Please note that for all problems in this course, the standard cutoff (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 handcalculating, 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.

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 pvalue 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 pvalue = 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 pvalue = 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 (pvalue = 0.453 > 0.05).
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