Solution
Pratibha answered on
Sep 10 2023
Statistical Analysis
Name of the student
Student ID
Variable Names and Scales of Measurement
Variable names and scales of measurement for the provided dataset:
Variable
Description
Data type
Id
Unique identifie
Nominal
Lastname
Last name of student
Nominal
Fisrtname
First name of student
Nominal
Genderidentity
Gender Identity (1 = Male, 2 = Female)
Nominal
Ethnicity
Ethnicity (1 = Asian, 2 = Black, 3 = Hispanic, 4 = White)
Ordinal
Yea
Student Yea
Ordinal
lowup
Lowup
Ordinal
section
Section
Ordinal
Gpa
GPA
Continuous
extc
External credits
ordinal
review
Review session attended or not
Ordinal
Quiz1,quiz2,quiz3,
quiz4,quiz5
Quiz Scores
continuous
Final
Final exam score
continuous
total
Total score
continuous
percent
Percentage score
continuous
grade
Grade (A,B, C,D)
Nominal
passfail
Pass/Fail (1=Pass, 0=Fail)
Nominal
Research Question and Hypotheses
Research Question: "What factors are associated with student performance and whether they pass or fail?"
Â· Null Hypothesis ($H_0$): "There is no significant relationship between the independent variables (e.g., gender, ethnicity, GPA) and student performance (pass/fail)."
Â· Alternate Hypothesis ($H_A$): "There is a significant relationship between the independent variables and student performance."
For testing the relationship between independent variables (e.g., gender, ethnicity, GPA) and student performance (pass/fail), we can use a chi-squared test of independence. This test is appropriate when you have categorical independent variables and a categorical dependent variable like "pass/fail." Specifically, we can perform a chi-squared test for independence or a chi-squared test for association.
Testing Assumptions:
The chi-square test of independence has some assumptions that need to be considered when applying it to a dataset. These assumptions are related to the nature of the data and the appropriateness of the test. Here are the key assumptions for the chi-square test of independence:
1. Independence of Observations: The observations in the contingency table (cross-tabulation) should be independent of each other. In other words, the data points should not be influenced by or dependent on each other. Violations of this assumption can lead to inaccurate results.
2. Random Sampling: The data should come from a random sample or a well-defined sampling process. This ensures that the sample is representative of the population from which it was drawn.
3. Expected Cell Frequencies: The expected cell frequencies (the values that would be expected under the null hypothesis of independence) should be greater than or equal to 5 for most cells in the contingency table. This assumption is known as the "5 or more" rule.
4. If the expected cell frequencies are very small (less than 5), the chi-square test may not be appropriate, and alternative tests (e.g., Fisher's Exact Test) should be considered.
5. Categories are Mutually Exclusive: The categories or levels of the categorical variables should be mutually exclusive, meaning that each observation should belong to only one category.
6. Ordinal or Nominal Data: The chi-square test is most appropriate for categorical data that is either ordinal (categories have a natural order) or nominal (categories have no natural order).
7. Large Sample Size: While the chi-square test is robust to violations of normality assumptions, it is more reliable with larger sample sizes. Small sample sizes can lead to less reliable results.
Results and Interpretation
The descriptive statistics presented summarize various characteristics of a dataset containing 105 valid data points across multiple variables. Here's a detailed summary of the key findings:
Â· The dataset appears to include a mix of categorical and numerical variables. Among the numerical variables, the mean GPA stands at 2.862, indicating an average academic performance. The "total" variable, with a mean of 61.838, suggests a scoring system or total points, and the "percent" variable has a mean of 100.086, possibly representing percentages.
Â· The categorical variables include "genderidentity" and "ethnicity," with means of 1.714 and 3.352, respectively. These values likely co
espond to categories or codes representing gender identity and ethnicity, but the specific interpretations would require additional context.
Â· The dataset includes several "quiz" variables (quiz1 to quiz5), each with mean values around 7.5, indicating relatively consistent quiz scores. The "passfail" variable has a mean of 0.543, suggesting that the majority of observations fall within one category.
Â· Standard e
ors, confidence intervals, and standard deviations provide information about the precision of the mean estimates and the variability in the data.
Â· The Shapiro-Wilk tests indicate that some variables deviate from a normal distribution, as reflected in their small p-values.
Â· In conclusion, these descriptive statistics offer insights into the central tendency, variability, and...