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Quantitative Research Methods and Data Analysis for Education Practitioners
Assignment 1: Applied Statistics
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Table of Contents
Part 1: Influence of years of teaching on average income
Input screenshots………………………………………………….. 2
Output screenshots…........................................................................ 3
Scatterplot…..................................................................................... 5
Co-relation coefficient….................................................................. 5
Corelation…..................................................................................... 5
T-Test…..…..................................................................................... 5
Part 2: Relationship between race and level of education
Input screenshots………………………………………………….. 2
Output screenshots…........................................................................ 3
Meaning of items….......................................................................... 5
Interpretation of regression results..................................................... 5
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Part I: influence of years of teaching on average income
Exploring the influence of years of teaching on average income
a) i) Input screen shots
Input Screen 1- Variable view
Input Screen 2 Data view
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a) Produce a scatterplot for average income and years of teaching
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b) Compute the correlation coefficient, r, between years of teaching and average income.
Step 1 select analyse>bivariate (after entry of variables ( and data)
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Correlations
Years of Teaching
Years of Teaching
Pearson Correlation
1
Average Teaching Income
.500*
Sig. (2-tailed)
N
Average Teaching
Income
.049
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16
Pearson Correlation
.500*
1
Sig. (2-tailed)
.049
N
16
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*. Correlation is significant at the 0.05 level (2-tailed).
The correlation coefficient, r, between years of teaching and average income= .500
c) Explain the results of the correlation obtained between years of teaching and average
income.
The relationship between years of teaching and average income was investigated using the
Pearson r statistic. The correlation coefficient/ Pearson r statistic, reveals the strength and
direction of the linear relationship between years of teaching and average income. The results
showed that there is a moderate positive/direct relationship between years of teaching and
average income (r = .500, p< 0.05). The relationship is significant (p=.049, < 0.05).
d) Conduct a T-test to explore whether the difference in salary between those with 10 years
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of teaching or less and those with greater than 10 years of teaching is significant.
Null hypothesis H°: There is no significant difference in the salaries of teachers with 10 years or
less teaching experience and the salaries of teachers with more than 10 teaching experience.
Alternative hypothesis H°: There is a significant difference in the salaries of teachers with 10
years or less teaching experience and the salaries of teachers with more than 10 teaching
experience.
Input screenshot 1 (create values for 10 and more years and more than 10 years)
Input screenshot 2- Data view
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Input screenshot 3
Input screenshot 4
Output table 1
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Group Statistics
Years of Teaching
Average Teaching Income
N
Mean
10 and less years
More than 10 years
Std. Deviation
Std. Error Mean
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30782.00
2828.837
1265.094
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32675.45
3738.158
1127.097
Output table 2
Independent Samples Test
Levene's Test
for Equality of
Variances
t-test for Equality of Means
95% Confidence
F
Average
Equal
Teaching
variances
Income
assumed
1.514
Sig.
.239
Equal
t
df
Sig.
Mean
Std. Error
Interval of the
(2-
Differenc
Differenc
Difference
tailed)
e
e
Lower
Upper
-1.002
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.333 -1893.455
1889.122
-5945.217 2158.308
-1.118
10.2
.289 -1893.455
1694.347
-5654.829 1867.920
variances not
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assumed
Output table 3
Independent Samples Effect Sizes
95% Confidence Interval
Standardizera
Average Teaching Income
Point Estimate
Upper
Cohen's d
3502.525
-.541
-1.607
.544
Hedges' correction
3705.248
-.511
-1.519
.514
Glass's delta
3738.158
-.507
-1.574
.585
a. The denominator used in estimating the effect sizes.
Cohen's d uses the pooled standard deviation.
Hedges' correction uses the pooled standard deviation, plus a correction factor.
Glass's delta uses the sample standard deviation of the control group.
Discussion
Lower
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The data was analysed using an independent sample t-test. Looking at the results from the
independent sample t-test, it can be seen that the comparison of the salaries of teachers who have 10
and less years experience with the salaries of those teachers who have more than 10 years
experience show no significant difference (t=-1.002, p=.333> .05). This means that there is no
significant difference in salaries according to years experience. The mean salary of teachers with
10 years and less experience is $30,782.00 while the mean salary of teachers with more than 10
years is $32,675.45 . The null hypothesis is therefore not rejected.
Part II: Relationship between race and level of education
a. Perform a linear regression analysis to examine the effect of the independent variables
(race and education) on the dependent variable (test score).
i) Input screen shots
Step 1: Input Screen 1- Variable view
Step 2: Input Screen 2- Variable view. Values entered for Level of Education and Race
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Input Screen- Enter data- Data view
Input Screen- Analyse-Regression-Linear
Input Screen- Enter Dependent and Independent Variables
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Output screen shots
Variables Entered/Removeda
Variables
Variables
Entered
Removed
Model
1
Level of
Method
. Enter
Education,
Participant raceb
a. Dependent Variable: Score on Math Test
b. All requested variables entered.
ANOVAa
Model
1
Sum of Squares
df
Mean Square
Regression
571.634
2
285.817
Residual
961.366
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73.951
1533.000
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Total
F
Sig.
.048b
3.865
a. Dependent Variable: Score on Math Test
b. Predictors: (Constant), Level of Education, Participant race
Residuals Statisticsa
Minimum
Predicted Value
Maximum
Mean
Std. Deviation
N
69.45
91.43
80.25
6.173
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-16.105
10.551
.000
8.006
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Std. Predicted Value
-1.750
1.812
.000
1.000
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Std. Residual
-1.873
1.227
.000
.931
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Residual
a. Dependent Variable: Score on Math Test
b) On the screenshot for the regression output, indicate each item as described below:
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Model Summaryb
Model
R
Std. Error of the
Square
Estimate
R Square
.611a
1
Adjusted R
.373
.276
8.599
a. Predictors: (Constant), Level of Education, Participant race
b. Dependent Variable: Score on Math Test
Circle the R Square, Box the Adjusted R Square
Coefficientsa
Standardized
Unstandardized Coefficients
Model
1
B
Std. Error
(Constant)
83.474
7.505
Participant race
-4.271
1.929
3.058
2.037
Level of Education
Coefficients
Beta
t
Sig.
11.123
.000
-.488
-2.214
.045
.331
1.501
.157
a. Dependent Variable: Score on Math Test
Double underline the three (3) B values; and Underline any significant t-values
c. Explain the meaning of each item in the four bullets listed above.
R Square
R square is also known as the coefficient of determination. It shows how close the data is to the
regression line and whether there is a relationship between two variables. -1 indicates a perfect
negative relationship while +1 indicates a perfect positive relationship, while 0 indicates that
there is no linear relationship (Bastick & Matalon, 2007).
Adjusted R Square
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Adjusted R square is a version of r squared that has been modified for the number of predictors
in the model (Bhalla, n.d.) It therefore gives a clearer picture of how well the data fits the
regression line. Adjusted R-squared increases only when an independent variable is significant
and affects the dependent variable. The Adjusted r-squared value will always be less than or
equal to the r-squared value.
The three (3) B values
The B values represent the unstandardized regression coefficient. Since they are measured in
their natural units, they are referred to as “unstandardized”. The B values are used in the
regression equation to predict the dependent variable from the independent variable.
Significant t-values
A t-value of 0 means that the results of the sample are exactly equal to the null hypothesis and
therefore there is no significant difference (Frost, n.d.). Therefore the closer the t-value is to 0,
the more likely that there is no significant difference. Conversely, the higher the t-value the
greater the significant difference. A negative t-value indicates that it lies to the left of the mean
while a positive t-value indicates that it lies to the right of the mean.
d. Explain what the regression results mean.
Race and test scores
Null hypothesis H0: Race has no effect on test scores.
Alternate hypothesis H1: Test scores are affected by the race of participants.
Explanation
A linear regression analysis was performed to examine the effect of the independent variable
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(race) on the dependent variable (math test score). There is no significant change in math test score
due to race. This is because the P-value (.045) is more than the acceptable significance level (0.05).
The null hypothesis is therefore not rejected.
Education and test scores
Null hypothesis H0: Education has no effect on test scores.
Alternate hypothesis H1: Test scores are affected by education levels.
Explanation
A linear regression analysis was performed to examine the effect of the independent variable
(education) on the dependent variable (math test score). There is no significant change in math test
scores due to level of education. This is because the P-value (.157) is more than the acceptable
significance level (0.05). The null hypothesis is therefore not rejected.
References
Bastick, T & Matalon, B.A. (2007). Research: new and practical approaches. 2nd Ed. U.W.I.
Chalkboard Press
Bhalla, D. (n.d.). Difference between adjusted r-squared and r-squared.
https://www.listendata.com/2014/08/adjusted-r-squared.html
Frost, J (n.d.). How t-tests work: t-values, t-distributions, and probabilities.
https://statisticsbyjim.com/hypothesis-testing/t-tests-t-values-t-distributions-probabilities/