College Skills The Collegiate Learning Assessment Plus is an exam that is meant to assess the intellectual gains made between one’s freshman and senior year of college. The exam, graded on a scale of 400 to 1600, assesses critical thinking, analytical reasoning, document literacy, writing, and communication. The exam was administered to 135 freshman in Fall 2012 at California State University Long Beach (CSULB). The mean score on the exam was 1191 with a standard deviation of 187. The exam was also administered to graduating seniors of CSULB in Spring 2013. The mean score was 1252 with a standard deviation of 182. Explain the type of analysis that could be applied to these data to assess whether CLA+ scores increase while at CSULB. Explain the shortcomings in the data available and provide a better data collection technique.

Verified step by step guidance

1. Identify the goal: We want to determine if the CLA+ scores increase from freshman to senior year at CSULB, which suggests comparing the means of two groups (freshmen and seniors).
2. Choose the appropriate analysis: Since we have two independent groups (freshmen and seniors) with their own means and standard deviations, a two-sample t-test for the difference of means can be used to assess if the mean score for seniors is significantly higher than that for freshmen.
3. Consider assumptions and data requirements: The two-sample t-test assumes that the samples are independent, the data in each group are approximately normally distributed, and the variances are roughly equal or adjustments are made if not.
4. Identify shortcomings in the current data: The freshmen and senior groups are different individuals measured at different times, so this is a cross-sectional comparison rather than a longitudinal one. This means individual growth is not tracked, and differences could be due to cohort effects or other confounding variables rather than true intellectual gains.
5. Suggest a better data collection technique: A longitudinal study design would be more appropriate, where the same students are tested as freshmen and then again as seniors. This paired data allows for a paired t-test, which controls for individual differences and better measures true changes over time.

Key Concepts

Hypothesis Testing for Comparing Two Means

Hypothesis testing is used to determine if there is a statistically significant difference between the mean scores of two groups—in this case, freshmen and seniors. A two-sample t-test can compare the average CLA+ scores to assess if scores increase over time. This test evaluates whether observed differences are likely due to chance or reflect a real change.

Limitations of Cross-Sectional Data

Cross-sectional data compares different groups at one point in time rather than tracking the same individuals over time. This approach can be confounded by cohort effects or differences unrelated to college experience, limiting causal conclusions about score improvements. Without longitudinal data, it’s hard to attribute score changes directly to attending CSULB.

Longitudinal Study Design

A longitudinal study follows the same students from freshman to senior year, measuring their CLA+ scores at multiple points. This design controls for individual differences and better captures true intellectual gains over time. It provides stronger evidence for causality by observing within-subject changes rather than comparing separate groups.