Dep-Ss t WS1 - Pigeons - Worksheet new format

WORKSHEET : Dependent-Samples t Test – Example 1 (Pigeon Schedule of Reinforcement) A total of 16 pigeons from 8 clutches (2 pigeons from each clutch) get trained to perform the same task. One pigeon from each clutch is assigned to Schedule A, and 1 from each clutch is assigned to Schedule B. The trainer wants to determine which reinforcement schedule (A or B) elicits more correct responses from pigeons. Step 1. State your hypotheses. a. Is it a one-tailed or two-tailed test? Two-tailed Note that the prediction is that scores on the dependent variable (in this case, the number of correct responses) will be different in the different conditions, so you are going to conduct a two-tailed test . b. Research hypotheses H A : Pigeons trained using Schedule A will give a different number of correct responses from pigeons trained using Schedule B. H 0 : Pigeons trained using Schedule A will NOT give a different number of correct responses from pigeons trained using Schedule B. The hypotheses should be written in the future tense because, at the time they are written, the researcher does not yet know whether the expectation will be supported or not. c. Statistical hypotheses H A : µ D ≠ 0 When the alternative hypothesis is that scores will be different in the two conditions, it implies that the mean difference will be either negative (i.e., less than 0) or positive (i.e., greater than 0). Either less than or greater than 0 means the same thing as not equal to 0 . H 0 : µ D = 0 When the alternative hypothesis is that the difference between the mean scores will be either less than or greater than 0, the null hypothesis must address the only other possibility: that the mean difference between will be the same as (i.e., equal to) 0 . Step 2. Set the significance level (  = .05). Determine the critical value of t. df = 7 t crit = +/- 2.365 Because this is a two-tailed test, you must be sure to look at the column in which the Proportion in Two Tails Combined shows 0.05 [note: the 0 before the decimal point in the t Table is not APA style], which is the fourth

of the six columns of p values. The degrees of freedom for this study equal n pairs – 1 = 7, so you should put a straight edge beneath the row at which df = 7 and, if needed, a straight edge to the right of the fourth column. There are both negative and positive critical values of t in this study because the prediction is that the pigeons trained using Schedule A will have different scores than the pigeons trained using Schedule B. “Different” implies that you anticipate that the mean difference scores will differ significantly from 0. Step 3. Compute the appropriate statistical test using the data provided in the two tables below. Pair # Schedule A Schedule B D D D − D ( D − D ) 2 1 6 4 2 1.25 0 0.750 .563 2 8 6 2 1.25 0 0.750 .563 3 5 2 3 1.25 0 1.750 3.063 4 7 6 1 1.25 0 -0.250 .063 5 5 3 2 1.25 0 0.750 .563 6 7 6 1 1.25 0 -0.250 .063 7 5 6 -1 1.25 0 -2.250 5.063 8 7 7 0 1.25 0 -1.250 1.563 ΣX=50 ΣX=40 ΣX = 10 ∑ ( D − D ) 2 = 11.504 n pairs = 8 X = 6.25 X = 5 X = 1.25 0 Notice that the cells in which you could choose to calculate the sample mean for the pigeons in Schedule A and Schedule B are not filled in. That’s because, in a dependent-samples t test, the difference scores for each pair are calculated first, then the mean difference score is calculated (see Column 3). It is unnecessary to know what the means of each sample are because the raw scores are only meaningful in the context of each pair’s matching score in the other condition. Note the sum of squared deviations of the difference scores from the mean of the difference scores (copied from above): SS D = ¿ 11.504 Calculate the variance of the difference scores (be careful to use the correct number for sample size—the number of pairs): s D 2 = ∑ ( D − D ) 2 n − 1 = ¿ 11.504 8 − 1 = ¿