1Which of the following is in common between single sample, paired sample and independent samples t-tests?
They all involve analysis of means
2What is the structure of the data for an independent samples t-test?
2 groups of people at 1 occasion
3What kind of variables are needed to run an independent samples t-test?
A nominal variable and an ordinal or ratio/interval variable
4What kinds of research questions are independent samples t-test used to answer?
Research questions that involve comparing two groups
5What is the unit of analysis for independent samples t-tests?
Difference between means
6What is the underlying logic of the independent samples t-test?
We are trying to figure out the probability of getting our two samples, of our sample sizes, if the null is true (i.e., they came from the same population).
7What does a typical null hypothesis look like for an independent samples t-test?
The groups are not different
8What does the typical alternative hypothesis look like for an independent samples t-test?
One group is lower/higher than the other group
9Degrees of Freedom
The number of data points that are free to vary. It goes on the bottom of various formulas (in the form of a letter minus a number)
10Which of the following is typically true for the mean of the sampling distribution for an independent samples t-test?
It is assumed to be zero because if the null hypothesis is true, on average there will be no difference between two samples from the same population.
11What is the sampling distribution for the independent samples t-test made up of?
All possible differences between means from two samples, or two given sample sizes, drawn from the same population
12What is the standard error of the sampling distribution for an independent samples t-test?
It is the average distance our differences between means are from zero
13What are the top and bottom of the t-test forumula for the independent samples t-test?
The difference between means you got in your data over the difference between means you might expect to get if the null hypothesis were true.
14What is a valid interpretation of t-score in an independent samples t-test?
They tell you how many standard deviations your difference between means is from the null populaiton mean
15Suppose a researcher gets a result of t = 1.25. Which of the following is a valid interpretation of these results?
The size of their difference between means is about one and a quarter times larger than they might expect due to chance, if the null hypothesis were correct.
16When you retain the null hypothesis in an independent samples t-test, how do you statistically interpret the results?
There is greater than a 5% chance of getting your size of difference between means, with your two sample sizes, if the null hypothesis were true (i.e., your means came from the same population).
17When you reject the null hypothesis in an independent samples t-test, how do you statistically interpret the results?
There is less than a 5% chance of getting your size of difference between means, with your two sample sizes, if the null hypothesis were true (i.e., your means came from the same population).
18What yields more power for an independent sample t test?
A larger difference between means
19You and your best friend each do a study comparing men and women on how much they use the word “like” in conversation. Both of you agreed to only get 50 people of each gender. Surprisingly, both of you ended up with the same means for men and women, but you rejected your null and he didn’t. Based on the central limit theorem, what’s likely going on?
Your samples had less variability, meaning your estimate of the population variance was smaller, giving you less sampling error.
20How is effect size Cohen’s d interpreted for independent samples t-tests?
It is an estimate of the distance between the means of the two populations assuming the alternative hypothesis is true.
21How are 95% confidence intervals interpreted for independent samples t-tests?
With repeated sampling, 95% of the time the true difference between population means will lie within that interval.
22Distribution of differences between means
All possible differences between means, of samples of those two sizes, drawn from the same null population
23Standard error (for independent samples t-test)
The average size of difference between means expected given null hypothesis
24Cohen's D
An effect size for tests of means that expresses the difference between two population means in standard deviation units.
25Confidence Intervals
Range of most plausible values for the true difference between population means.
26Power
Probability of rejecting the null IF the alternative hypothesis is true
27Research question for paired sample t test?
Is there change over time on average?
28Type of data in a paired sample t-test
One sample and one variable, but at two time points (two waves)
29What is the unit of analysis for a paired sample t test?
Difference of means
30Underlying logic for a paired sample t test
Determining the likelihood of getting sample mean difference, from a population with zero average change
31Research question for a independent sample t test
Are these two groups different?
32Type of data in independent sample t test
Uses the data from 2 groups, but from one wave
33Unit of analysis for indenpendent sample t-test
Difference between means
34Underlying logic for a independent sample t-test?
Determining the likelihood of getting that size of difference between sample means, with given sample sizes, from the same population
35What is a similarity between the single sample z-test and single same t-test?
They both are for comparing your sample to a known population
36In what situation should you use a single sample t-test instead of a single sample z-test?
When the population standard deviaiton is unknown
37In what situations should you use a paired samples t-test instead of a single sample t-test?
When you want to study changed across two time points
38What is the underlying logic of a single sample t-test?
We are trying to figure out the probability of getting our sample mean, with our sample size, from the null hypothesis population.
39What is the underlying logic of the paired samples t-test?
We are trying to figure out the probability of getting our sample mean difference, with our sample size, from the null hypothesis population
40How do the t-test formulas compare to the z-test formulas?
The t-test forumulas use SD in place of o(standard deviation)
41How do we alter the formula for the sample standard deviation to make it an unbiased estimate of the population standard deviation?
Divide by N-1 instead of N
42Where does the mean of the null hypothesis population typically come from for a paired samples t-test for analyzing change?
It is assumed to be zero based on the null hypothesis that there is no change
43What is the sampling distribution for the single sample t-test made up of?
All possible means from samples of a given sample size from the null hypothesis population
44What is the standard error of the sampling distribution for a single sample t-test?
It is the average distacne sample means in the sampling distribution are from the mean of the null hypothesis population
45What is the sampling distribution for the paired samples t-test made up of?
All possible means of change scores from samples of a given sample size, drawn from the null hypothesis population(where there is no change on average)
46What is the standard error of the sampling distribution for a paired samples t-test?
It is the average distance sample means of change scores in the sampling distribution are from the mean of the null hypothesis population (which is typically zero).
47Suppose a researcher gets a result of t (499) = -2.50. Which of the following is a valid interpretation of these results?
The distance between the sample mean and the mean of the null hypothesis population is 2.50 times larger than might be expected by chance, if the null hypothesis were true.
48Suppose a researcher gets a result of t (99) = .50. Which of the following is a valid interpretation of these results?
Their sample mean is .50 standard deviations above the mean of the null hypothesis population.
49Which of the following is true regarding the relationship between t-scores and p-values?
They are inversely related (if one is larger, the other is smaller, and vice versa).
50When you reject the null hypothesis in a single sample t-test, how do you statistically interpret the results?
There is less than a 5% chance of getting your sample mean, with a sample of your size, from the null hypothesis population.
51When you retain the null hypothesis in a paired samples t-test, how do you statistically interpret the results?
There is greater than a 5% chance of getting your sample mean difference, with a sample of your size, from the null hypothesis population where there is no change.
52There is less than a 5% chance of getting your sample mean difference, with a sample of your size, from the null hypothesis population where there is no change.
53What yields more power in a single sample t-test or paired samples t-test?
The sample size is larger.
54As sample size increases (say, from 50 to 100), which of the following is true regarding the t-critical for t-tests?
It gets smaller (i.e., decreases towards 1.96).
55What is an accurate interpretation of p = .02 for a single sample t-test?
There is a 2% chance of getting that sample mean, with that sample size, from the null hypothesis population.
56What is the interpretation of a Cohen’s d of 2.00?
The alternative hypothesis population mean is two standard deviations above the null hypothesis population mean.
57Which of the following leads to a larger Cohen’s d effect size?
Larger difference between sample and population mean
58If a paired samples t-test is statistically significant (p < .05), which of the following will also be true regarding the confidence interval?
It will not contain the mean of the null population, which is typically 0
59Degrees of freedom
The number of data points that are free to vary. It's our sample number minus one and goes on the bottom of various formulas
60T distribution
The sampling distribution for t tests, which is symmetrical two tailed distribution of t scores
61What are the two interpreations of t?
Ratio of your outcome (distance of sample mean from population mean) to the outcome expected given null hypothesis (standard error of means) OR distance sample mean is from population mean in standard deviation units
62Distribution of means (for paired samples t-test)
All possible mean difference, from a given sample size, drawn from the null hypothesis population (where there is zero average difference)
63Standard error (for paired samples t-test)
The average size of mean difference (average amount of change) expected given null hypothesis.
64T critical
Critical value for t tests, which is based on degrees of freedom.
65Which of the following is a true similarity or difference between independent samples t-tests and ANOVA?
Independent samples t-tests are confined to two groups, whereas ANOVAs can compare two or more groups.
66What types of research questions do one-way ANOVAs address?
Questions about how two or more groups vary on some ordinalatio outcome.
67What kind of data are needed for one-way ANOVAs?
A nominal group variable (or IV) and an ordinalatio outcome variable (or DV).
68What is the unit of analysis for ANOVAs?
Variance
69What does the typical alternative hypothesis look like in ANOVA?
The outcome varies across your groups.
70If you have more than two groups in your data, why is it typically recommended that you do a single ANOVA rather than multiple independent samples t-tests?
If you do multiple tests, your chance of Type I error will be more than 5%.
71What is the logic of ANOVA?
We are trying to figure out the likelihood of getting means that vary as much as ours do (with samples of our sample sizes), if drawing them all from the same population.
72In ANOVAs, which number tells us how much our means vary?
Between-groups variance
73Which number tells us how much we expect our means to vary by chance, if the null is true and they all come from the same population?
Within-groups variance
74What is the general logic of the F-ratio?
How much our group means vary / how much we expect our group means to vary by chance given the null hypothesis that they are all from one population.
75F Ratio
Ratio of BG variance to WG variance
76What are the three interpretations of F?
Ratio of how much the group means vary (BG) to how muhc people within groups vary, top is sampling error plus the effect (if there), while bottom is just sampling error, ratio of your outcome (variance among means) to the outcome expected given null hypothesis (variance expected among means due to sampling error)
77What is the sampling distribution in ANOVA made up of?
All possible F-ratios you could get, with your number of groups and your sample sizes, if drawing your samples from same population.
78What does the F-distribution look like?
A one-tailed test, skewed to the right, starting with 0 and with the mode being 1.
79Which formula captures variability of group means around the grand mean?
∑(Mgroups−GM) (squared)
80How do you interpret rejecting the null in an ANOVA?
There is less than a 5% chance of getting an F-ratio as large as yours if the null hypothesis is true and your groups all came from the same population.
81How do you interpret retaining the null in an ANOVA?
There is greater than a 5% chance of getting an F-ratio as large as yours if the null hypothesis is true and your groups all came from the same population.
82If a researcher gets an F=4.00, with F-critical of 3.86, which of the following is an accurate interpretation?
The group means vary four times more than you would expect them to vary by chance if the null hypothesis is correct.
83Alpha Inflation
Change of Type I error goes up with each hypothesis test
84Total variance
Variance of individuals around the total average (grand mean)
85Between groups variance
Variance of groups means around the total average, captures both sampling error and effect
86Within groups variance
Variance of individuals within each group around their own group mean, indication of sampling error (the larger the WG, the larger the sampling error)
87F-ratio
Ratio of BG variance to WG variance, should equal 1 if no effect
88F-distribution
All possible F ratios, of samples of our size, drawn from the same null population.
One tailed, skewed distribution
Will have a lower bound at 0, a mode of 1
89Research Question for ANOVA
Does the outcome vary across groups?
90Type of data in ANOVA
2 or more groups, but only one wave
91Unit of analysis for ANOVA
Variance among means
92Underlying logic for ANOVA
Determine likelihood of getting means that vary as much as ours, with given sample sizes, from the same population
93What do you learn from the F-test in ANOVA
Whether or not the DV varies significantly across the IV
94What are the limitations of the F-test in ANOVA?
It doesn’t tell you which groups are significantly different from which other groups, It doesn’t tell you how strongly the IV (group variable) is related to the DV (outcome variable), It doesn’t tell you the sizes of differences between specific pairs of groups.
95What do you learn from pairwise comparisons?
Whether or not the differences between particular pairs of groups are significant.
96What do you learn from R-squared?
The proportion of variance in the DV accounted for by the IV.
97What is the logic of the pairwise comparison in ANOVA?
We are trying to figure out the likelihood of getting this large of a difference between two means, with our sample sizes, if drawing them from the same population.
98What is the typical process for running an ANOVA with pairwise comparisons?
Run the F-test, and then if it is statistically significant, run the pairwise comparisons.
99If you run an ANOVA with four IV groups, and get a statistically significant F-ratio, what might you expect?
At least the pairwise comparisons of the outer groups (the groups with the lowest and highest means) will be significant.
100What are key differences between the F-test and the pairwise comparisons?
The F-test assesses variances across all group means, while the pairwise comparisons assess differences between two of the means.
101How would you interpret R2 = .25?
The IV accounted for 25% of the variance in the DV, and it is a large effect.
102Which of the following is true regarding power in ANOVA?
Even if the F-test is sufficiently powered, some of the pairwise comparisons still might not be sufficiently powered.
103Which ANOVA extension allows for the analysis of change over time across two or more occasions?
Repeated Measures ANOVA
104Which ANOVA extension involves a single IV and multiple DVs?
MANOVA
105Which ANOVA extension involves multiple IVs?
Factorial ANOVA
106ANOVA
Stands for "analysis of variance": Hypothesis test for analysing variance among means of two or more groups
107Between groups variance (BG)
Variance of groups means around the total average (grand mean) or variance in outcome due to groups
108Between groups degrees of freedom
kgroups-1
109Between groups sum of squares
110Within groups variance (BG)
Variance of individuals within each group around their own group mean or vaiance in outcome due to individual differences of group members
111Within groups sum of squares
112Within groups degrees of freedom
N-kgroups
113Total variance
Variance of individuals around the total average (grand mean) (BG variance + WG Variance)
114f-critical
Depends on df (BG) and df (WG). Typically it's around 3-4
115Alpha inflation
Chance of making a type I error goes up with each hypothesis test
116Steps to writing an APA style write-up
State test you ran.
• Reference your research question/hypothesis.
• Report your results in APA style. Indicate your t-score, and your p-value.
• If you know exact p-value, report it, otherwise just state the level of significance (e.g., p<.05,
p<.01, p<.001, or ns for non-significant results). Even if know exact p-value, put p<.001 if p
smaller than .001.
• Typically significance testing results are separated by a comma, whereas things like means
are inserted within parentheses.
• Report effect size Cohen’s d, in parentheses or after hypothesis testing results.
• Report 95% confidence interval