ESE 633 Assignment: Statistical Analysis in Education - Fall 2024

This statistics assignment for ESE 633 focuses on applying statistical methods to analyze and interpret educational data. The assignment covers a range of statistical concepts, including standard deviation, hypothesis testing, t-tests, ANOVA, regression analysis, and chi-square tests. The student addresses questions related to data distribution, relationships between variables, and the application of appropriate statistical tests. The analysis includes interpreting p-values, making conclusions about the significance of findings, and understanding the assumptions underlying various statistical techniques. The assignment demonstrates the student's ability to apply statistical knowledge to real-world educational scenarios, interpret results, and draw meaningful conclusions from data.

Running head: STATISTICS IN EDUCATION
Statistics in Education
Name of the Student:
Name of the University:
Author note:

1
STATISTICS IN EDUCATION
Table of Contents
Answer to the question 1............................................................................................................2
Answer to the question 2............................................................................................................2
Answer to the question no 3.......................................................................................................2
Part (a)....................................................................................................................................2
Part (b)....................................................................................................................................3
Part (c)....................................................................................................................................3
Answer to the question 4............................................................................................................3
Part (a)....................................................................................................................................3
Part (b)....................................................................................................................................3
Answer to the question 5............................................................................................................4
Part (a)....................................................................................................................................4
Part (b)....................................................................................................................................4
Answer to the question 6............................................................................................................4
Answer to the question 7............................................................................................................5
Part (a)....................................................................................................................................5
Part (b)....................................................................................................................................5
Answer to the question 8............................................................................................................5
Part (b)....................................................................................................................................6
Part (c)....................................................................................................................................6
Part (d)....................................................................................................................................6
Part (e)....................................................................................................................................6
Answer to the question 9............................................................................................................6
Part (a)....................................................................................................................................6
Part (b)....................................................................................................................................7
Answer to the question 10..........................................................................................................7
Part (a)....................................................................................................................................7

2
STATISTICS IN EDUCATION
Part (b)....................................................................................................................................7
Part (c)....................................................................................................................................7
Answer to the question 11..........................................................................................................7
Part (a)....................................................................................................................................7
Part (b)....................................................................................................................................7
Part (c)....................................................................................................................................7
Part (d)....................................................................................................................................8
Part (e)....................................................................................................................................8
Bibliography...............................................................................................................................9

3
STATISTICS IN EDUCATION
Answer to the question 1
The standard deviation defines how tightly the values are clustered among the mean
of the data. When the shape of the curve bell and steep, then the standard deviation is small.
In other words when the bell-shaped is relatively flat, and this defines the large standard
deviation. Moreover, the large standard deviation shows the extreme score.
The graph for class X is bell-shaped and steep. Thus this indicates their standard
deviation is low and the distribution of the score is not too extreme.
In other words, the graph for class Y is bell-shaped and flatted as compared to class
X. Thus this indicates their standard deviation is large and the distribution of the score is
extreme.
Answer to the question 2
Given that
Males= 48.8
Female = 49.1
Hence the mean = (48.8+49.1)/2
= 97.9/2
= 48.95
The standard deviation for male is 3.56 and for the female is 4.46
Answer to the question no 3
Part (a)
Null hypothesis (H0) There is no association between females and males on the purpose of
smartphone use in the school.
Alternative hypothesis (H1) There is an association between females and males on the
purpose of smartphone use in the school.
Part (b)
The allowance of the smartphone in school has been divided into two categories, man
and woman and yes and no. This is the reason that applies the chi-square test to determine the

4
STATISTICS IN EDUCATION
association between male and female. Hence if the data set is categorical, then always the
chi-square test is suitable to determine the association.
Part (c)
The table shows that P-Value = 0.0001, which is less than the alpha (either 5% or
1%). It means that the hypothesis is significant. Hence it may be concluded that there is an
association between females and males on the purpose of smartphone use in the school.
Answer to the question 4
Part (a)
The X-axis in the figure shows the hours spent on playing video games and the Y-axis
shows the reading score. It has been seen from the figure that all the data points are close to
the diagonal line. Thus this means that there is a positive and strong relationship between the
hours spent on playing video games and reading scores.
Part (b)
The statistical test like regression analysis and t-test has been applied to determine the
relationship between two variable.
Answer to the question 5
Part (a)
The regression analysis has been applied to predict the length of jump using height.
The regression analysis is the best test to predict the variable. Moreover, the regression is the
only test that modeling the value of one variable as corresponding to others.
Part (b)
The assumption of regression analysis are as below
 No correlation has been seen in the residual term. If this phenomenon is absent then it
is called autocorrelation.
 The variable which is independent should not be correlated. If this phenomenon is
absent then it is called multicollinearity.
The multicollinearity has been seen when the independent variable highly correlated.
In this case, the independent variable ‘height’ is highly correlated with span of jump.

5
STATISTICS IN EDUCATION
Answer to the question 6
In general, a t-test has been applied when there is some chance to create a type 1
error. This test is usually defined at the level of 5%. The general step is to calculate the error
rate for multiple t-test, which is not easy to multiply 5% by the number of tests. It is clear that
when making a lot of multiple comparisons, then the results are not too different. At that time
the accuracy of the three t-tests is 15%. This is called an unusual error. The ANOVA is the
test that controls the type 1 error and this remains at 5%. Thus this shows more confident
results and results of statistical significance not running the lots of tests. Moreover, the
dependent variable is normalin each group which can be compared only in the ANOVA.
Hence to determine the significance of group ANOVA is better.
Answer to the question 7
Part (a)
 To determine the relationship between male and female subjects.
 To test the relationship between inductive and deductive reasoning.
 To determine the association between gender and reasoning skill.
Part (b)
The two-sample t-test has been applied to the relationship between male and female
subjects and the relationship between inductive and deductive reasoning. Similarly, the chi-
square test has been conducted to determine the association between gender and reasoning
skills.
Answer to the question 8
From the table of scores on statistics shows that there are three treatments. These are
using video using clips, using the worksheet and using flash cards. It has been seen that each
of the treatment takes 20 observations. The mean of using video clips is 27.20. Similarly, the
mean of using flashcards is 23.40. The mean of using worksheets is more than 0.30 as
compared to using flashcards.
The standard deviation of using video clips is 3.05. Similarly for using worksheets is
3.31. The standard deviation of using flashcards is less than 0.70 as compared to flash cards.
The standard error of using flashcards is 1.02 and the standard error for the using worksheets
is more than 0.02 as compared to using flashcards. Similarly, the standard error for using
video clips is 0.96, which is less than 1.

6
STATISTICS IN EDUCATION
Part (b)
The standard error of using flashcards is 1.02 and the standard error for the using
worksheets is more than 0.02 as compared to using flashcards. Similarly, the standard error
for using video clips is 0.96, which is less than 1.
Part (c)
The Levene Statistic of the test is 0.115.
Part (d)
Test statistic = 4.467
P-value = 0.031
It has been seen that the P-value is lesser than the alpha at 5%. Hence the test is
significant at 5% level of significance.
Part (e)
From the Tukey HSD results it has been seen that some of the mean diffeeence is
positive and some of negative. The value of the standard error is 1.431. Moreover all the
relationship lectuce with video clips, lectuce only and small group are not significant.
Answer to the question 9
Part (a)
 To determine the relationship between memory, verbal reasoning,
metacognition, spatial reasoning and mathematical ability.
 To determine the coefficient of determination in the above relationship.
 To test the relationship between gender and reasoning.
Part (b)
The table on the above study shows the correlation matrix. There are some
relationship strong and some of weak, but both are positive.
Answer to the question 10
Part (a)
Both the Kolmogorov-smirnov and Shapiro-wilk test used to cheek the normality of
the data set.

7
STATISTICS IN EDUCATION
Part (b)
The Kolmogorov smirnov test is a test which cheek the normality and where the mean
and variance are completely specified. On the other hand the Shapiro-wilk test is a test which
cheek the normality and where the mean and variance are not completely specified.
Part (c)
The P- Value < alpha (at either 5% or 1%). Hence he null hypothesis is significant.
There for it may concluded that the the data set on the above test in not normally distributed.
Answer to the question 11
Part (a)
There are two types of observations has been seen. One is pretest and the other
posttest. Each of the type carries 30 observations. The mean of the posttest is larger than the
pretest. But the standard deviationand the standard error of mean of the pretest is larger than
the posttest.
Part (b)
Null hypothesis: There is no relationship between the pretest and posttest.
Part (c)
Alternative hypothesis: There is a relationship between the pretest and
posttest.
Part (d)
The data in the above table are given in paired, that is pre test and posttest. Both the
event that is pre or post test happens one after another. This is the reason to apply paired t-
test.
Part (e)
The P-Value < alpha (at either 5% or 1%). It means that the null hypothesis is
significant. Hence it may be concluded that there is a relationship between the pretest and
posttest.

8
STATISTICS IN EDUCATION
Bibliography
de Mesquita Lopes, M., Branco, V. T. F. C., & Soares, J. B. (2013). Utilização dos testes
estatísticos de Kolmogorov-Smirnov e Shapiro-Wilk para verificação da normalidade
para materiais de pavimentação. Transportes, 21(1), 59-66.
De Winter, J. C. (2013). Using the Student's t-test with extremely small sample sizes.
Practical Assessment, Research, and Evaluation, 18(1), 10.
Holcomb, Z. C. (2016). Fundamentals of descriptive statistics. Routledge.
Kim, H. Y. (2015). Statistical notes for clinical researchers: post-hoc multiple comparisons.
Restorative dentistry & endodontics, 40(2), 172-176.
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: a
practical primer for t-tests and ANOVAs. Frontiers in psychology, 4, 863.
McHugh, M. L. (2013). The chi-square test of independence. Biochemia medica: Biochemia
medica, 23(2), 143-149.
Oktaviani, M. A., & Notobroto, H. B. (2014). Perbandingan tingkat konsistensi normalitas
distribusi metode kolmogorov-smirnov, lilliefors, shapiro-wilk, dan skewness-
kurtosis. Jurnal Biometrika dan Kependudukan, 3(2), 127-135.
Pereira, D. G., Afonso, A., & Medeiros, F. M. (2015). Overview of Friedman’s test and post-
hoc analysis. Communications in Statistics-Simulation and Computation, 44(10),
2636-2653.
Plonsky, L. (2015). Statistical power, p values, descriptive statistics, and effect sizes: A
“back-to-basics” approach to advancing quantitative methods in L2 research. In
Advancing quantitative methods in second language research (pp. 23-45). Routledge.
Ye, J. (2013). Multicriteria decision-making method using the correlation coefficient under
single-valued neutrosophic environment. International Journal of General Systems,
42(4), 386-394.

9
STATISTICS IN EDUCATION