bstat 5325_group 8_project report

BSTAT 5325 Advanced Statistical Methods Fall 2016

Effect of Action Video Games on Math

Performance

Group 8 Project Report

Team Members

Anish Grandhi

Manikandan Sundarapandian

Sathya Narayanan Manivannan

Smruti Chandan Chhatwani

Table of Contents 1. Project Abstract ............................................................................................................................... 1

2. Project Motivation .......................................................................................................................... 1

3. Questions of Interest ....................................................................................................................... 1

4. Dataset Details ................................................................................................................................ 1

5. Statistical Methods: ......................................................................................................................... 3

6. Statistical Analysis, Results, and Interpretation .............................................................................. 4

i. Definitions, Notations, and Assumptions ................................................................................... 4

ii. Details of the Analysis and Interpretations ................................................................................. 5

iii. Diagnostics Checks ................................................................................................................... 19

7. Criticisms and Possible Extensions ............................................................................................... 20

8. Conclusions ................................................................................................................................... 20

9. Appendix ....................................................................................................................................... 22

1

1. Project Abstract The aim of our project is to conduct an experimental study on a dataset containing 30

observations. The dataset includes pre-test and post-test performance of students from different

majors. By default, students are made to play non-action video game before pre-test. Each

student is made to write a math test which includes Geometry, Word, and Non-word problems.

Their anxiety levels, confidence level, and speed for doing the calculations are all measured

(Pre-test scores). The students are made to play an action video game after which they are made

to take the math test where the performance is measured again (Post-test scores). Statistical

analysis is performed on the data obtained and conclusions are made.

2. Project Motivation Curiosity is the main driving factor for this project. Two main points of interest that

caught out attention - Does playing an action game before an exam affect the score and if

gender plays a role too. A lot of research had showed that playing a video game indeed does

improve the scores of examinations and Pilots drove better after they were subjected to an

action video game. We wanted to prove this by conducting statistical analysis on a group of

students and checking their math scores. And, if gender had any role or not.

3. Questions of Interest Is there a change in overall performance of the students after playing an AVG (Action

Video Game) and a Non-AVG (Non-Action Video game)?

Does ‘Gender’ attribute play a role in affecting the overall performance?

4. Dataset Details Dataset has been obtained from the website -

https://figshare.com/articles/BJET_Data_Entry/1167496

The number of variables in the dataset are 31.

The number of observations in the dataset- 30 Observations

Student Number - A unique number was assigned to each student

Group - Action Video Game (AVG) versus non-Action Video Game (non-AVG)

group

Gender - Female/Male

https://figshare.com/articles/BJET_Data_Entry/1167496

2

Description of the variables –

Attributes Description Values

Student Number Student ID No Numeric Value

Group Type of Game the

students played

AVG- Action Video

Game

Non- AVG- Non-

Action Video Game

Gender Student Gender Male and Female

Working Memory Assessment- Pre-Test Measures

WM_AbsoluteOSPAN_Pretest Pretest OSPAN score

WM_TotalCorrect_Pretest Pretest Total number of correct answers

WM_MathErrors_Pretest Pretest Number of Math errors

WM_MathSpeedErrors_Pretest Pretest Math Speed Errors

WM_MathAccuracyErrors_Pretest Pretest Accuracy Errors

Working Memory Post-test Measures:

WM_AbsoluteOSPAN_Posttest Posttest OSPAN score

WM_TotalCorrect_Posttest Post Total number of correct answers

WM_MathErrors_Posttest Posttest Number of Math errors

WM_MathSpeedErrors_Posttest Posttest Math Speed Errors

WM_MathAccuracyErrors_Posttest Posttest Accuracy Errors

Mathematics Anxiety and Confidence in Learning Mathematics

Pretest Measures (1-min; 5-max):

Confidence_Pre Pretest Confidence Measure

Anxiety_Pre Pretest Anxiety Measure

Post-test Measures (1-min; 5-max):

Confidence_Post Posttest Confidence Measure

Anxiety_Post Posttest Anxiety Measure

Mathematics Assessment

The mathematics performance test included geometry, word, and non-word

problems sections.

Pretest Measures:

Math_Geometry_Pre Geometry score in % correct

Math_Word_Pre Mathematics word problems score in % correct

Math_NonWord_Pre Math non-word problems score in % correct

Math_Total_Pre Total score on mathematics test in % correct

TimePre Time spent on mathematics test (in min)

Post-test Measures:

Math_Geometry_Post Geometry score in % correct

Math_Word_Post Mathematics word problems score in % correct

Math_NonWord_Post Math non-word problems score in % correct

Math_Total_Post Total score on mathematics test in % correct

TimePost Time spent on mathematics test (in min)

Perceived Cognitive Load (1-min; 9-max)

CogLoadPre Pretest cognitive load

CogLoadPost Post-test cognitive load

Mental Rotation Test (MRT)

3

MRT_Pre Pretest MRT score

MRT_Post Post-test MRT score

Each record contains pre-test and post test scores relative to the game played.

5. Statistical Methods: a) Is there a change in overall performance of the students after playing an AVG (Action

Video Game)?

For this experiment, we considered:

One dependent variable that is continuous – Math_Total_Post

1 independent variable with two categories – Group (Non Action Video Game,

Action Video Game)

To answer the question of interest, we need determine whether action video gamers and

non-action video gamers perform equally in the final math exam. This allows us to

check whether there is a change in overall performance of the students after playing the

action video game. So, we chose to perform ANOVA (Analysis of Variance) method

between independent and dependent variables.

b) Does ‘Gender’ attribute play a role in affecting the overall performance?

For this experiment, we considered:

One Independent Variable with 2 categories. (male, female)

One dependent variable that is continuous – Math_Total_Post

To determine whether gender attribute has any effect on the overall performance of

mathematics test, we performed ANOVA method on the dependent and independent

variables. To check whether there was a linear dependency, linear regression with

gender as independent variable and Total Math Score (Post) as dependent variable.

4

6. Statistical Analysis, Results, and Interpretation

i. Definitions, Notations, and Assumptions

a) ANOVA definition – Analysis of variance, a statistical method in which the

variation in a set of observations is divided into distinct components.

b) Linear Regression definition – In statistics, linear regression is an approach for

modelling the relationship between a scalar dependent variable y and one or more

explanatory variables (or independent variables) denoted X. The case of one

explanatory variable (independent variable) is called simple linear regression.

c) F-Statistic definition –An F statistic is a value you get when you run an ANOVA

test or a regression analysis to find out if the means between two populations are

significantly different.

d) Parameters measured and their notations –

SST - Sum of Squares Treatment

SSE - Sum of Squares Error

SS (Total) – Sum of Squares Total

B0 - y intercept

B1 - Coefficient of Independent Variable

ŷ – Predicted Value

k – Number of Categories of Independent Variable

N – Number of Observations

MST – Mean Square of Treatment

MSE – Mean Square of Error

e) Assumptions of ANOVA -

1 dependent variable that is continuous

1 independent variable with two or more categories

Independent of observations

No significant outliers

Normally distributed data

Homoscedasticity

f) Assumptions of Linear Regression –

Linear relationship exists between DV and IV

Independence of observations

The residuals (errors) of the regression line are approximately Normally

distributed

Equal Variances (homoscedasticity) – Variances along line of best fit

remains similar as move along line.

No significant outliers

5

ii. Details of the Analysis and Interpretations

a. Analysis for Question of Interest 1 (Is there a change in overall performance of the

students after playing an Action Video Game?)

We conducted Analysis of Variance method to check for this question.

We had 12 persons who played action video game and 18 persons who played non-

action video game in our dataset. Figure 1 gives a report about the observations.

Figure 1

Important Note – Non AVG group is transformed to 1 and AVG group to 0 for

calculation purposes.

Test for outliers: To check for outliers, we used the following options to create a

box plot for our dependent variable.

Analyze Descriptive Statistics Explore (give dependent variable)

Statistics (check Outliers)

Figure 2

Figure 2 shows the box plot output in SPSS. No points lie outside the box plot.

We can interpret that there are no outliers.

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Figure 3

Figure 3 shows the extreme values on the higher and lower side.

Test for normality:

Option used in SPSS:

Analyze Descriptive Statistics Explore (give dependent variable) Plots

(Histogram, Normality plot with tests)

Figure 4

Figure 4 shows that Shapiro Wilk’s test has significance value 0.030 which is less

than 0.05. This means that the dependent variable is normally distributed.

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Figure 5

Figure 5 shows a normally distributed histogram of the dependent variable.

Test for equal variance (Homoscedasticity):

We considered the Null Hypothesis(H0) as group means are equal and the

alternative hypothesis(H1) as the group means differ from each other.

H0 = Group means are equal

H1 = Group means differ from each other


Analyze Compare means One way ANOVA Options (Homogeneity of

variance test)

Figure 6

The output of the Homogeneity of variances test is shown in Figure 6. Since Sig

value we got is greater than 0.05, we reject H0 and conclude that there is a

difference in group means.

8

ANOVA results:

Between groups – Treatment

Within groups – Error

SST 3274.175

SSE 12539.42

SS Total 15813.59

k 2

N 30

MST 3274.175

MSE 447.836

F Stat 7.311

P value 0.012

Figure 7

Figure 7 shows that the significance is less than 0.05. This means that the F-

statistic is significant. This proves that the type of game played has effect on

Math_Total_Post (the total post score of math exam).

To find the value of contrast between the two groups (AVG group and Non-AVG

group):


Analyze Compare means One way ANOVA (Contrasts).

The contrast coefficient is the weightage given to each group. ‘Coefficient total’

should always be zero.

9

Figure 8

Figure 8 shows the values of the coefficients. They should add up to the value

zero.

From Figure 9, the values from ‘Does not assume equal variance’ are considered

for analysis as our experiment failed in Levene’s test of equal variance. The value

of significance is 0.017 which is less than 0.05 and so we can conclude that the

results are significant.

The value of contrast between two groups is found to be 21.324.

To determine the size of the difference (Effect size):


Analyze Compare means Options ANOVA table and ETA

Figure 10

Figure 10 shows the magnitude of the difference in means is given by the Eta

Squared value. Eta Squared value is found to be 0.207.

Figure 9

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b. Analysis and Interpretation for Question of Interest 2 (Does ‘Gender’ attribute play

a role in affecting the overall performance?).

We conducted Analysis of Variance to check for this question.

Our dataset contains 14 males and 16 females.

Figure 11

Important Note – Values of males are transformed as 1 and females as 0 for


Test for outliers: To check for outliers, we used the following options to create a

box plot for our dependent variable -

Analyze Descriptive Statistics Explore (give dependent variable)

Statistics (check Outliers)

Figure 12

Figure 12 shows the box plot output in SPSS. No points lie outside the box

plot. We can interpret that there are no outliers

11

Test for normality:

To check for normality, we performed Shapiro Wilk’s test.


Analyze Descriptive Statistics Explore (give dependent variable) Plots

(Histogram, Normality plot with tests)

Figure 13

Figure 13 shows that the significance value is less than 0.05. This means that the

dependent variable is normally distributed

Test for equal variance (Homoscedasticity):

To check for homogeneity of variances, we performed Levene’s test.

We considered null hypothesis(H0) and alternate hypothesis(H1) as -

H0 = Group means are equal

H1 = Group means differ from each other


Analyze Compare means One way ANOVA Options (Homogeneity of

variance test)

Figure 14

Figure 14 shows that significance value is greater than 0.05, we reject H0 and

conclude that there is a difference in group means.

ANOVA Test

The ANOVA test helps us determine if there is a difference between the mean total

math scores that males and females have received.

12

Figure 15

Figure 15 shows us that the significance value is less than 0.05. This means that

the F statistic is significant. We concluded that gender has a role in determining

the final math score.

Since we failed Levene’s test, we went ahead and performed Custom Contrasts

test.

To find the value of contrast between the two genders (AVG and Non-AVG):


Analyze Compare means One way ANOVA (Contrasts).

The contrast coefficient is the weightage given to each group. ‘Coefficient total’

should always be zero.

The value of contrast is 39.05.

Figure 16

Figure 17

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To determine the size of the difference (Effect size):


Analyze Compare means Options ANOVA table and ETA

Figure 19

The magnitude of the difference in means is given by the Eta Squared value.

Figure 19 shows that the Eta Squared value to be 0.207

c. Linear Regression on Question of Interest 2 (Does ‘Gender’ attribute play a role

in affecting the overall performance?)

We conducted Linear Regression to check if there was a dependency between

gender and the final math score.

The scatter plot shows that the first assumption was violated and there exists no

linear relationship between gender and Math_Total_Post


Graphs Chart builder Scatter/Dot (Choose dependent and independent

variables)

Figure 20 shows that a scatterplot between gender and Math_Total_Post scores.

Figure 18

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Figure 20

We have tried different transformations and none of them revealed any linear

dependency.

Figure 21

Figure 21 shows the graph between transformed log value of Math Total Post

score and gender. Observation shows that there is no linear dependency between

the two.

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Figure 22

Figure 22 is a plot between log value of gender vs log value of Math Total Post

score. There is no linear dependency between the two variables.

Figure 23

Figure 23 shows a plot between reciprocal value of Math Total Post score and

gender. There is no linear dependency between the variables.

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Figure 24

Figure 24 shows a plot between square root of Math Total Post scores and gender

variable. Once again, there is no linear dependency between two variables.

Figure 25

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Figure 25 shows a plot between log value of gender and log value of Math Total

Post score. SPSS took only one value on the X axis and plotted the scatterplot.

To check for normality in residuals, we plotted a scatterplot between residual and

predicted value of the dependent variable. Figure 26 below is the residual plot.

We can see that the residuals are scattered around.


Analyze Regression Plots (ZPRED on x axis, ZRESID on y axis, check Histogram)

Figure 26

Figure 27 is a histogram which shows that the residuals are normally distributed.

Figure 27

18

To check for Auto correlation and Linear Regression Analysis


Analyze Regression Linear (Check R squared change, part and partial

correlations, confidence intervals - 95%, Durbin Watson, Casewise Diagnostics)

The Durbin-Watson statistic which is used to check for autocorrelation in the

residuals from a regression analysis gave us 1.856. Since this value is less than 2,

we can conclude that there is a strong serial correlation.

R value is 0.849 which is the correlation coefficient. This value shows that there

is a high correlation between gender and final math score.

R2 value 0.72 which is the coefficient of determination. So gender accounted for

72 % of variation in Math total score.

The ANOVA table showed us that the significance value is less than 0.05. This

proves that the F statistic is significant and gender significantly predicts the total

math score.

The linear model is ŷ = 30.721 + 39.059 x + e where ‘e’ denotes error from

other factors.

Figure 28

Figure 30

Figure 29

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The slope of the regression line is 39.05 which says that when there is a change

in gender, the average change in final math score is 39.059

So, to find the estimated final math score for male and female, we substitute x

= 1 and x = 0 in the above equation respectively (on the assumption that error

value is equal to 0).

The estimated math total final score for male is 69.78. The estimated math total

final score for female is 30.721.

iii. Diagnostics Checks

a. All ANOVA assumptions were plausible. The checks that we have performed for

each assumption are-

1 dependent variable that is continuous – Math_Total_Post is a continuous

variable.

1 independent variable with two or more categories – Independent variable

Group has 2 values - Non-Action Video Game (Non AVG), Action Video

Game (AVG). We transformed Non AVG as 1 and AVG as 0 for


Independent of observations – All the observations in the dataset were

carried out separately and are independent. Every student performed the

experiment alone without any interference.

No significant outliers – Box plot was used to check for outliers Normally

distributed data – Shapiro Wilk’s test was used to check if the dataset is

normally distributed.

Homoscedasticity – Levene’s test was performed to check for equal

variances.

b. All Linear Regression assumptions were plausible. The checks that we performed

for each assumption are-

Transformations - We transformed male as 1 and females as 0 for


Linear relationship exists between DV and IV – Scatterplot was created to

check if there was any linear relationship between dependent and

independent variables. Though this assumption failed, we wanted to

check what if there would have been a linear relationship between gender

and final math score.

Independence of observations – All the observations in the dataset were

carried out separately and are independent. Every student performed the

experiment alone without any interference.

The residuals (errors) of the regression line are approximately Normally

distributed – The residuals plot was drawn to check if regression line is

approximately Normally distributed.

Equal Variances (homoscedasticity) - Durbin-Watson value was

determined to check for equal variances along the line of best fit. No significant outliers – Box plot was used to check for outliers Normally

distributed data.

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7. Criticisms and Possible Extensions

i. For Question of Interest 1 (Is there a change in overall performance of the students

after playing an AVG (Action Video Game)?)

Our experiment was to find whether action video gamers and non-action video gamers

had a difference in performance in their math final score. Our conclusion is that there

was a difference and group attribute affects math final score. Our conclusion is

subjected for these 30 observations. Thus, we cannot generalize the conclusion for

gamers. A generalized conclusion requires a lot more observations.

ii. For Question of Interest 2 (Does ‘Gender’ attribute play a role in affecting the overall

performance?)

Our experiment concludes that the final math score depends on gender and females in

our dataset scored comparatively less than males. To defend against such an allegation,

we would explain that these results are for these 30 observations. We cannot generalize

the results of our experiment and end up in a biased conclusion. Our dataset had only

30 samples which cannot be applied on a large scale. And, there are a lot more factors

which might affect the final math score like IQ, memory test score etc.

We proceeded with Simple Linear Regression under the assumption that there is a linear

relationship between dependent variable (Math final score) and independent variable

(Gender). So, based on that assumption, we proceeded with rest of the tests. The scatter

plots did not show any linear relationship between gender and final math score. The

main motive for us was to try out the whole experiment with the curiosity that 'what

would have happened if gender played a role?'

8. Conclusions The conclusions we that we have come to for each question of interest –

Question of Interest 1 - Is there a change in overall performance of the students after

playing an AVG (Action Video Game)?

Conclusion – We performed ANOVA analysis for this question. The significance is

less than 0.05. So, F statistic (7.311) is significant. This proves that the type of game

played has effect on Math Total Post score.

Question of Interest 2 - Is ‘Gender’ attribute play a role in affecting the overall

performance?

Conclusion – Firstly, we performed ANOVA test to determine if there is a difference

between the mean total math scores that males and females have received.

The significance value is less than 0.05 and the F statistic (72.123) is significant. We

conclude that gender has role in determining the Math Total Post score.

Secondly, we wanted to check if there exists a linear dependency between the math

total post scores and gender. We failed one of the assumptions (Linear relationship

exists between math total post scores and gender). Out of curiosity, we wanted to check

what would be the result if there was a linear dependency.

The linear model that we got is ŷ = 30.721 + 39.059 x + e.

21

The estimated math total final score for male is 69.78. The estimated math total final

score for female is 30.721.

We cannot generalize the results of our experiment and end up in a biased conclusion.

Our dataset had only 30 samples which cannot be applied on a large scale. And, there

are a lot more factors which might affect the final math score like IQ, memory test score

etc.

22

9. Appendix

The results obtained from SPSS for section –

ONEWAY Math_Total_Post BY Gender

/CONTRAST=-1 1

/STATISTICS DESCRIPTIVES HOMOGENEITY WELCH

/MISSING ANALYSIS.

Oneway

Notes

Output Created 26-NOV-2016 13:15:33

Comments

Input Active Dataset DataSet1

Filter <none>

Weight <none>

Split File <none>

N of Rows in Working Data

File

30

Missing Value Handling Definition of Missing User-defined missing values are

treated as missing.

Cases Used Statistics for each analysis are

based on cases with no missing

data for any variable in the

analysis.

Syntax ONEWAY Math_Total_Post

BY Gender

/CONTRAST=-1 1

/STATISTICS

DESCRIPTIVES

HOMOGENEITY WELCH

/MISSING ANALYSIS.

Resources Processor Time 00:00:00.00

Elapsed Time 00:00:00.06

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Descriptives

Math_Total_Post

N Mean Std. Deviation Std. Error

95% Confidence Interval for Mean

Lower Bound Upper Bound

0 16 30.72115385000 13.588685250000 3.397171313000 23.48025460000 37.96205310000

1 14 69.78021978000 11.274812610000 3.013320420000 63.27033679000 76.29010277000

Total 30 48.94871795000 23.351578060000 4.263395353000 40.22909540000 57.66834050000

Descriptives

Math_Total_Post

Minimum Maximum

0 7.692307692 53.846153850

1 38.461538460 80.769230770

Total 7.692307692 80.769230770

Test of Homogeneity of Variances

Math_Total_Post

Levene Statistic df1 df2 Sig.

1.518 1 28 .228

ANOVA

Math_Total_Post

Sum of Squares df Mean Square F Sig.

Between Groups 11391.226 1 11391.226 72.123 .000

Within Groups 4422.364 28 157.942

Total 15813.590 29

24

Math_Total_Post

Statistica df1 df2 Sig.

Welch 73.984 1 27.936 .000

a. Asymptotically F distributed.

Contrast Coefficients

Contrast

Gender

0 1

1 -1 1

Contrast Tests

Contrast Value of Contrast Std. Error t

Math_Total_Post Assume equal variances 1 39.05906593000 4.599226845000 8.493

Does not assume equal

variances

1 39.05906593000 4.541021128000 8.601

Contrast Tests

Contrast df Sig. (2-tailed)

Math_Total_Post Assume equal variances 1 28 .000

Does not assume equal variances 1 27.936 .000

MEANS TABLES=Math_Total_Post BY Gender

/CELLS=MEAN COUNT STDDEV

/STATISTICS ANOVA.

Means

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File

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Missing Value Handling Definition of Missing For each dependent variable in a

table, user-defined missing

values for the dependent and all

grouping variables are treated as

missing.

Cases Used Cases used for each table have

no missing values in any

independent variable, and not all

dependent variables have

missing values.

Syntax MEANS

TABLES=Math_Total_Post BY

Gender

/CELLS=MEAN COUNT

STDDEV

/STATISTICS ANOVA.



Case Processing Summary

Cases

Included Excluded Total

N Percent N Percent N Percent

Math_Total_Post * Gender 30 100.0% 0 0.0% 30 100.0%

26

Report

Math_Total_Post

Gender Mean N Std. Deviation

0 30.72115385000 16 13.588685250000

1 69.78021978000 14 11.274812610000

Total 48.94871795000 30 23.351578060000

ANOVA Table

Sum of Squares df Mean Square

Math_Total_Post * Gender Between Groups (Combined) 11391.226 1 11391.226

Within Groups 4422.364 28 157.942

Total 15813.590 29

ANOVA Table

F Sig.

Math_Total_Post * Gender Between Groups (Combined) 72.123 .000

Within Groups

Total

Measures of Association

Eta Eta Squared

Math_Total_Post * Gender .849 .720

EXAMINE VARIABLES=Math_Total_Post

/PLOT BOXPLOT HISTOGRAM NPPLOT

/COMPARE GROUPS

/STATISTICS DESCRIPTIVES EXTREME

/CINTERVAL 95

/MISSING LISTWISE

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/NOTOTAL.

Explore

Notes


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30

Missing Value Handling Definition of Missing User-defined missing values for

dependent variables are treated

as missing.

Cases Used Statistics are based on cases with

no missing values for any

dependent variable or factor

used.

Syntax EXAMINE

VARIABLES=Math_Total_Post

/PLOT BOXPLOT

HISTOGRAM NPPLOT

/COMPARE GROUPS

/STATISTICS

DESCRIPTIVES EXTREME

/CINTERVAL 95

/MISSING LISTWISE

/NOTOTAL.



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Case Processing Summary

Cases

Valid Missing Total

N Percent N Percent N Percent

Math_Total_Post 30 100.0% 0 0.0% 30 100.0%

Descriptives

Statistic Std. Error

Math_Total_Post Mean 48.94871795000 4.263395353000

95% Confidence Interval for

Mean

Lower Bound 40.22909540000

Upper Bound 57.66834050000

5% Trimmed Mean 49.40170940000

Median 44.23076923000

Variance 545.296

Std. Deviation 23.351578060000

Minimum 7.692307692

Maximum 80.769230770

Range 73.076923080

Interquartile Range 36.538461540

Skewness -.165 .427

Kurtosis -1.266 .833

Extreme Values

Case Number Value

Math_Total_Post Highest 1 5 80.769230770

2 26 80.769230770

3 6 76.923076920

4 10 76.923076920

5 17 76.923076920a

Lowest 1 4 7.692307692

29

2 15 11.538461540

3 2 11.538461540

4 28 18.461538460

5 14 19.230769230

a. Only a partial list of cases with the value 76.923076920 are shown in the table of

upper extremes.

Tests of Normality

Kolmogorov-Smirnova Shapiro-Wilk

Statistic df Sig. Statistic df Sig.

Math_Total_Post .174 30 .021 .922 30 .030

a. Lilliefors Significance Correction

Math_Total_Post

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GET DATA

/TYPE=XLS

/FILE='F:\MS 1st sem\BSTAT\Project\AVGnonAVGDataset_Test.xls'

/SHEET=name 'AVG without q7i Spring 2014 FIN'

/CELLRANGE=FULL

/READNAMES=ON

/DATATYPEMIN PERCENTAGE=95.0.

EXECUTE.

DATASET NAME DataSet1 WINDOW=FRONT.

* Chart Builder.

GGRAPH

/GRAPHDATASET NAME="graphdataset" VARIABLES=Gender Math_Total_Post

MISSING=LISTWISE

REPORTMISSING=NO

/GRAPHSPEC SOURCE=INLINE.

BEGIN GPL

SOURCE: s=userSource(id("graphdataset"))

32

DATA: Gender=col(source(s), name("Gender"), unit.category())

DATA: Math_Total_Post=col(source(s), name("Math_Total_Post"))

GUIDE: axis(dim(1), label("Gender"))

GUIDE: axis(dim(2), label("Math_Total_Post"))

SCALE: linear(dim(2), include(0))

ELEMENT: point(position(Gender*Math_Total_Post))

END GPL.

GGraph

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Syntax GGRAPH

/GRAPHDATASET

NAME="graphdataset"

VARIABLES=Gender

Math_Total_Post

MISSING=LISTWISE

REPORTMISSING=NO

/GRAPHSPEC

SOURCE=INLINE.

BEGIN GPL

SOURCE:

s=userSource(id("graphdataset")

)

DATA: Gender=col(source(s),

name("Gender"),

unit.category())

DATA:

Math_Total_Post=col(source(s),

name("Math_Total_Post"))

GUIDE: axis(dim(1),

label("Gender"))

GUIDE: axis(dim(2),

label("Math_Total_Post"))

SCALE: linear(dim(2),

include(0))

ELEMENT:

point(position(Gender*Math_To

tal_Post))

END GPL.



[DataSet1]

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Notes


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Filter <none>

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Syntax GGRAPH

/GRAPHDATASET

NAME="graphdataset"

VARIABLES=Gender

Log_Math_Total_Post

MISSING=LISTWISE

REPORTMISSING=NO

/GRAPHSPEC

SOURCE=INLINE.

BEGIN GPL

SOURCE:

s=userSource(id("graphdataset")

)

DATA: Gender=col(source(s),

name("Gender"),

unit.category())

DATA:

Log_Math_Total_Post=col(sour

ce(s),

name("Log_Math_Total_Post"))

GUIDE: axis(dim(1),

label("Gender"))

GUIDE: axis(dim(2),

label("Log_Math_Total_Post"))

SCALE: linear(dim(2),

include(0))

ELEMENT:

point(position(Gender*Log_Mat

h_Total_Post))

END GPL.



36

REGRESSION

/DESCRIPTIVES MEAN STDDEV CORR SIG N

/MISSING LISTWISE

/STATISTICS COEFF OUTS CI(95) BCOV R ANOVA COLLIN TOL CHANGE ZPP

/CRITERIA=PIN(.05) POUT(.10)

/NOORIGIN

/DEPENDENT Math_Total_Post

/METHOD=ENTER Gender

/SCATTERPLOT=(*ZRESID ,*ZPRED)

/RESIDUALS DURBIN HISTOGRAM(ZRESID) NORMPROB(ZRESID)

/CASEWISE PLOT(ZRESID) OUTLIERS(3).

Regression

Notes


Comments


Filter <none>

Weight <none>

Split File <none>


File

30

Missing Value Handling Definition of Missing User-defined missing values are

treated as missing.

Cases Used Statistics are based on cases with

no missing values for any

variable used.

37

Syntax REGRESSION

/DESCRIPTIVES MEAN

STDDEV CORR SIG N

/MISSING LISTWISE

/STATISTICS COEFF OUTS

CI(95) BCOV R ANOVA

COLLIN TOL CHANGE ZPP

/CRITERIA=PIN(.05)

POUT(.10)

/NOORIGIN

/DEPENDENT

Math_Total_Post

/METHOD=ENTER Gender

/SCATTERPLOT=(*ZRESID

,*ZPRED)

/RESIDUALS DURBIN

HISTOGRAM(ZRESID)

NORMPROB(ZRESID)

/CASEWISE PLOT(ZRESID)

OUTLIERS(3).



Memory Required 2928 bytes

Additional Memory Required

for Residual Plots

680 bytes

Descriptive Statistics

Mean Std. Deviation N

Math_Total_Post 48.94871795000 23.351578060000 30

Gender .47 .507 30

38

Correlations

Math_Total_Post Gender

Pearson Correlation Math_Total_Post 1.000 .849

Gender .849 1.000

Sig. (1-tailed) Math_Total_Post . .000

Gender .000 .

N Math_Total_Post 30 30

Gender 30 30

Variables Entered/Removeda

Model Variables Entered

Variables

Removed Method

1 Genderb . Enter

a. Dependent Variable: Math_Total_Post

b. All requested variables entered.

Model Summaryb

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

Change Statistics

R Square Change F Change df1

1 .849a .720 .710 12.567480280000 .720 72.123 1

Model Summaryb

Model

Change Statistics

df2 Sig. F Change

1 28 .000 1.856

a. Predictors: (Constant), Gender

b. Dependent Variable: Math_Total_Post

39

ANOVAa

Model Sum of Squares df Mean Square F Sig.

1 Regression 11391.226 1 11391.226 72.123 .000b

Residual 4422.364 28 157.942

Total 15813.590 29


b. Predictors: (Constant), Gender

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig. B Std. Error Beta

1 (Constant) 30.721 3.142 9.778 .000

Gender 39.059 4.599 .849 8.493 .000

Coefficientsa

Model

95.0% Confidence Interval for B Correlations

Collinearity

Statistics

Lower Bound Upper Bound Zero-order Partial Part Tolerance

1 (Constant) 24.285 37.157

Gender 29.638 48.480 .849 .849 .849 1.000

Coefficientsa

Model

Collinearity Statistics

VIF

1 (Constant)

Gender 1.000


40

Coefficient Correlationsa

Model Gender

1 Correlations Gender 1.000

Covariances Gender 21.153


Collinearity Diagnosticsa

Model Dimension Eigenvalue Condition Index

Variance Proportions

(Constant) Gender

1 1 1.683 1.000 .16 .16

2 .317 2.305 .84 .84


Residuals Statisticsa

Minimum Maximum Mean Std. Deviation N

Predicted Value 30.72115326000 69.78022003000 48.94871795000 19.819205290000 30

Residual -

31.318681720000

23.125000000000 .000000000000 12.348898730000 30

Std. Predicted Value -.920 1.051 .000 1.000 30

Std. Residual -2.492 1.840 .000 .983 30


41

Charts

bstat 5325_group 8_project report

Documents