t-Tests
What is a t-test used to determine?
The difference between the means of two groups.
What is an ANOVA used to determine?
The amount of variation among group means.
What is the shape of the F-distribution?
What is the shape of the F-distribution?
What does an effect size tell you?
Whether the differences between your groups is meaningful.
What is the conceptual formula for a t-test?
Observed difference in group means divided by error in the difference between means.
How is a between-subjects design different from a within-subjects design?
Between-subjects: Comparing two different groups of people on a variable.
Within-subjects: Comparing a single group of people across some condition (usually time).
When would you use an ANOVA instead of a t-test?
When you have three (or more) groups.
Can F-values be positive, negative, or both?
They’re always positive.
When is it appropriate to report an effect size? Why?
When you have statistically significant results.
What is the formula for degrees of freedom in a t-test?
(n1 - 1) + (n2 - 1)
*Please note: You can also just say (n - 2)
What levels of measurement do you need for your IV and DV to perform a t-test?
IV = nominal or ordinal.
DV = interval or ratio.
Why should you use an ANOVA instead of running multiple t-tests? Don’t they accomplish the same thing?
Using only one test reduces our chances of making a Type-1 error (i.e., rejecting the null when we shouldn’t have).
What are the values on the top and along the left side of the page of the F-table?
Dfb (top of page) and dfw (left of page).
What is the relationship between power and effect sizes?
Power is your ability to detect effects in your data.
*Note: The more power you have (i.e., the larger your sample), the better your ability to detect an effect if one exists.
You have a t-value = 4.2
A 2-tailed test
df = 6
α (alpha; significance level) = .05.
Is your t-value significant?
Yes.
The critical t-value for 6 df is 2.447.
Why is the t-value significant?
• The critical t-value for 6 df is 2.447. Our t-value of 4.2 is greater than 2.447 (4.2 > 2.447)
Does a directional hypothesis require a 1-tailed or 2-tailed test?
1-tailed.
What is the “one-way” in a one-way ANOVA?
One factor (i.e., one IV).
*Note: In our example, this was juice.
What are the two sources of a variation in an ANOVA? What’s the difference between them?
Between and within.
Within-groups is error variation; between-groups is attributed to mean differences between groups.
Your Cohen’s d value is .18. What does this tell you (i.e., what is the magnitude of the effect; small/edium/large)?
The effect size is small.
What is the conceptual formula for an ANOVA?
Between groups variance divided by within groups variance.
What is the measure of effect size for a t-test?
Cohen’s d.
What is the measure of effect size for an ANOVA?
Eta-squared (η2)
What does a Tukey post-hoc test tell you?
TAhe Turkey post-hoc tells us which pairs of means differ from one another.
What are the possible values of eta-squared?
0 (no effect) to 1 (total overlap)
What is the formula for degrees of freedom in an ANOVA?
F (b, w).
• b is between groups variance (number of groups – 1) and
• w is within groups variance (total number of observations – number of groups)