Problem Description
Assessing the Educational Intervention's Impact on Reading Scores: This data analysis assignment investigates the effectiveness of an educational intervention, analyzing data to determine if it led to significant improvements in reading scores. Additionally, it compares the outcomes between two intervention groups to understand the program's overall impact on academic performance.
Analysis Project: Assessing the Impact of an Educational Intervention
In this analysis project, we examine the effectiveness of an educational intervention by analyzing data on reading performance. Important questions:
- Were there significant differences between the starting reading scores and end reading scores?
To address this question, we will perform a paired samples t-test to assess whether the intervention had a statistically significant impact on reading scores.
- Were there significant differences between the intervention groups on end reading scores?
To answer this question, we will conduct an independent samples t-test to compare the end reading scores between two different intervention groups.
Data Preparation: The first step involves importing and preparing the data. The data consists of 200 observations with seven variables: Biosex, Intervention, ReadStart, ReadEnd, Confidence, Engagement, and SchoolSES.
R- Code
# Importing and structuring the data
setwd("C:/Users/Joaquin/Desktop/Reading Data")
reading <- read.csv(file = "martinez-reading.csv", header = TRUE)
# Converting variables to appropriate types
reading$Biosex <- as.factor(reading$Biosex)
reading$Intervention <- as.factor(reading$Intervention)
reading$SchoolSES <- as.factor(reading$SchoolSES)
reading$ReadEnd <- as.numeric(reading$ReadEnd)
Analysis 1: Were there significant differences between starting and end reading scores?
Step 1: State the hypotheses.
Hypotheses:
- Null Hypothesis (H0): μ_D = 0. There is no mean difference in reading level after the intervention versus reading level before the intervention.
- Alternative Hypothesis (H1): μ_D ≠ 0. There is a mean difference in reading level after the intervention versus reading level before the intervention.
Step 2: Set the criteria for a decision.
- Significance Level (α): 0.05
- Two-tailed test
- Degrees of freedom (df) = 199
Step 3: Compute the test statistic.
# Calculating differences in scores
reading$diff <- reading$ReadEnd - reading$ReadStart
# Checking the normality of score differences
shapiro.test(reading$diff)
The normality assumption was satisfied as the p-value was greater than 0.05.
# Performing the paired samples t-test
t.test(reading$ReadEnd, reading$ReadStart, paired = TRUE)
Step 4: Make a decision.
The observed t-value (31.202) is greater than the critical t-value (1.972), so we reject the null hypothesis. There were significant differences between the starting and end reading scores.
The estimated effect size (Cohen’s d) is 2.21, indicating a large effect.
Analysis 2: Were there significant differences between the intervention groups on end reading scores?
Step 1: State the hypotheses.
Hypotheses:
- Null Hypothesis (H0): μ_1 - μ_2 = 0. Mean end reading scores do not differ for the new intervention group and the original intervention group.
- Alternative Hypothesis (H1): μ_1 - μ_2 ≠ 0. Mean end reading scores differ for the new intervention group and the original intervention group.
Step 2: Set the criteria for a decision.
- Significance Level (α): 0.05
- Two-tailed test
- Degrees of freedom (df) = 198
Step 3: Compute the test statistic.
Assumptions:
- Normality of scores in each population
- Random sampling
- Independence of measurements
- Equal variances in each population
Normality tests were conducted for both groups and the assumption of equal variances was satisfied.
# Normality tests
shapiro.test(reading$ReadEnd[reading$Intervention == "Traditional"])
shapiro.test(reading$ReadEnd[reading$Intervention == "New"])
# Assumption of equal variances
ratio <- 39.38343 / 31.25414
# Performing the independent samples t-test
t.test(ReadEnd ~ Intervention, data = reading, var.equal = TRUE)
Step 4: Make a decision.
The observed t-value (25.22) is greater than the critical t-value (1.972), so we reject the null hypothesis. There were significant differences between the intervention groups on end reading scores.
The estimated effect size (Cohen’s d) is 3.57, indicating a large effect.
Conclusion:
In summary, the data analysis indicates that the educational intervention had a significant and positive impact on reading scores. Additionally, there were significant differences in end reading scores between the two intervention groups, with the new intervention group outperforming the traditional intervention group. These findings are substantiated by large effect sizes, highlighting the practical significance of the results.