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)

Answer 1

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.

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

dependent variable: final grade,

scale of measurement: Ratio

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

independent variables:

1).math anxiety level, BS

2). Teaching Approch, BS

Paste appropriate SPSS output. (3 pts)

SPSS syntax:

UNIANOVA final BY approach anxiety

/METHOD=SSTYPE(3)

/INTERCEPT=INCLUDE

/PRINT ETASQ DESCRIPTIVE

/CRITERIA=ALPHA(.05)

/DESIGN=approach anxiety approach*anxiety.

OUTPUT:

Descriptive Statistics
Dependent Variable:   final
approach	anxiety	Mean	Std. Deviation	N
standard	low	82.70	11.576	10
	average	77.50	6.553	10
	high	75.30	6.550	10
	Total	78.50	8.842	30
new	low	89.00	4.216	10
	average	83.60	5.562	10
	high	76.10	9.735	10
	Total	82.90	8.572	30
Total	low	85.85	9.074	20
	average	80.55	6.692	20
	high	75.70	8.086	20
	Total	80.70	8.914	60

Tests of Between-Subjects Effects
Dependent Variable:   final
Source	Type III Sum of Squares	df	Mean Square	F	Sig.	Partial Eta Squared
Corrected Model	1418.600a	5	283.720	4.685	.001	.303
Intercept	390749.400	1	390749.400	6452.742	.000	.992
approach	290.400	1	290.400	4.796	.033	.082
anxiety	1030.900	2	515.450	8.512	.001	.240
approach * anxiety	97.300	2	48.650	.803	.453	.029
Error	3270.000	54	60.556
Total	395438.000	60
Corrected Total	4688.600	59
a. R Squared = .303 (Adjusted R Squared = .238)

To test the effect of approach, calculated F = 7.796,P=0.033 which is < 0.05 level of significance. Approach is significant.

To test the effect of anxiety, calculated F = 8.512,P=0.001 which is < 0.05 level of significance. Anxiety is significant.

To test the interaction effect, calculated F= 0.803,P=0.453 which is > 0.05 level of significance. Interaction is not significant.