1. Statistics
2. Hypothesis Testing
3. Type I and Type II Errors
4. 607434

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Complete the following:

Use an existing dataset to compute a factorial ANOVA. All SPSS output should be pasted into your document. The "Activity 5a.sav" file contains a dataset of a researcher interested in finding the best way to educate elementary age children in mathematics. In particular, she thinks that 5th grade girls do better in small class sizes while boys excel in larger classes. Through the school district, she has arranged a pilot program in which some classroom sizes are reduced prior to the state-wide mathematics competency assessment. In the dataset, you will find the following variables:
• Participant: unique identifier
• Gender: Male (M) or Female (F)
• Classroom:
• Small (1) - no more than 10 children
• Medium (2) - between 11 and 19 children
• Large (3) - 20 or more students
• Score - final score on the statewide competency assessment.
Complete the following:
1. Exploratory Data Analysis.
a. Perform exploratory data analysis on all variables in the data set. Realizing that you have six groups, be sure that your exploratory analysis is broken down by group. When possible, include appropriate graphs to help illustrate the dataset.
b. Give a one to two paragraph write up of the data once you have done this.
c. Create an APA style table that presents descriptive statistics for the sample. Need Help!
2. Factorial ANOVA. Perform a factorial ANOVA using the "Activity 5a.sav" data set.
a. Is there a main effect of gender? If so, explain the effect. Use post hoc tests when necessary (or explain why they are not required in this specific case).
b. Is there a main effect of classroom size? If so, explain the effect. Use post hoc tests when necessary (or explain why they are not required in this specific case).
c. Is there an interaction between your two variables? If so, using post hoc tests, describe these differences.
d. Is there support for the researcher's hypothesis that girls would do better than boys in classrooms with fewer students? Explain your answer.
e. Write up the results in APA style and interpret them. Be sure that you discuss both main effects and the presence/absence of an interaction between the two.
I will send you the dataset to see if I am correct.
a. Univariate Analysis of Variance
Between-Subjects Factors
Value Label N
Gender F Female 30
M Male 30
Classroom size 1 10 or less 20
2 11-19 20
3 20 or more 20

Descriptive Statistics
Dependent Variable: Math_Score
Gender Classroom size Statistic Bootstrapa
Bias Std. Error 95% Confidence Interval
Lower Upper
Female 10 or less Mean 93.8000 -.0387 1.2656 91.1269 96.2222
Std. Deviation 3.93841 -.26167 .58828 2.21756 4.67600
N 10 0 3 5 16
11-19 Mean 88.5000 -.0533 1.2674 85.8008 90.7994
Std. Deviation 3.97911 -.26788 .76830 2.08267 5.05513
N 10 0 3 5 16
20 or more Mean 79.2000 .0087 1.3152 76.5000 81.7114
Std. Deviation 4.18463 -.29105 .86490 2.13735 5.45372
N 10 0 3 5 16
Total Mean 87.1667 -.1038 1.3071 84.2823 89.6118
Std. Deviation 7.26865 -.15522 .73886 5.66778 8.66478
N 30 0 4 22 37
Male 10 or less Mean 92.7000 -.0081 1.0338 90.7513 94.7496
Std. Deviation 3.43350 -.25288 .73675 1.66823 4.58248
N 10 0 3 5 17
11-19 Mean 89.7000 -.0045 .7466 88.2222 91.1992
Std. Deviation 2.40601 -.16643b .40852b 1.30384b 2.96808b
N 10 0 3 5 16
20 or more Mean 91.2000 -.0284 .9791 89.3636 93.3750
Std. Deviation 3.22490 -.27323 .77314 1.41421 4.42708
N 10 0 3 5 16
Total Mean 91.2000 -.0068 .5777 89.9722 92.3782
Std. Deviation 3.19914 -.08720 .40556 2.29237 3.93418
N 30 0 4 23 38
Total 10 or less Mean 93.2500 -.0418 .7928 91.6667 94.7497
Std. Deviation 3.64005 -.12772 .39691 2.70859 4.28900
N 20 0 4 13 27
11-19 Mean 89.1000 -.0287 .7233 87.6119 90.5000
Std. Deviation 3.25900 -.10581 .47500 2.19814 4.04429
N 20 0 4 13 27
20 or more Mean 85.2000 -.0501 1.5271 82.1255 88.0619
Std. Deviation 7.14953 -.23091 .83113 5.27188 8.42616
N 20 0 4 13 27
Total Mean 89.1833 -.0404 .7395 87.6179 90.6000
Std. Deviation 5.92750 -.07552 .60066 4.71454 7.00723
N 60 0 0 60 60
a. Unless otherwise noted, bootstrap results are based on 1000 bootstrap samples
b. Based on 999 samples

Levene's Test of Equality of Error Variancesa
Dependent Variable: Math_Score
F df1 df2 Sig.
.822 5 54 .539
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
a. Design: Intercept + Gender + Classroom + Gender * Classroom

Tests of Between-Subjects Effects
Dependent Variable: Math_Score
Source Type II Sum of Squares df Mean Square F Sig. Partial Eta Squared Noncent. Parameter Observed Powerb
Corrected Model 1381.483a 5 276.297 21.576 .000 .666 107.882 1.000
Intercept 477220.017 1 477220.017 37266.639 .000 .999 37266.639 1.000
Gender 244.017 1 244.017 19.056 .000 .261 19.056 .990
Classroom 648.233 2 324.117 25.311 .000 .484 50.621 1.000
Gender * Classroom 489.233 2 244.617 19.102 .000 .414 38.205 1.000
Error 691.500 54 12.806
Total 479293.000 60
Corrected Total 2072.983 59
a. R Squared = .666 (Adjusted R Squared = .636)
b. Computed using alpha = .05

Estimated Marginal Means

1. Gender
Dependent Variable: Math_Score
Gender Mean Std. Error 95% Confidence Interval Bootstrap for Meana
Lower Bound Upper Bound Bias Std. Error 95% Confidence Interval
Lower Upper
Female 87.167 .653 85.857 88.477 -.028 .734 85.641 88.530
Male 91.200 .653 89.890 92.510 -.014 .549 90.034 92.291
a. Unless otherwise noted, bootstrap results are based on 1000 bootstrap samples

2. Gender * Classroom size
Dependent Variable: Math_Score
Gender Classroom size Mean Std. Error 95% Confidence Interval Bootstrap for Meana
Lower Bound Upper Bound Bias Std. Error 95% Confidence Interval
Lower Upper
Female 10 or less 93.800 1.132 91.531 96.069 -.039 1.266 91.127 96.222
11-19 88.500 1.132 86.231 90.769 -.053 1.267 85.801 90.799
20 or more 79.200 1.132 76.931 81.469 .009 1.315 76.500 81.711
Male 10 or less 92.700 1.132 90.431 94.969 -.008 1.034 90.751 94.750
11-19 89.700 1.132 87.431 91.969 -.005 .747 88.222 91.199
20 or more 91.200 1.132 88.931 93.469 -.028 .979 89.364 93.375
a. Unless otherwise noted, bootstrap results are based on 1000 bootstrap samples

3. Classroom size
Dependent Variable: Math_Score
Classroom size Mean Std. Error 95% Confidence Interval Bootstrap for Meana
Lower Bound Upper Bound Bias Std. Error 95% Confidence Interval
Lower Upper
10 or less 93.250 .800 91.646 94.854 -.023 .810 91.644 94.818
11-19 89.100 .800 87.496 90.704 -.029 .739 87.550 90.536
20 or more 85.200 .800 83.596 86.804 -.010 .832 83.570 86.721
a. Unless otherwise noted, bootstrap results are based on 1000 bootstrap samples

Post Hoc Tests

Classroom size
Multiple Comparisons
Dependent Variable: Math_Score
Scheffe
(I) Classroom size (J) Classroom size Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
10 or less 11-19 4.1500* 1.13162 .002 1.3015 6.9985
20 or more 8.0500* 1.13162 .000 5.2015 10.8985
11-19 10 or less -4.1500* 1.13162 .002 -6.9985 -1.3015
20 or more 3.9000* 1.13162 .005 1.0515 6.7485
20 or more 10 or less -8.0500* 1.13162 .000 -10.8985 -5.2015
11-19 -3.9000* 1.13162 .005 -6.7485 -1.0515
Based on observed means.
The error term is Mean Square(Error) = 12.558.
*. The mean difference is significant at the .05 level.

Bootstrap for Multiple Comparisons
Dependent Variable: Math_Score
Scheffe
(I) Classroom size (J) Classroom size Mean Difference (I-J) Bootstrapa
Bias Std. Error 95% Confidence Interval
Lower Upper
10 or less 11-19 4.1500 -.0131 1.0950 2.0319 6.4051
20 or more 8.0500 .0083 1.7181 4.7251 11.4385
11-19 10 or less -4.1500 .0131 1.0950 -6.4051 -2.0319
20 or more 3.9000 .0213 1.6625 .6087 7.0823
20 or more 10 or less -8.0500 -.0083 1.7181 -11.4385 -4.7251
11-19 -3.9000 -.0213 1.6625 -7.0823 -.6087
a. Unless otherwise noted, bootstrap results are based on 1000 bootstrap samples

Homogeneous Subsets
Math_Score
Scheffea,b
Classroom size N Subset
1 2 3
20 or more 20 85.2000
11-19 20 89.1000
10 or less 20 93.2500
Sig. 1.000 1.000 1.000
Means for groups in homogeneous subsets are displayed.
Based on observed means.
The error term is Mean Square(Error) = 12.806.
a. Uses Harmonic Mean Sample Size = 20.000.
b. Alpha = .05.

Univariate Analysis of Varianc

Between-Subjects Factors
Value Label N
Gender F Female 30
M Male 30
Classroom size 1 10 or less 20
2 11-19 20
3 20 or more 20

Descriptive Statistics
Dependent Variable: Math_Score
Gender Classroom size Mean Std. Deviation N
Female 10 or less 93.8000 3.93841 10
11-19 88.5000 3.97911 10
20 or more 79.2000 4.18463 10
Total 87.1667 7.26865 30
Male 10 or less 92.7000 3.43350 10
11-19 89.7000 2.40601 10
20 or more 91.2000 3.22490 10
Total 91.2000 3.19914 30
Total 10 or less 93.2500 3.64005 20
11-19 89.1000 3.25900 20
20 or more 85.2000 7.14953 20
Total 89.1833 5.92750 60

Levene's Test of Equality of Error Variancesa
Dependent Variable: Math_Score
F df1 df2 Sig.
.822 5 54 .539
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
a. Design: Intercept + Gender + Classroom + Gender * Classroom

Tests of Between-Subjects Effects
Dependent Variable: Math_Score
Source Type II Sum of Squares df Mean Square F Sig. Partial Eta Squared Noncent. Parameter Observed Powerb
Corrected Model 1381.483a 5 276.297 21.576 .000 .666 107.882 1.000
Intercept 477220.017 1 477220.017 37266.639 .000 .999 37266.639 1.000
Gender 244.017 1 244.017 19.056 .000 .261 19.056 .990
Classroom 648.233 2 324.117 25.311 .000 .484 50.621 1.000
Gender * Classroom 489.233 2 244.617 19.102 .000 .414 38.205 1.000
Error 691.500 54 12.806
Total 479293.000 60
Corrected Total 2072.983 59
a. R Squared = .666 (Adjusted R Squared = .636)
b. Computed using alpha = .05

Estimated Marginal Means
1. Gender
Dependent Variable: Math_Score
Gender Mean Std. Error 95% Confidence Interval
Lower Bound Upper Bound
Female 87.167 .653 85.857 88.477
Male 91.200 .653 89.890 92.510

2. Gender * Classroom size
Dependent Variable: Math_Score
Gender Classroom size Mean Std. Error 95% Confidence Interval
Lower Bound Upper Bound
Female 10 or less 93.800 1.132 91.531 96.069
11-19 88.500 1.132 86.231 90.769
20 or more 79.200 1.132 76.931 81.469
Male 10 or less 92.700 1.132 90.431 94.969
11-19 89.700 1.132 87.431 91.969
20 or more 91.200 1.132 88.931 93.469

3. Classroom size
Dependent Variable: Math_Score
Classroom size Mean Std. Error 95% Confidence Interval
Lower Bound Upper Bound
10 or less 93.250 .800 91.646 94.854
11-19 89.100 .800 87.496 90.704
20 or more 85.200 .800 83.596 86.804

Post Hoc Tests
Classroom size
Multiple Comparisons
Dependent Variable: Math_Score
Scheffe
(I) Classroom size (J) Classroom size Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
10 or less 11-19 4.1500* 1.13162 .002 1.3015 6.9985
20 or more 8.0500* 1.13162 .000 5.2015 10.8985
11-19 10 or less -4.1500* 1.13162 .002 -6.9985 -1.3015
20 or more 3.9000* 1.13162 .005 1.0515 6.7485
20 or more 10 or less -8.0500* 1.13162 .000 -10.8985 -5.2015
11-19 -3.9000* 1.13162 .005 -6.7485 -1.0515
Based on observed means.
The error term is Mean Square(Error) = 12.806.
*. The mean difference is significant at the .05 level.
Homogeneous Subsets
Math_Score
Scheffea,b
Classroom size N Subset
1 2 3
20 or more 20 85.2000
11-19 20 89.1000
10 or less 20 93.2500
Sig. 1.000 1.000 1.000
Means for groups in homogeneous subsets are displayed.
Based on observed means.
The error term is Mean Square(Error) = 12.806.
a. Uses Harmonic Mean Sample Size = 20.000.
b. Alpha = .05.