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

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).