Question

Please note that for all problems in this course, the standard cut-off (alpha) for a test of significance will be .05, and you always report the exact power unless SPSS output states p=.000 (you’d report p<.001). Also, remember when hand-calculating, always use TWO decimal places so that deductions in grading won’t be due to rounding differences.

Problem Set 1: (22 pts) A teacher wanted to see if a new pedagogical approach was beneficial to students, and if the effects vary by amount math anxiety. To examine this, students completed math anxiety surveys and were grouped into “low”, “average”, and “high” levels of math anxiety. She then randomly assigned equal numbers of students from each group into one of two classes – one taught using her “standard” approach; the other class was taught using a new approach. The data presented in the table below are the final grade percentages of the 60 children (30 per class). Conduct the most appropriate statistical analysis to determine whether final grades in a math class were affected by teaching approach and/or amount of math anxiety. Final grade (%) Low Average High Standard approach 72 80 77 68 85 71 73 73 73 75 81 69 97 73 90 73 91 74 95 73 76 88 73 67 89 71 81 97 75 75 New approach 88 78 68 89 90 79 93 89 58 89 88 83 79 75 81 88 80 69 92 86 86 91 88 88 94 85 81 87 77 68

1. What is the dependent variable and its scale of measurement in this scenario? (3 pts)

2. State the independent variable(s) in the scenario and label as either “BS” (between subjcts) or “WS” (within subjects). (2 pts)

3. Paste appropriate SPSS output. (3 pts)

4. Paste appropriate SPSS graph(s), formatted in APA (2 pts). Write an appropriate figure caption using APA format for each figure (begin numbering with 1 – e.g., Figure 1). (2 pts per graph + 2 pts per caption = 8 pts total for this question).

5. Write an APA-style Results section based on your analysis. All homework “Results sections” should follow the examples provided in the presentations and textbooks. They should include the statistical statement within a complete sentence that mentions the type of test conducted, whether the test was significant, and a decision about each null hypothesis tested. Include effect sizes, post hoc analyses / interpretations, and refer the reader to Figure(s) created above, when appropriate (4 pts).

6. Identify a potential confounding variable with the study as it was presented (you can use your imagination!). Justify why you think it may be a confound rather than an extraneous variable. (2 pts)

Answer 1

What is the dependent variable and its scale of measurement in this scenario? (3 pts)

Ans: The dependent variable is the final grade percentage and its scale of measurement is the interval.

2. State the independent variable(s) in the scenario and label as either “BS” (between subjcts) or “WS” (within subjects). (2 pts).

Ans: The independent variables are math anxiety and teaching approach. Both the independent variables are "BS".

3. Paste appropriate SPSS output.

Tests of Between-Subjects Effects
Dependent Variable:Grade
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Corrected Model	1418.600a	5	283.720	4.685	.001
Intercept	390749.400	1	390749.400	6452.742	.000
Math_anxiety	1030.900	2	515.450	8.512	.001
Teaching_approach	290.400	1	290.400	4.796	.033
Math_anxiety * Teaching_approach	97.300	2	48.650	.803	.453
Error	3270.000	54	60.556
Total	395438.000	60
Corrected Total	4688.600	59

4.  Paste appropriate SPSS graph(s), formatted in APA (2 pts). Write an appropriate figure caption using APA format for each figure (begin numbering with 1 – e.g., Figure 1). (2 pts per graph + 2 pts per caption = 8 pts total for this question).

From the above plot, we see that the lines are nearly parallel to each other. Hence, there may not be an interaction between the math anxiety and teaching approach.

5. Write an APA-style Results section based on your analysis. All homework “Results sections” should follow the examples provided in the presentations and textbooks. They should include the statistical statement within a complete sentence that mentions the type of test conducted, whether the test was significant, and a decision about each null hypothesis tested. Include effect sizes, post hoc analyses/interpretations, and refer the reader to Figure(s) created above, when appropriate (4 pts).

Ans: The p-value for the interaction effect is 0.453. Hence, there is no interaction effect on the model at the 0.05 significance level. But, the p-values for the math anxiety and teaching approach are 0.001 and 0.033 respectively. hence, both factors have a significant effect on the final grade at the 0.05 significance level.