Statistical Analysis of Educational Factors Affecting Student Performance: A Case Study Approach
Case study on how educational factors impact student outcomes.
Anna Wilson
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Case Study 1:
An educational statistics professor is examining his grade book to
determine the relationship and differences among a variety of
assignment scores. He is examining these scores to determine if his
course is effective. Every semester, the professor gives his students a
pretest and a posttest to determine if they improved in their
understanding of the course concepts. Thus, the first question he
examines is as follows: Is there a difference in the number of points
students earned on their educational statistics pretests and posttests?
Here the null hypothesis is 𝐻: There is no difference in the number of
points students earned on their educational statistics pre-tests and post-
tests.
vs the alternative hypothesis 𝐻ଵ: There is difference in the number of
points students earned on their educational statistics pre-tests and post-
tests.
The main assumptions are as follows:
1) The number of points earned by the students in the pre-test
(𝑋ଵ, 𝑋ଶ, … , 𝑋) and that in the post-test i.i.d (𝑌ଵ, 𝑌ଶ, … , 𝑌), where n
is the sample size, when paired {(𝑋ଵ, 𝑌ଵ), (𝑋ଶ, 𝑌ଶ), … , (𝑋, 𝑌)} follow
Bivariate Normal Distribution with mean (𝜇ଵ, 𝜇ଶ) and variance
covariance matrix Σ.
2) The sample must consist of 2 related groups, here they are the
scores of the pre-test prior to the course and a post-test after the
course.
3) There are no significant outliers in the differences between the
two related groups.
Thus in this case 𝐻: 𝜇ଵ = 𝜇ଶ vs 𝐻ଵ: 𝜇ଵ ≠ 𝜇ଶ
The test used is a paired sample t-test.
Let 𝑑 = 𝑋 − 𝑌
Then 𝑑̅ = 𝑋ത − 𝑌ത ~ N (0, 𝜎ଶ) where 𝜎ଶ can be derived from Σ.
An educational statistics professor is examining his grade book to
determine the relationship and differences among a variety of
assignment scores. He is examining these scores to determine if his
course is effective. Every semester, the professor gives his students a
pretest and a posttest to determine if they improved in their
understanding of the course concepts. Thus, the first question he
examines is as follows: Is there a difference in the number of points
students earned on their educational statistics pretests and posttests?
Here the null hypothesis is 𝐻: There is no difference in the number of
points students earned on their educational statistics pre-tests and post-
tests.
vs the alternative hypothesis 𝐻ଵ: There is difference in the number of
points students earned on their educational statistics pre-tests and post-
tests.
The main assumptions are as follows:
1) The number of points earned by the students in the pre-test
(𝑋ଵ, 𝑋ଶ, … , 𝑋) and that in the post-test i.i.d (𝑌ଵ, 𝑌ଶ, … , 𝑌), where n
is the sample size, when paired {(𝑋ଵ, 𝑌ଵ), (𝑋ଶ, 𝑌ଶ), … , (𝑋, 𝑌)} follow
Bivariate Normal Distribution with mean (𝜇ଵ, 𝜇ଶ) and variance
covariance matrix Σ.
2) The sample must consist of 2 related groups, here they are the
scores of the pre-test prior to the course and a post-test after the
course.
3) There are no significant outliers in the differences between the
two related groups.
Thus in this case 𝐻: 𝜇ଵ = 𝜇ଶ vs 𝐻ଵ: 𝜇ଵ ≠ 𝜇ଶ
The test used is a paired sample t-test.
Let 𝑑 = 𝑋 − 𝑌
Then 𝑑̅ = 𝑋ത − 𝑌ത ~ N (0, 𝜎ଶ) where 𝜎ଶ can be derived from Σ.
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Subject
Education