mean and a score of 1.05
32
How much of the total are under the curve is found between the mean and a z score of -1.48?
Area= 0.4306
| Approximately 43.06%
33
How much of the area is found between the z scores of -1.74 and 3.24?
.4591 + 0.4994= 0.9585, 95.85%
34
1. Find the area between z(+/- 2.50)
2. Area beyond z = 1.96
3. Area between z(1.50) and z(2.10)
4. Area between mean and 1.225
1. 0.9876
2. 0.0250
3. 0.0489
4. 0.3898
35
M= 6, SD= 1.5
Chocolate consumption= 10
z score?
What proportion of ppl ate just as much chocolate or less than me?
z= 2.67
proportion= 0.9962 (99.6%)
36
What IQ score would a person need to get to be in the top 5%?
IQ scores are normally distributed with M= 100, SD= 15
Make a rough estimate of the Z score where
the shaded area stops. Based on what we know, 5%
falls somewhere in between a Z score of 1 & 2. It can’t
be greater than 2 because only ~2% of the scores are
above 2 SD.
Look for smaller portion of 0.505 on the Normal Distribution Table.
The closest of 0.05 9s 0.505 so Z= 1.64
If Z= 1.64, a person would need an IQ of at least 124.6 to be in the top 5%. (Need to put in the rearranged formula)
37
What is the analytic view of probability? (2)
Definition of probability in terms of an analysis of possible outcomes.
What we think will happen but without support of actual data.
38
If this is the equation of a given event A: P(A)= f/N what do the variables represent?
```
P(A)= probability of a given event
f= the number of ways a given a given A can occur
N= the total of all possible outcomes
```
39
What is the probability of rolling a 3 or less?
1/2
40
What is a frequentist view of probability?
Defined in terms of past performance. Determines probability of an outcome based on past performance.
Eg. landing heads
f= 500, N=1000
f/N= 0.5
41
What is subjective probability?
Probability represents an individual's subjective beliefs in the likelihood of the occurrence of an event?
Eg. What the probability of the Dodger's winning the world series?
42
What is Bayesian probability?
Subjective probability.
Bayesian belief that science is about doing research to adjust our pre-existing beliefs based on the evidence (data) we collect.
Probability of the hypothesis given the data.
43
What is an event vs. independent events?
event= the outcome of a trial
- the probability of an event is always between 0 & 1.
- the probability of all possible events is 1.
Independent events= the outcome for one event does not depend of the outcome of another event.
44
```
Which one of the following scenarios is least likely if I
flip the coin 5 times?
a) H, H, H, T, H
b) T, H, T, T, T
c) T, H, T, H, T
d) H, H, H, H, H
e) They are equally as likely.
```
e) They are all equally as likely because they are independent events.
45
What is gambler's fallacy?
The occurrence of one doesn't effect the likelihood of the next result.
Mistaken fallacy= if it happens once, it becomes less likely.
46
Independent?
A drawer contains 3 red paperclips, 4 green paperclips,
and 5 blue paperclips. One paperclip is taken from the
drawer and then replaced. Another paperclip is taken
from the drawer. What is the probability that the first paperclip is red and the second paperclip is blue?
Yes independent because you put it back.
47
Independent?
A drawer contains 3 red paperclips, 4 green paperclips,
and 5 blue paperclips. One paperclip is taken from the
drawer and is NOT replaced. Another paperclip is taken
from the drawer. What is the probability that the first
paperclip is red and the second paperclip is blue?
No, because you don't replace it, it is effected by the first event.
48
If five people are asked to estimate the height of a professor is this independent?
If outloud, it is not independent because you adjust to the first guess.
49
What is mutually exclusive?
Two events are mutually exclusive when the occurrence of one precludes the occurrence of the other/
Eg. you can only get a head or tail with one toss of a coin.
50
Are the following events mutuallyexclusive?
Rolling a 3 / Rolling a 4 (in one roll)
a) Yes b) No
Rolling a 3 / rolling a value less than 4 (in one roll)
a) Yes b) No
1. Yes
| 2. No
51
3 rules that are used for calculating probability
1. Addition rule
2. Multiplication rule
3. A combination of the addition and multiplication rule
52
What is the addition rule?
Considered in terms of a single event. "What is the probability of A OR B OR C?"
Involves a mutually exclusive event (we won't discuss when there is a joint/overlapping event)
53
Additive law of probability.
Given a set of mutually exclusive events, the probability of the occurrence of one event or another is equal to the sum of their separate probabilities.
P(A or B)= P(A) + P(B)
54
What is the probability of selecting an Ace or a King?
0.1538
55
What is the multiplication rule?
The probability of 2 or more events occurring at the same time "What is the probability of A & B & C?"
56
What is the multiplicative law of probability?
The probability of the joint occurrence of two or more independent events in the product of their individuals probabilities
P (A and B)= P(A) x P(B)
57
What is the probability that on the first roll of a die we get a 2 and on the second roll we get a 4?
0.0278
58
What if we don't care about the order of events? Probability that on 2 rolls we get a 2 and a 4.
Use Combination
-use both addition and multiplication rules
P(2 and 4)+ P(4 and 2)
=0.0556
59
What is joint probability?
The probability of the co-occurrence of 2 or more events.
Example= the probability of pulling an ace and a kind. These are 2 independent events- we can use the multiplication rule.
But if not independent- use different approach that we don't learn.
60
The probability that one event will occur given the occurrence of some other event.
Conditional probability.
61
Sample vs Population.
Population: entire group of people to which a
researcher intends the results of a study to apply;
larger group to which inferences are made on the
basis of a particular set of people (sample studied)
Sample: scores of a particular group of people
studied; usually considered to be representative of the
scores in some larger population
62
How do we describe populations vs samples?
Population= descriptive measures are called parameters and are symbolized by greek letters
• Mean: μ(mu); Standard deviation: σ(sigma);
Variance σ2 (sigma-squared)
Sample= descriptive measures are called statistics and are symbolized by Roman letters.
• Mean: , Standard deviation: SD; variance: SD^2
63
```
Population of 500 hedgehogs
whose ages are normally
distributed
μ(mean) = 60 days
σ (SD) = 10.2 days
```
1) What is the z-score for age 45?
2) What proportion of hedgehogs are 45 days or
younger?
3) How many hedgehogs are 45 days or younger
4) What is the probability of selecting a hedgehog
that is 45 days or younger?
1. 45 – 60 / 10.2 = -1.4706
2. Area beyond Z= -1.47= 0.708
3. How many hedgehogs are 45 days or younger?
500x 0.0708= 35.4 (35 hed)
4. p= 0.0708 (probability= proportion)
64
Samples must be created with some form of random provess so that (2)
1. Samples represents an unbiased selection of participants
2. Scores (or any form of data from participants) are independent from each other
It is easier to make strong inderences to explain behaviour when no other bias is influencing behaviour.
65
What is simple or true random sampling?
Each individual is chosen randomly from a larger set (population)
this is rare.
66
Convenience sampling?
Who shows up for an experiment?
67
Method of selecting participants for the study
sampling
68
What is random sampling with restriction?
1. To meet an experimenter-determined criterion
Eg. Need people with certain scores of depression (Need participants with moderate and high scores on a measure o depressive symptoms)
69
Random assignment with restriction
To meet an experimenter-determined criterion
Eg. Need certain number of males or females in each condition (cannot randomly assign without taking into consideration gender)
70
What is stratified random sampling?
Pre-existing representation in a sample
Eg. Proportionate representation of religious diversity of the community in the study
```
Breakdown of religion:
• 55% no religious affiliation
• 30% Christian
• 6% Buddhist
• 3% Sikh
• 2% Muslim
• 2% Jewish
• 2% Hindu
```
If N= 100, you would need 55 no religious affiliation, 30 with christians etc.
71
A researcher wants to have 30 younger adults (Age
18-25) and 30 older adults (Age 65-85) in each experimental condition. She has already recruited her participants but now has to assign participants to the two conditions.
What method is she using?
a) Stratified random sampling
b) Stratified random assignment
c) Random assignment
d) Random assignment with restriction
d) Random assignment with restrictions
72
What is inferential analysis?
- Systematic procedure for determining whether the results of an experiment provide support for a particular theory of practical innovation
- make inferences about the performance of participants in our sample
- standardized and objective method used to evaluate data
- helps the researcher decide whether the observed data might have occurred but chance or whether the data are likely to represent a systematic change
73
What is hypothesis testing?
Procedure for deciding whether the outcome of a study (results for a sample) supports a particular theory or practice innovation (which is thought to apply to a population)
74
If mew= 63.2m
SD= 4.8
What's the likelihood of a player skating for than 2 SD above or less than 2SD below the mean?
0.0456
75
In the NHL example, what is the sample and what is the population?
Sample= single NHL player, population= all NHL players
76
What are the 6 steps to follow for hypothesis testing?
1. Specify the alternative and null hypothesis
2. Select the appropriate null (sampling) distributing
3. Set critical value alpha
4. Gather data, compute a descriptive statistics and use them to generate a test statistics
5. Compare p(obs) with alpha or compare z-score observed and z-critical and make a statistical decision
6. Draw a general "conclusion" about the meaning of data
77
What is the alternative (research hypothesis)
H1
| The Hypothesis that for the experiment was designed to investigate
78
What is the null hypothesis?
H0
The statistical hypothesis tested by the statistical procedure. Usually a hypothesis involving no difference or no relationship/
79
What is the null hypothesis for NHL example?
Yoga has no effect on skating.
80
What are the test statistics?
The results of a statistical test
when we only use one participant and wish to compare it to a normal distribution of scores where we have the mean and SD.
We then use the standard normal distribution as the sampling distribution, (this is the only case where population distribution looks EXACTLY like the sampling distribution)
81
What happens when you convert to standard normal distribution, what does this mean?
Z-score, where mew=0 and sigma=1
82
What is alpha?
Proportion of area under the curve at that end of the tail(s)
Will reflect a 1-tailed or 2-tailed value as determined by your alternative hypothesis
83
What is a one-tailed test?
Directional. A test that rejects extreme outcome in one specified tail of the distribution.
84
What is a two-tailed test?
Nondirectional. A test that rejects extreme outcomes in either tail of the distribution.
85
Determine the risk level level for the critical value
5%, 10%, 1%
In psychology, researchers typically define the risk level at alpha=0.05
86
If alpha=0.10 what is the z-critical for a one tailed test?
| Two tailed?
1.28=1tailed
+/- 1.645=2tailed
87
What does the critical value differ depending on?
Depending on whether you have a 1 or 2 tailed test and what alpha level you set.
88
What is a test ratio?
Z= (X-µ)/σ
89
What is test statistic?
Statistical value that results when the test ratio is applied to data.
It produces a standard score from a sample statistic.
Each computed test statistic is associated with proportion of area under the curve on the sampling distribution.
Test statistical value is placed in the sampling distribution to compare the outcome to the probabiliy it represents.
90
What do you compare p(obs) with?
alpha or compare z-score observed and z-critical and make a statistical decision
91
What happens when z(obs) does not fall in the rejection region?
Retain H0 or fail to reject H0.
Suspend judgment on H1 until further data are collected.
Outcome is inconclusive.
92
What happens when Z(obs) falls in the rejection region?
Reject the null hypothesis that nothing systematic is happening.
93
What is the exact probability of getting z=1.83 or a value for extreme? For a two-tailed test.
0.0672
94
A p-value represents:
a) the probability, given the null hypothesis is true,
that the results could have been obtained purely
on the basis of chance alone.
b) the probability, given the alternative hypothesis is
true, that the result could have been obtained
purely on the basis of chance alone.
c) the probability that the results could have been
obtained purely on the basis of chance alone.
d) Two of the above are proper representations of a
p-value.
a) the probability, given the null hypothesis is true,
that the results could have been obtained purely
on the basis of chance alone.
95
When comparing p(obs) with alpha, when do you retain H0?
When p(obs) is greater than alpha, you retain H0, or fail to reject it.
Suspend judgment on H1 until further data is collected.
The outcome is inconclusive.
96
When comparing p(obs) with alpha, when do you reject H0?
When p(obs) is less than alpha, you reject the null.
97
What is the critical value for Z if we assume alpha=0.05 and is 1tailed?
+1.945
98
What is the probability of getting z=1.83 or a value more extreme that Z=+1.83?
0.0336
99
What does an APA report need to include?
- Brief description of study, X, mean and SD of population.
- Whether it was a one or two tailed test.
- Whether the outcome was significantly different from the average of the population.
- Stats to include: z(obs) and p(obs)
- Include any criticism (eg. no baseline)
100
What if you did a two-tailed test and then a one-tailed test? (0.025 on neg side, 0.05 on pos)
You can't do this- your alpha would actually be 0.075! Important to decide this ahead of time.
101
Setting your alpha level also determines the probability of a _______
type 1 error
102
What is a Type 1 error?
Error of rejecting the null hypothesis when it is true.
| alpha=probability of a type 1 error.
103
What is a type II error?
When you retain the null when you shouldn't be.
Beta
104
What happens if you make the alpha smaller?
This decreased your Type 1 error, but increases your Type II error.
105
What is a Type III error?
Can only occur when the hypotheses is directional.
Outcome is the opposite direction of what was predicted.
106
What are the 3 types of distributions?
1) Population
2) Sample
3) Sampling (Comparison) Distribution
107
What is the measure of central tendency, measure of spread and the shape of a population?
CT: mu
Spread: sigma
Shape: any shape
Numerical values for population parameters may or may not be known
108
What type of data is a population?
Researcher defined.
| Real or theoretical data
109
What is the measure of central tendency, measure of spread and the shape of a sample?
CT: x-bar
Spread: SD
Shape: varies depending on data
110
What type of data is a sample?
Reflects data from the experiment.
Each data point in independent of other data due to the random process used to establish sample.
Read data.
111
What is sampling distribution?
What distribution do we compare our sample to in order to see if our findings are extreme enough that we can reject the null hypothesis?
112
What is our model of hypothesis testing for sampling distribution?
Random sampling
113
What is our research design for sampling distribution?
Single-participant design
114
What is the type of data used for sampling distribution?
Score (interval/ratio)
115
What info is available about the population parameters for sampling distribution?
Mu, sigma
116
What is the statistic for analysis for sampling distribution?
X (N=1 so we only have one score)
117
We know the population parameters and we have only
one participant. This mean we can almost just compare
the participant to the population. What do we need to do first though?
Convert to Standard Normal distribution.
118
For the sample we are using in class, what is the shape?
1 participant so shape is not relevant.
119
It has been shown many times that on a certain memory test, recognition is substantially better than recall. However, the probability value p(obs) for the data from your sample was .12, so you were unable to reject the null hypothesis that recall and recognition produce the same results. What type of error did you make?
Type II.
In this example, there is really a difference in the population between recognition and recall, but you did not find a significant difference in your sample. Failing to reject a false null hypothesis is a Type II error.
120
In the population, there is no difference between men
and women on a certain test. However, you found a
difference in your sample. The probability value for the
data was .03, so you rejected the null hypothesis.
What type of error did you make?
Type I.
There is no difference in the population, but you found
a difference in your sample. A Type I error occurs
when a significance test results in the rejection of a
true null hypothesis.
121
What is different if our sampling distribution is more than one person?
The research design is: single-sample design.
| The statistic for analysis is: X-bar (M).
