ESTIMATING THE DIFFERENCE BETWEEN THE MEANS OF DEPENDENT POPULATIONS Flashcards
What re independent/dependent populations?
Independent: two sets of scores are not related to eachother (selection process - are you matching pairing, measuring same people many times… - for one group is not related to the other)
Independent: groups don’t influence each other.
Dependent: sets of scores are connected, like pairs or repeated measurements on the same individuals.
A within-group design uses a dependent populations approach. How does that work?
You have a sample coming from a given population and from that one sample 2 sets of scores (each participant will be tested twice).
INTERVAL ESTIMATE WHEN POPULATIONS ARE DEPENDENT.
What are we interested in? What is the global idea?
Because we have repeated measures, we are interested in the difference of scores (time 2 - time 1)!!! (cause yea you wanna see if your treatment worked in that given participant!!!). Once you have your differences of scores, you just have to find the mean of this difference of scores, as well as the standard deviation.
mean of difference of scores = X avec barre en haut avec un petit D (for difference)
When calculating the standard deviation of the difference of scores, keep in mind that : sum of (score-sample mean) = 0 ALWAYS (cause mean is the middle point of those scores) !!!!1
When calculating the confidence interval when populations are dependent, how does that look like?
CI - point estimate +/- cri x SE
point estimate: X barre petit D
SE(standard error): standard deviation of the difference of scores/ sample size
Having dependent populations means…
We have an association between scores (association because same person is measured twice or more)
these designs are referred to as repeated measures design or within subjects design.
In these designs subjects are tested under two different circumstances: control condition and experimental condition (basically before and after treatment)
dependent populations = comprising pairs of related scores (meaning knowing one of the two scores allows us to make a fairly reasonable prediction about the other score
during the exam, only the problem for dependent populations will have raw data, it will be our clue for what approach we should take (since there are repeated measurements)
:)
What is the goal of an interval estimate for dependent populations?
To estimate the difference between the means of dependent populations!
What are the steps for when you’re estimating the difference between the means of dependent populations?
- convert the 2 scores (of each participant) to 1 (difference of scores!)
- Calculate the mean of the difference of scores as well and the standard deviation of the difference of scores (SD)
- Once you know the standard deviation of the difference of scores, calculate the standard error (of the SAMPLING distribution of the difference of scores)
standard error is also referred to as SMD
rappelle toi standard error - standard deviation in a distribution of samples:)
1 - alpha is what ?
the confidence coefficient
How many degrees of freedom for when we have dependent populations?
n-1 (we only lose one degree of freedom, cause we only have one sample)
what does it mean to test the mean of difference scores or to test the difference between two means…
means we are doing hypothesis testing, to see whether our results are significant or not
How do you formulate the research and null hypothesis when you’re testing the mean of difference scores ?
**UMD = 0, cause we assume no effect of treatment!!!!
H0: UD = 0
H1: UD pas égal a 0
If mean of population one is greater than population two (right tail)
H1: UD>0
if mean of population one less than population two, left tail
HI: UD<0
How do we call a t-test for dependent means?
The paired t-test.
Also called a repeated measures t-test or within-subjects t-test
What re the steps for t-test for dependent means?
always the same idea:
1) formulate the null and alternative hypothesis
2) Determine the characteristics of the comparison distribution
3) select the significance value
4) select the test statistics and calculate its value
5) determine the critical value(s) on the comparison distribution at which the null hypothesis should be rejected.
when two tails, precise +/- t critical !!!!!!!!!!
6) Compare calculated and critical values and reach a conclusion about the null hypothesis.
is test statistic (t obt.) more extreme than critical value?
should be written like this:
t(df)= test statistic score, p> or < alpha!!! then say whether you accept and reject and what would that mean when referring to the problem and research hypothesis.
What si the comparison distribution?
Distribution of difference means!!!
Testing difference of means with confidence intervals. How do you conclude whether results are significant or not!!!
If the confidence interval does not include the mean of the null hyp, which is 0, we declare the results of the study significant
Effect size when testing dependent sample means, same idea dans thus les scenarios où pop standard deviation is unknown. Which is….
Effect size is subject to sampling error!
so you have to calculate the standard error of d, if you wanna know if the effect size you found is significant or not (using a confidence interval around d)
If the confidence interval does not contain 0, the effect is considered significant.
Why is it that in the confidence interval around d, we use a Z critical and not a t critical?
- What t is Designed For
The t critical value adjusts for small sample sizes and the uncertainty of estimating the population standard deviation from a sample.
When calculating confidence intervals for raw scores or means, small sample sizes introduce variability, and
t corrects for this.
t changes with degrees of freedom (sample size), reflecting that smaller samples lead to more uncertainty.
2. Why Effect Sizes Don’t Need t
Effect sizes like
d are standardized measures, meaning:
They’re based on differences scaled by a standard deviation (pooled or population).
They don’t estimate raw data directly (like a mean); instead, they summarize the magnitude of a difference.
Even though we often calculate
d from sample data,
d itself doesn’t change with sample size because it’s designed to be independent of it. The variability in
d (reflected in its confidence interval) isn’t tied to estimating means or raw scores—so
t isn’t needed.
- Z Critical and Normality Assumption
The distribution of
d (especially in larger samples) is approximately normal.
Since normal distributions use Z values, we use
Z critical to compute confidence intervals for
d.
The t critical value would only be used if we believed that small-sample variability directly affected
d, but it doesn’t. - What Your Teacher Means:
When your teacher says we use
Z critical for
d because sample size doesn’t affect
d, they mean that:
The value of
d (the effect size) doesn’t directly change based on how many people are in your study.
d tells you how big the difference is between two groups in standard deviation units, and that’s true no matter the sample size.
