Statistics and Probability Homework: SPSS Analysis and Interpretation

This homework assignment presents a comprehensive analysis of statistical data using SPSS. The student addresses various problems, including regression analysis, ANOVA, and t-tests. Each section includes a description of the problem, the specific questions being answered, and the relevant SPSS outputs (tables, graphs). The student interprets the outputs, providing the relevant statistical values (F-values, R^2 values, etc.) to support their conclusions. The assignment covers hypothesis testing, identifying statistically significant differences between variables, and analyzing means. The student applies these techniques to different datasets, demonstrating a strong understanding of statistical concepts and their practical application using SPSS. The document adheres to APA formatting, including a title page, table of contents, page numbers, and an honesty statement.

SPSS

TABLE OF CONTENTS
12.2..................................................................................................................................................3
Regression....................................................................................................................................3
12.4..................................................................................................................................................6
A..................................................................................................................................................6
12.12................................................................................................................................................7
A. Implication of experimental technique to be used in analyzing the outcomes.......................7
B. Analyzing the means of variables...........................................................................................7
12.14................................................................................................................................................8
A. Identification of the treatment to be followed........................................................................8
12.22................................................................................................................................................8
SAS..............................................................................................................................................9
12.24..............................................................................................................................................11
12.26..............................................................................................................................................12
Regression..................................................................................................................................12
12.36..............................................................................................................................................14
Regression..................................................................................................................................14
REFERENCES..............................................................................................................................16

12.2
Regression
Hypothesis:
Null hypothesis (H0): There is no statistically significant difference in the mean values of
dependent variable round and independent variable power
Alternative hypothesis (H1): There is a statistically significant difference in the mean values of
dependent variable round and independent variable power
Variables Entered/Removeda
Model Variables
Entered
Variables
Removed
Method
1 POWERb . Enter
a. Dependent Variable: ROUND
b. All requested variables entered.
Model Summaryb
Model R R Square Adjusted R
Square
Std. Error of the
Estimate
Durbin-Watson
1 .234a .055 .023 1.123 .214
a. Predictors: (Constant), POWER
b. Dependent Variable: ROUND
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1
Regression 2.181 1 2.181 1.730 .198b
Residual 37.819 30 1.261
Total 40.000 31
a. Dependent Variable: ROUND
b. Predictors: (Constant), POWER
Coefficientsa

Model Unstandardized Coefficients Standardized
Coefficients
t Sig. Collinearity Statistics
B Std. Error Beta Tolerance VIF
1 (Constant) -2.137 3.531 -.605 .550
POWER .004 .003 .234 1.315 .198 1.000 1.000
a. Dependent Variable: ROUND
Collinearity Diagnosticsa
Model Dimension Eigenvalue Condition Index Variance Proportions
(Constant) POWER
1 1 1.998 1.000 .00 .00
2 .002 35.553 1.00 1.00
a. Dependent Variable: ROUND
Residuals Statisticsa
Minimum Maximum Mean Std. Deviation N
Predicted Value 1.76 2.95 2.50 .265 32
Residual -1.806 1.782 .000 1.105 32
Std. Predicted Value -2.795 1.697 .000 1.000 32
Std. Residual -1.608 1.588 .000 .984 32
a. Dependent Variable: ROUND

12.4
A.
Hypothesis
Null hypothesis (H0): There is no statistically significant difference in the mean values of
dependent variables (Overrun & score) and factor variable power
Alternative hypothesis (H1): There is a statistically significant difference in the mean values of
dependent variables (Overrun & score) and factor variable power

One way ANOVA
ANOVA
Sum of Squares df Mean Square F Sig.
OVERRUN
Between Groups 9669.958 23 420.433 . .
Within Groups .000 0 .
Total 9669.958 23
SCORE
Between Groups 1.171 28 .042 .365 .938
Within Groups .344 3 .115
Total 1.515 31
12.12
A. Implication of experimental technique to be used in analyzing the outcomes
T-test: To identify the statistical differences between group and score there will be
implication of t-test techniques which will bring the adequate outcomes. Moreover, in relation
with analyzing the independent T-test outcomes on which it can be said that there have been
implication of two or more variables which will be categories as per denoting them groups. Thus,
it will be helpful approach which in turn used for comparing the mean value of two independent
groups on which the statistical determination of the statistical evidences based on population
means are significantly different.
B. Analyzing the means of variables
T-test:
Group Statistics
GROUP N Mean Std. Deviation Std. Error Mean
SCORE 1 11 .4400 .17053 .05142
2 11 .2655 .15260 .04601

Independent Samples Test
Levene's Test for
Equality of
Variances
t-test for Equality of Means
F Sig. t df Sig. (2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower Upper
SCORE
Equal
variances
assumed
.020 .888 2.530 20 .020 .17455 .06900 .03062 .31847
Equal
variances not
assumed
2.530 19.758 .020 .17455 .06900 .03051 .31858
12.14
A. Identification of the treatment to be followed.
In relation with ascertaining the outcomes there have been use of various outcomes. In
relation with analyzing the outcomes as considering population there is needed to have adequate
determination of the facts (Annotated output, 2018). Thus, considering descriptive analysis, one
way ANOVAs and various techniques which will be helpful in determining outcomes.
12.22
One way ANOVA
Null hypothesis (H0): There is no statistically significant difference in the mean values of
dependent variable GROUP and other independent variable SOCRE.
Alternative hypothesis (H1): There is a statistically significant difference in the mean values of
variable GROUP and other independent variable SOCRE.
ANOVA
GROUP

Sum of Squares df Mean Square F Sig.
Between Groups 42.833 34 1.260 .932 .593
Within Groups 12.167 9 1.352
Total 55.000 43
SAS
Frequencies
Statistics
GROUP SCORE
N Valid 44 44
Missing 1 1
Mean 2.50 .2923
Std. Error of Mean .170 .03396
Median 2.50 .3150
Mode 1a .20a
Std. Deviation 1.131 .22528
Variance 1.279 .051
Skewness .000 -.834
Std. Error of Skewness .357 .357
Kurtosis -1.378 .590
Std. Error of Kurtosis .702 .702
Range 3 .97
Minimum 1 -.35
Maximum 4 .62
Percentiles
25 1.25 .1600
50 2.50 .3150
75 3.75 .4700
a. Multiple modes exist. The smallest value is shown
Frequency Table
GROUP

Frequency Percent Valid Percent Cumulative
Percent
Valid
1 11 24.4 25.0 25.0
2 11 24.4 25.0 50.0
3 11 24.4 25.0 75.0
4 11 24.4 25.0 100.0
Total 44 97.8 100.0
Missing System 1 2.2
Total 45 100.0
SCORE
Frequency Percent Valid Percent Cumulative
Percent
Valid -.35 1 2.2 2.3 2.3
-.25 1 2.2 2.3 4.5
-.14 1 2.2 2.3 6.8
.00 1 2.2 2.3 9.1
.02 1 2.2 2.3 11.4
.04 1 2.2 2.3 13.6
.10 2 4.4 4.5 18.2
.12 1 2.2 2.3 20.5
.15 1 2.2 2.3 22.7
.16 2 4.4 4.5 27.3
.18 1 2.2 2.3 29.5
.20 3 6.7 6.8 36.4
.21 1 2.2 2.3 38.6
.22 1 2.2 2.3 40.9
.26 1 2.2 2.3 43.2
.29 1 2.2 2.3 45.5
.30 1 2.2 2.3 47.7
.31 1 2.2 2.3 50.0
.32 1 2.2 2.3 52.3
.34 1 2.2 2.3 54.5
.36 1 2.2 2.3 56.8
.39 1 2.2 2.3 59.1

.40 1 2.2 2.3 61.4
.42 1 2.2 2.3 63.6
.43 2 4.4 4.5 68.2
.44 1 2.2 2.3 70.5
.46 1 2.2 2.3 72.7
.47 2 4.4 4.5 77.3
.50 3 6.7 6.8 84.1
.51 1 2.2 2.3 86.4
.52 1 2.2 2.3 88.6
.53 1 2.2 2.3 90.9
.58 2 4.4 4.5 95.5
.61 1 2.2 2.3 97.7
.62 1 2.2 2.3 100.0
Total 44 97.8 100.0
Missing System 1 2.2
Total 45 100.0
Descriptive Statistics
N Minimum Maximum Mean Std. Deviation
GROUP 44 1 4 2.50 1.131
SCORE 44 -.35 .62 .2923 .22528
Valid N (listwise) 44
12.24
One way ANOVA
Hypothesis:
Null hypothesis (H0): There is no statistically significant difference in the mean values of
dependent variable abstract and other independent variable factor (day).
Alternative hypothesis (H1): There is a statistically significant difference in the mean values of
variable abstract and other independent variable factor (day).

ANOVA
absrate
Sum of Squares df Mean Square F Sig.
Between Groups 94.199 4 23.550 .989 .424
Within Groups 952.169 40 23.804
Total 1046.368 44
12.26
Regression
Hypothesis
Null hypothesis (H0): There is no statistically significant difference in the mean values of power
and other independent variables (boxer & round).
Alternative hypothesis (H1): There is a statistically significant difference in the mean values of
power and other independent variables (boxer & round).
Descriptive Statistics
Mean Std. Deviation N
POWER 1253.34 71.690 32
BOXER 4.50 2.328 32
ROUND 2.50 1.136 32
Correlations
POWER BOXER ROUND
Pearson Correlation
POWER 1.000 .204 .234
BOXER .204 1.000 .000
ROUND .234 .000 1.000
Sig. (1-tailed)
POWER . .132 .099
BOXER .132 . .500
ROUND .099 .500 .

N
POWER 32 32 32
BOXER 32 32 32
ROUND 32 32 32
Variables Entered/Removeda
Model Variables Entered Variables
Removed
Method
1 ROUND, BOXERb . Enter
a. Dependent Variable: POWER
b. All requested variables entered.
Model Summary
Model R R
Square
Adjusted R
Square
Std. Error of
the Estimate
Change Statistics
R Square
Change
F
Change
df1 df2 Sig. F
Change
1 .310a .096 .034 70.470 .096 1.541 2 29 .231
a. Predictors: (Constant), ROUND, BOXER
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1
Regression 15306.627 2 7653.313 1.541 .231b
Residual 144016.592 29 4966.089
Total 159323.219 31
a. Dependent Variable: POWER
b. Predictors: (Constant), ROUND, BOXER
Coefficientsa
Model Unstandardized
Coefficients
Standardized
Coefficients
t Sig. 95.0% Confidence Interval
for B
B Std. Error Beta Lower Bound Upper Bound
1 (Constant) 1188.254 39.112 30.381 .000 1108.262 1268.247
BOXER 6.277 5.437 .204 1.154 .258 -4.843 17.397

ROUND 14.738 11.142 .234 1.323 .196 -8.051 37.526
a. Dependent Variable: POWER
Regression analysis
Null hypothesis (H0): There is no statistically significant difference in the mean values of power
and other independent variables (boxer & round).
Alternative hypothesis (H1): There is a statistically significant difference in the mean values of
power and other independent variables (boxer & round).
12.36
Regression
Descriptive Statistics
Mean Std. Deviation N
OVERRUN 510.54 20.504 24
HOUSE 2.50 1.142 24
WT 1.50 .511 24
Correlations
OVERRUN HOUSE WT
Pearson Correlation
OVERRUN 1.000 .762 .139
HOUSE .762 1.000 .000
WT .139 .000 1.000
Sig. (1-tailed)
OVERRUN . .000 .258
HOUSE .000 . .500
WT .258 .500 .
N
OVERRUN 24 24 24
HOUSE 24 24 24
WT 24 24 24

Variables Entered/Removeda
Model Variables Entered Variables
Removed
Method
1 WT, HOUSEb . Enter
a. Dependent Variable: OVERRUN
b. All requested variables entered.
Model Summary
Model R R
Square
Adjusted R
Square
Std. Error of
the Estimate
Change Statistics
R Square
Change
F
Change
df1 df2 Sig. F
Change
1 .775a .600 .562 13.568 .600 15.764 2 21 .000
a. Predictors: (Constant), WT, HOUSE
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1
Regression 5804.050 2 2902.025 15.764 .000b
Residual 3865.908 21 184.091
Total 9669.958 23
a. Dependent Variable: OVERRUN
b. Predictors: (Constant), WT, HOUSE
Coefficientsa
Model Unstandardized
Coefficients
Standardized
Coefficients
t Sig. 95.0% Confidence Interval
for B
B Std. Error Beta Lower Bound Upper Bound
1
(Constant) 467.958 10.726 43.627 .000 445.651 490.265
HOUSE 13.683 2.477 .762 5.524 .000 8.532 18.835
WT 5.583 5.539 .139 1.008 .325 -5.936 17.103
a. Dependent Variable: OVERRUN

REFERENCES
Annotated output. 2018. [Online]. Available through :<
https://stats.idre.ucla.edu/other/annotatedoutput/>.