Slides for Chapter 11: The t-test for Two Related Samples

B. Matched Subjects Design

- A research design in which participants are matched experimentally or naturally, based on the common characteristics or traits they share. - Different, yet paired, participants are observed in each treatment (e.g. twins, couples, people w same IQ). - Scores from each matched pair are compared. - Limited to two in each pair (with t-test).

A. Repeated Measures Designs

- A research design in which the same participants are observed more than once on the same dependent variable. Used to study change over time. Includes: - Pre-Post design - measure DV before & after some treatment. - Example - you could measure athletic performance of soccer players before and after a skills training camp. - Within-subjects design - observe the same participants across time, but not necessarily before/after a treatment. - Example - you could measure students' study skills early in first semester and at end of second semester of college. Note: same people measured across time is also called longitudinal. If you observe more than twice use a repeated ANOVA not a t-test.

II. Introducing the Related Samples t Test

- A statistical procedure used to test hypotheses concerning two related samples. - Compares the average difference between pairs of scores. - Difference score - obtained by subtracting two paired scores {usually in this order: Time2 score - Time1 score}. - In this t test, the difference is calculated for each pair - prior to computing the average difference or MD. - This eliminates the error associated with differences between participants within each group (within-group variance)

IV. Comparing Designs: Advantages of Related Samples Designs

- Fewer subjects needed: RM design requires fewer subjects, more efficient (e.g., 20 SS in RM = 20 per condition, while 20 SS in Indep.(IM) = only 10 per condition). - Study changes over time: RM is excellent if you're interested in studying change. - Eliminates Individual differences: RM reduces error variation due to individual differences, so its more powerful when individual differences are an issue (see next slide). Less error means more power!

Only 2 Assumptions with Related-Samples t-test

- Independence: Observations within each treatment are independent of other participants (The pairs are related - but they aren't related to other pairs of participants). - Normality: Population distribution of difference scores (D) is approximately normal. - Don't have to worry about = variance since each person's individual differences do not affect the t-test. People differ at T1 (individual differences in the DV) but the related test only looks at each person's change over time so no individual differences due to starting level.

I. Two Research Designs: Independent or Related Samples?

- Independent samples - participants in each group or sample are unrelated - and observed only once. Examples: - Participants are selected from two or more populations (e.g., employed, unemployed). Quasi-exp design. - Participants are selected from a single population and randomly assigned to different treatment groups (e.g., high stress, low stress). Experimental design.

More on Matching ...

- Matching through experimental manipulation is typical for experiments -the researcher wants to 'control for' a trait or characteristic - so matches participants on that trait. - Must measure the trait or characteristic before matching. - E.g., - you measure intelligence then match the top two participants, then match the next two highest.. - then assign to randomly to 2 conditions. - Matching through natural occurrence is typical for quasi-experiments in which participants are matched based on their preexisting traits or characteristics. - Eg., you could match participants based on genetics (e.g., identical or fraternal twins, siblings). - People in relationships - friends or married couples are also natural pairs.

Related-Sample Designs

- Related or Dependent samples - participants are analyzed as pairs not individuals because they are linked. - Participants can be related in two ways: 1. They are same person observed more than once (Repeated Measures design). 2. They are matched, experimentally or naturally, based on the common characteristics or traits that they share. (Matched Pairs design)

III. Hypothesis Testing Steps with Related-Samples t

- Step 1: State hypotheses (H0 and H1) - Step 2: Set decision criteria Use α = .05, unless otherwise specified Compute df = n - 1 (where n = # of pairs of scores) Use t-table to select critical value - Step 3: Compute sample stats variance of difference scores: standard error: test statistic: - Step 4: Make decision If |calculated t| > |critical t|, Reject H0 and conclude that there IS a difference. If |calculated t| < |critical t|, Do not reject H0 and conclude that there is NO difference.

df - familiar, but a little tricky

- The degrees of freedom for the related-samples t tes. - NOTE: # of pairs- 1, not # scores - 1 16 best friends in a study of friendship: - tom-jerry, dick-jane, kyle-kylie, etc 16 peopleà but 8 pairs so df = 8 -1= 7

Review of Hypotheses for Related Samples

- The hypotheses are about the average difference in the population that each individual or pair will show H0: μD = 0 H1: μD ≠ 0 - For directional tests H0: μD ≥ 0 and H1: μD < 0 scores lower or H0: μD ≤ 0 and H1: μD > 0 scores higher

Disadvantages of Repeated-Measures

- The outcome of RM studies can be contaminated by other factors. - Two types of problems: - Carryover effects: subject's score at Time 2 is altered by aftereffects of participating earlier in Time 1: - practice effect +, - fatigue effect -, not naïve (can't see T2 'fresh'). - To stop some direct effects of participation - can counterbalance the order (half get AàB, half BàA). - Progressive error: subject's responses may change over time due to factors outside of the study (e.g., person's mood, health) or in longitudinal study confounding outside events (studying stress and 9/11 happens). - Advantage of Independent Design is all subjects are naïve - not influenced by prior experimental treatment, Time is not a confound.