Question

# Please note that for all problems in this course, the standard cut-off (alpha) for a test...

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)
1. State the independent variable(s) in the scenario and label as either “BS” (between subjcts) or “WS” (within subjects). (2 pts)
1. Paste appropriate SPSS output. (3 pts)

1. 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).
1. 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).

1. 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)

First, entering the given data as three separate variables, namely:

Our objective, here, is to examine whether to see if a new pedagogical approach was beneficial to students, and if the effects vary by amount math anxiety; It implies that we need to find out whether the final grades in a math class were affected by teaching approach and/or amount of math anxiety.

Hence, the dependent variable here, would be the final grades, that is measured in a ratio scale (Continuous variable). The independent variables would be the two factors -Teaching approach and Level of math anxiety, which can be labelled as "BS" since, we are interested in obtaining a significant difference between the factors and their levels and are not currently interested in the variation in the final grades for each combination of the levels of two factors.

To test:

Teaching approach has no significant effect on the final grades Vs Teaching approach has a significant effect on the final grades Level of math anxiety has no significant effect on the final grades Vs    Level of math anxiety has a significant effect on the final grades    There is no interaction between the Teaching approach and Level of anxiety Vs There is a significant interaction between the Teaching approach and Level of anxiety

To test the above claim, the appropriate statistical test would be a two way ANOVA:

.

We get the output:

Looking at the p-value of the effect of factors Teaching approach (0.033 < 0.05) and Anxiety level (0.001 <0.05), we may conclude that their effect on the final grade is significant at say, 5% level.

The means plot supports our conclusion. However, we find that the there is no significant interaction among these factors.

Stating the results in APA format:

A two factor ANOVA was conducted to test the effects of Teaching approach (2 Levels) and Level of math anxiety (3 Levels) on the final grades of students.Both the factors were found to have a significant effect on the grades at 5% level of significance.The main effect for factor Level of math anxiety yielded an F(2,54) ratio of 8.512, with p-value = 0.001 < 0.05 indicating a significant difference in grades for the anxiety levels: Low and High (p - value < 0.001). The main effect for factor Teaching approach yielded an F(1,54) ratio of 4.796, with p-value = 0.033 < 0.05 indicating a significant difference in grades for the the new and standard approaches.However the interaction effect between the two factors was not significant (p-value = 0.453 > 0.05).