PSYC204 post midterm content

starting from 11/5/26 lecture

how to do the calculation example with two groups

determine critical value for decision rule using the degrees of freedom

calculate mean and sum of squares for each group

calculate the pooled variance

calculate the SE of the mean difference and the t-statistic.

in addition to the result of the hypothesis test, we can calculate the (estimated) effect size (cohen’s d) = x₁-x₂)/sqrt(s_p²)

what does a cohen’s d of -1.68 mean, in the example

the money handling group has 1.68 standard deviations less discomfort than the non money handling group. tells you the size of the effect that is largely independent of the sample size.

how do you interpret r²?

Always between 0 and 1. the percentage of variance in the dependent variable that we can explain using the independent variable.

what is the confidence interval formula for estimating 𝜇₁-𝜇₂

[mean difference estimate from the sample data] ± [critical t value corresponding to the alpha and df for the hypothesis test] multiplied by [standard error of the mean difference, from the sample data.]

what is the rule for confidence intervals when estimating mean difference

if the C.I. includes 0, then it is not a significant effect. if it doesn’t, the group difference was significant.

null hypothesis for mean differences

𝜇₁-𝜇₂ = 0

assumptions you make when using an independent samples t-test

1. observations from each sample are independent

2. the two populations the samples come from must have a normally distributed dependent variable

3. the two populations the samples come from must have equal variances of the dependent variable (also called the homogeneity of variance assumption)

Hartley’s F-max test : what do large and small variances indicate?

large value indicates large difference between sample variance

small value (near 1.00) indicates similar sample variances

4 things you need to know to conduct the hypothesis test about the homogeneity of variances

1. alpha level

2. K - how many samples you have

3. Df - for each sample variance

4. critical value is either in or not within critical region

dependent samples (or paired sample) t test. repeated measures/within-subjects design

used when you have two scores from each participant. two time points of data from the same group of people. (eg comparing ppl before and after treatment). you can have a repeated measures design with more than two time points (but the dependent samples t test is specific to situations where you compare two time points).

what is difference score in repeated-measures designs

difference score = D = X₂-X₁. where X₁ is the person’s score in the first treatment and X₂ is the score in the second treatment. The null states that the mean difference is zero.

what does the alternative hypothesis indicate in repeated-measures research design

reflects the true mean difference in the population (not sampling error, which is measured by the standard error of the differences)

dependent samples t statistic

mean difference score for the group, over the standard error of the mean of the difference scores. structurally, it is similar to the other statistics we have learned, the key difference is that the mean is not from the raw score, it is the difference between two scores.

standard error for dependent samples t statistic formula

advantages of repeated-measures designs

the same ppl measured twice tend to have less variability than two different groups of ppl. less variability can make it easier to se and detect an effect, repeated measures design can have more statistical power. even though the ppl are different from one another, their differences aren’t. it’s the mean and standard dev of these differences you are interested in for this test.

disadvantages of repeated-measures designs

you sometimes lose ppl in the study (drop-outs), which decreases your sample size. Order effects or having people participate in two treatments can influence the results of a study.

effect size for dependent samples t-test

what do you need to calculate the confidence interval for the dependent samples t test

1. alpha value from corresponding statistical test

2. critical t-value associated with that alpha value

3. the mean of the differences from the sample data

4. the standard error of the mean of the differences, estimated from the sample data.

assumptions for a dependent samples t test

observations within each treatment condition must be independent. So, your original sample of ppl that you got for both measurements was independent and random. population of difference scores (D values) must be normally distributed.

example of dependent samples t test

table with all score

get difference scores, then get the mean x^bar _D . Get deviation scores. (D-x_D) and sum of squares. do hypothesis test. H₀: 𝜇_D= 0. if you’re using alpha=.05, then you’re looking for the t value that cuts of 2.5% in the tail. with whatever degrees of freedom you have. if df=8, it’s ±2.306. t=(x^bar_D-𝜇_D)/S_xD. s²= SS/n-1. S_xD = sqrt(s²_D/n). if t=-4, you would reject the null hypothesis in this scenario. this would say that the treatment has an effect and it’s bad.

assuming that the sample mean difference remains the same, which of the following sets of data is most likely to produce a significant t statistic?

n =15 and SS=10

n=15 and SS=100

n=30 and SS=100

n=30 and SS=10

n = 30 and SS =10