Skip to content
Solved Assignments

Statistical Analysis of Educational Factors Affecting Student Performance: A Case Study Approach

Case study on how educational factors impact student outcomes.

Preview 4 of 11 pages

See the first 4 pages exactly as they appear in the document.

  1. Page 1
    Read page 1 as text

    Statistical Analysis of Educational Factors Affecting Student Performance: A Case Study Approach How do various educational factors influence student performance, and what statistical methods can be used to analyze these factors? (Word count: 800 - 1000 words)

  2. Page 2
  3. Page 3
    Read page 3 as text

    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 𝐻 ଵ : 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 ( 𝑋 ଵ , 𝑋 ଶ , … , 𝑋 ௡ ) and that in the post - test i.i.d ( 𝑌 ଵ , 𝑌 ଶ , … , 𝑌 ௡ ), where n is the sample size, when paired {( 𝑋 ଵ , 𝑌 ଵ ) , ( 𝑋 ଶ , 𝑌 ଶ ) , … , ( 𝑋 ௡ , 𝑌 ௡ ) } follow Bivariate Normal Distribution with mean ( 𝜇 ଵ , 𝜇 ଶ ) 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 ௢ : 𝜇 ଵ = 𝜇 ଶ vs 𝐻 ଵ : 𝜇 ଵ ≠ 𝜇 ଶ The test used is a paired sample t - test. Let 𝑑 ௜ = 𝑋 ௜ − 𝑌 ௜ Then 𝑑 ̅ = 𝑋 ത − 𝑌 ത ~ N (0, 𝜎 ଶ ) where 𝜎 ଶ can be derived from Σ .

  4. Page 4
    Read page 4 as text

    Let S= ∑ ( 𝑑 ೔ − 𝑑 ത ) మ ೙ ೔ = భ ௡ − ଵ Thus under null , 𝑑 ത ೄ √ ೙ follows t distribution with n - 1 degrees of freedom. We reject null at 0.05 level of significance if the value of | 𝑑 ത ೄ √ ೙ |> 𝑡 ( ௡ − ଵ ) , 0 . 0ఱ మ In this case, The following output was received from SPSS: T - TEST PAIRS=postest WITH pretest (PAIRED) /CRITERIA=CI(.9500) /MISSING=ANALYSIS. T - Test Notes Output Created 07 - Mar - 2013 02:18:56 Comments Input Data C: \ Users \ Abhishek \ Downloa ds \ zFinal (3).sav Active Dataset DataSet1 Filter <none> Weight <none> Split File <none> N of Rows in Working Data File 105 Missing Value Handling Definition of Missing User defined missing values are treated as missing.

7 more pages in the full document

Unlock it once and it stays in your library, ready to chat with or turn into flashcards.

Unlock the full document

More Education study materials

See all

Study this document with CramX

Once it is in your library, every tool can work from it.