Question

4. Repeated-measures ANOVA Aa Aa Suppose you are interested in studying whether lighting brightness affects spatial reasoning abilities. You decide to test spatial reasoning using completion time scores for the paper-folding test with five people, repeating the test on each person with three different lighting levels (800, 1,000, and 1,200 lux) In this experiment, the null hypothesis is that: O There are no individual differences in the completion time means O The completion time mean for at least one lighting brightness is different from another O There are no differences in the mean completion times among the lighting levels compared The factor of interest is the , and the dependent variable is the The results of the study are presented in the following data table. All scores are times necessary to complete the paper-folding task, recorded in seconds Lighting Brightness 1,000 lux 800 lux 3.42 3.19 3.50 3.75 3.90 Participant 1,200 lux 3.50 3.27 3.54 3.83 3.70 Participant Totals P 10.32 P 9.98 P= 10.74 P= 11.70 P= 11.76 n E 3.52 3.70 4.12 4.16 N 15 G- 54.50 EX2 199.1488 T 17.76 SS 0.3115 T 17.84 SS 0.1803 T-18.90 SS 0.4784 The three treatments in the experiment define three populations of interest. You use an ANOVA to test the hypothesis that the three population means are equal. Present the results of your analysis in the following ANOVA table by entering the missing df values and selecting the correct values for the The three treatments in the experiment define three populations of interest. You use an ANOVA to test the hypothesis that the three population means are equal. Present the results of your analysis in the following ANOVA table by entering the missing df values and selecting the correct values for the missing SS, MS, and F entries. (Note: For best results, retain at least two additional decimal points throughout your calculations. Depending on the order in which you do these calculations and the number of digits you retain, you may find slight rounding differences in the last digit between your answers and the answer choices.) ANOVA Table Source Between treatments Within treatments df MS 0.0809 Between subjects 0.2157 Error Total 14 F Distribution Numerator Degrees of Freedom- 26 Denominator Degrees of Freedom - 26 5000 5000 2 1.00 Use the Distributions tool to find the critical value for α = .01. The critical value is F = F Distribution Numerator Degrees of Freedom -26 Denominator Degrees of Freedom = 26 5000 .5000 8 4 1.00 Use the Distributions tool to find the critical value for α-.01. The critical value is F- At a significance level of α-.01, evaluate the null hypothesis that the population means for all treatments are equal. The null hypothesis is You conclude that lighting brightness affects spatial reasoning abilities.

Answer 1

Null Hypothesis:

• There are no differences in the mean completion times among the lighting levels compared.

The factor of interest is the lighting level, and the dependent variable is the completion time.

Source	SS	df	MS	F
between treatments	0.1613	2	0.0807	6.0035
within treatment	0.9708	12	0.0809
between subject	0.8627	4	0.2157
error	0.1075	8	0.0134
total	1.1321	14

critical value = 8.6491

the null hypothesis is not rejected

you cannot conclude