Overview
This lecture covers SPSS-based descriptive data analysis of student performance, comparing GPA and quiz scores by gender using histograms and descriptive statistics.
Data Visualization: Histograms
- Two histograms were created: one for male and one for female students.
- Female students' histogram shows GPA is not normally distributed, with grades clustered and some skewness.
- Male students' histogram shows GPA is normally distributed and leptokurtic (peaked in the center).
Descriptive Statistics: Females
- Female students (n=64): Mean GPA = 2.99, SD = 0.68, Skewness = 0.343, Kurtosis = -0.71.
- Female quiz 3: Mean score = 7.23, SD = 1.58, Skewness = 0.097, Kurtosis = -0.63.
Descriptive Statistics: Males
- Male students (n=41): Mean GPA = 2.79, SD = 0.68, Skewness = 0.069, Kurtosis = -0.06.
- Male quiz 3: Mean score = 7.29, SD = 1.44, Skewness = 0.147, Kurtosis = -0.02.
Interpretation of Skewness and Kurtosis
- GPA distribution for both genders is negatively skewed (tail on the left).
- Quiz 3 scores are positively skewed (tail on the right).
- Male GPA skewness is closer to zero, indicating near-normality.
- Kurtosis values near zero suggest approximate normality for males’ GPA; females' GPA and quiz 3 are less normal.
Key Terms & Definitions
- Histogram — a bar graph showing the distribution of numerical data.
- Central Tendency — statistical measures indicating the center of a dataset (e.g., mean).
- Dispersion — statistical measures of data spread (e.g., standard deviation).
- Skewness — a measure of the asymmetry of the probability distribution.
- Kurtosis — a measure of the "tailedness" or peakedness of the data distribution.
- Leptokurtic — a distribution that is more peaked than a normal distribution.
Action Items / Next Steps
- Review histograms and tables for both genders.
- Study the definitions of skewness and kurtosis and their impact on data interpretation.
- Prepare to discuss implications of different distributions in next class.