# Conducting and analyzing data using descriptive statistics

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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.

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##### Solution Summary

The solution gives detailed steps on conducting and analyzing data using descriptive statistics, ANOVA and ANCOVA respectively.

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