Chapter 10: Paired Samples t Test

How are difference scores made?

Difference scores are made by subtracting a person's first score from their second score

t statistic formula for paired-samples t test

(Mdifference - μM)/ sM

What is an order effect?

- It refers to how a participant's behavior changes when the dependent variable is presented a second time -This is also sometimes called Practice Effects

What is a paired samples t test?

-a paired samples t test is used to compare means in a within-groups design -it is also called a dependent samples t test -It can be used to analyze data from many studies where one score depends on the other score ***EVERY participant is in BOTH GROUPS

What is counterbalancing?

-counterbalancing is a procedure that aims to limit confounding influence of order effects -it minimizes order effects by varying the order of presentation of different levels of the independent variable from one participant to the next

What does Cohen's d tell us?

Cohen's d tells us how many standard deviations the sample mean difference is away from the population mean difference

What is the first step for the paired samples t test?

Step 1: Find the populations, distribution and assumptions -for the paired samples t test, we use a distribution of mean difference scores for the distribution rather than a distribution of means -the comparison distribution is based on the null hypothesis which posits no mean difference -this means that the mean of the comparison distribution is zero (0)

What is step 1 of finding a confidence interval for a paired samples t test?

Step 1: draw a t distribution with the confidence interval included -to do this, add the SAMPLE mean difference in the center

What is step two for the paired samples t test?

Step 2: State the hypotheses -for the paired samples t test, the null hypothesis states that there will be no difference between the two scores -For the research hypothesis, there WILL be a difference between the two scores

What is step 2 of finding the confidence interval for a paired samples t test?

Step 2: indicate the bounds of the confidence interval on the drawing, writing the percentages under each segment of the curve

What is step three of the paired samples t test?

Step 3: Determine the characteristics of the comparison distribution -to do this, we find the mean and standard error of the comparison distribution based on the null hypothesis -the mean is ALWAYS ZERO for the paired samples t test comparison distribution -standard error uses the difference scores rather than scores in each condition -subtract the first from the second score -to help with this, make a chart with columns saying X, Y, Difference, Difference - Mean difference, Squared Deviation -find the SS (sum of squared differences), with the equation √SS/(N-1) -find the standard error with sm=s/√N

What is step 3 of finding the confidence interval for a paired samples t test?

Step 3: add the critical t statistics to the distribution. look up the t values for lower and upper ends of the confidence interval in the t table

What is step 4 of finding the confidence interval for a paired samples t test?

Step 4: convert the t statistics back into raw mean differences -to do this, use the equations: Mlower = -t(sM)+Msample and Mupper = t(sM)+Msample to find the upper and lower bounds

What is step four of the paired samples t test?

Step 4: find the cutoffs and critical values -this is the same as the single sample t test, except that the df is the number of PARTICIPANTS, not the number of scores -use the degrees of freedom equation df = N-1 -plug the number you get into the t table to find the cutoffs

What is step five of the paired samples t test?

Step 5: calculate the test statistic

What is step 5 of finding the confidence interval for a paired samples t test?

Step 5: verify that the confidence interval makes sense -to do this, subtract each critical value from the sample mean difference. If the numbers are the same, the confidence interval makes sense

What is step six of the paired samples t test?

Step 6: make a decision -if the t statistic falls within the critical values, reject the null -if the t statistic falls within the confidence interval, fail to reject the null

What must we do differently for the steps of a paired samples t test?

We have to create difference scores for every participant in order to make a distribution of mean differences

How do we create a distribution of mean difference scores?

We write the two scores of each participant on a card for every participant, then we pick three cards out of the pile and subtract the second score from the first score for all of them to get the difference scores. Then we calculate the mean by adding all of the differences scores together and dividing by the number of difference scores

How does one find effect size for a paired samples t test?

d=(M- μ)/s - μ is ALWAYS ZERO (0) for the paired samples t test