Dep Ss WS3 - Productivity - Worksheet - revised 2023

WORKSHEET : Dependent-Samples t Test – Example 3 (Productivity Level) A researcher wants to know if people are more productive when they use a larger computer monitor than when they use a smaller monitor. Each of 10 participants completed a task first on a 42-inch monitor and then completed the same task again on a 15-inch monitor. Productivity was operationalized by measuring how long it took the participants to complete the task. This implies that the faster they completed the task, the more productive they were. Therefore, the researchers were predicting that participants would take less time to complete the task on the 42-inch monitor than on the 15-inch monitor. Step 1. State your hypotheses. a. Is it a one-tailed or two-tailed test? Answer: One-tailed When the prediction is that scores on the dependent variable (in this case, the time to complete the task) will be lower in one condition than the other, this indicates that you are going to conduct a one-tailed test . b. Research hypotheses H A : When participants use a 42-inch monitor, they will take less time to complete the task then when they use a 15-inch monitor. H 0 : When participants use a 42-inch monitor, they will NOT take less time to complete the task then when they use a 15-inch monitor. When conducting a study using dependent samples, the hypotheses and conclusion often require that the comparison be worded to compare “when X happens” to “when Y happens” in order to make it clear that the study uses a dependent-samples design. Notice that the hypotheses are written in the future tense because, at the time they are written, the researcher does not yet know whether the expectation of less time will be supported or not. Also, this is a true experiment. Quasi-experiments use present tense for both hypotheses and conclusions. c. Statistical hypotheses H A : µ D < 0 When the alternative hypothesis is that scores will be lower (less time) in the first than in the second condition, it implies that the mean difference will be negative. H 0 : µ D ≥ 0 When the alternative hypothesis is that the mean difference will be less than 0, the null hypothesis must address the other two possibilities: that the mean difference will be either more than or equal to 0 (more or the same amount of time).

Step 2. Set the significance level (  = .05). Determine the critical value of t. df = 9 t crit = 1.833 Because this is a one-tailed test, you must be sure to look at the column in which the Proportion in One Tail shows 0.05 [note: the 0 before the decimal point in the t Table is not APA style], which is the third of the six columns of p values. The degrees of freedom for this study equal n pairs - 1 = 10 - 1 = 9, so you should put a straight edge beneath the row at which df = 9 and, if needed, a straight edge to the right of the third column. There is only a negative critical value of t in this study because the prediction is that the participants using the larger monitor will take less time than the participants using the smaller monitor. “Less” implies that you anticipate that the mean difference scores will be lower than 0. This is what happens when you subtract generally smaller numbers (for the 42-inch monitor) minus generally larger numbers (for the 15-inch monitor). Because subtracting smaller minus larger numbers yields negative numbers, the results should be less than 0. Step 3. Complete the cells in the columns labeled D and D − ¯ D . They are filled in light blue. Then compute the appropriate statistical test using the data provided in the table. Participant # 42 in. 15 in. D (42 inch – 15inch) D D − D ¿ 1 2 5 -3 -1.500 -1.500 2.250 2 3 4 -1 -1.500 0.500 0.250 3 1 4 -3 -1.500 -1.500 2.250 4 3 2 1 -1.500 2.500 6.250 5 3 6 -3 -1.500 -1.500 2.250 6 1 3 -2 -1.500 -0.500 0.250 7 4 5 -1 -1.500 0.500 0.250 8 2 2 0 -1.500 1.500 2.250 9 1 2 -1 -1.500 0.500 0.250 10 2 4 -2 -1.500 -0.500 0.250 ΣD = -15 ∑ of Squares = ¿ 𝚺 ¿ n pairs = 10 D = ∑ D n =− 1.500 Notice that the cells in which you could choose to calculate the sample mean for the 42-inch monitor and the sample mean for the 15-inch monitor are not filled in. That is 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 4

Step 4. Make a decision. To determine whether the value of the test statistic is in the critical region: Draw and label the critical value(s) using one color, shade the critical region(s), and draw and label the obtained value a different color. t obt = -3.50 t crit = -1.833 Is t obt in the critical region? Yes Should you reject or retain the H 0 ? Reject Are your results significant or nonsignificant? Significant Step 5. Report the statistical results. t (9) = -3.50 , p < .05 Notice that there is no space between the t and the open parenthesis, but there should be a space on both sides of the = symbol and of the < symbol. Round the obtained value of t to 2 decimal places even when that requires adding an ending 0. Italicize the symbols t (the name of the inferential test statistic) and p (for probability). Because the value of p can never be greater than 1.0, you should not put a 0 before the decimal point.

Step 6. Write a complete APA-style conclusion. When participants used a 42-inch monitor, they took less time to complete the task than when they used a 15- inch monitor ( M diff = -1.50, SD diff = 1.35 ). Using a larger monitor significantly increased their productivity, t (9) = -3.50 , p < .05. The first sentence addresses the operational definition of the construct (time to complete the task); the second addresses the hypothetical construct (productivity). At the end of the second sentence come the statistical results . Use a comma (rather than a period) before the statistical results, write the statistical results exactly as in Step 5, and end everything with a period. There should be a space on both sides of each = symbol and of the < symbol. Round the mean difference and the SD of the difference to 2 decimal places even when that requires adding an ending 0. Italicize the symbol M (for mean) and SD (for standard deviation). Write the conclusion in the past tense because, at the time it is written, the researcher knows that the expectation of less time to complete the task when using the 42-inch than in the 15-inch monitor was supported. When the results are significant (i.e., they are consistent with the alternative hypothesis), the easiest way to write the conclusion is to copy the alternative hypothesis and make changes to it: change the tense from future to past, add the mean difference and standard deviation of the difference, and add the statistical conclusion. As shown here, the first sentence contains the comparison between the measure of the DV in both conditions. The second sentence translates that comparison into plain English. The statistical information (mean difference, SD of the difference, and the statistical conclusion) can go at the end of either sentence, but the first two must stay together. Step 7. Compute the estimated d if it’s appropriate. If it’s not appropriate, please explain why. estimated d = D s D = − 1.500 1.354 = 1.11 Notice that in this version of the formula, the denominator is the estimated (sample) standard deviation rather than the square root of the estimated variance. If you use this formula, it is crucial that you remember that you calculated the estimated variance earlier, and so far have not calculated the estimated SD. Therefore, you must calculate the estimated SD by taking the square root of the estimated variance (which you already found to be 1.833) before you put the estimated SD in the formula above. To be on the safer side, you could simply substitute the formula shown above for the one in which the denominator is the square root of s D 2 : estimated d = D √ s D 2 Take the mean difference and SD of the difference scores out to 3 places because they are part of the calculations leading up to the result, then round the result to 2 places.