Explore BrainMass

Explore BrainMass

    Conducting and analyzing data using descriptive statistics

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com June 4, 2020, 5:13 am ad1c9bdddf
    https://brainmass.com/statistics/type-i-and-type-ii-errors/conducting-analyzing-data-descriptive-statistics-607434

    Attachments

    Solution Summary

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

    $2.19

    ADVERTISEMENT