Lecture 10: Mean comparisons, effect size, and variance Flashcards
What are the 2 types of mean comparisons
- Paired (dependent samples) comparisons
- Unpaired (independent samples) comparisons
What do we mean by dependent samples?
Each measurement in one group/condition has a corresponding measurement in the other group/condition
What type of design are paired comparisons typically used? (2 and one of them is an example)
- Within-subjects/Repeated measure designs
- Where subjects in one group are siblings/spouses of corresponding subjects
What do we mean by independent samples?
measurements in the two conditions are completely independent of each other
What type of design are unpaired comparisons typically used?
Between subjects designs - we randomly assign different subjects to different conditions
For paired comparisons how do we compute the CI for the mean difference?
The same way we compute a CI for a single population mean!
The only diff is that the mean we’re interested in is the mean of corresponding differences
How do we calculate the sample mean difference in a paired comparison (3)
- Find the difference between paired samples
- Calculate the mean of the differences
- Compute SD, Margin of error, and CI for the population mean difference
Can we compute a vector of differences for unpaired mean comparisons?
Nope. There are no corresponding “partners” in the second group to subtract from each value in the first group
What is the sample mean difference (estimate of the population mean difference)
The difference between the mean in group 1 and the mean in group 2
The standard of the mean difference is computed in 2 ways:
- Using the “pooled” standard deviation from both groups
- Using the “unpooled” standard deviation
What does using the “pooled” SD from both groups result in?
- Smaller SD = smaller standard error = narrow CI
- The validity of the method depends on knowing the population SD is the same in both groups (cause it’s never known)
What does using the “unpooled” SD result in
The valid on average even when the population standard deviations are different
What is effect size?
Size of the effect (of the independent variable on the dependent variable) in an experiment
What is the raw effect size?
The population mean difference in original units of the variable
What is the raw effect size estimate
The sample mean difference!
What is the standardized effect size?
The population mean difference as a number of standard deviations
What is the standardized effect size estimate for unpaired comparisons? (+ What’s it sometimes called?)
The sample mean difference divided by the pooled standard deviation in the sample
Also known as Cohen’s d
Like z-scores standardized effect sizes are useful when?
the units of the variable aren’t easy to interpret
variance in terms of the sd
the standard deviation squared
What is the population variance?
sigma squared
what’s the sample variance?
s squared
