+
+
+
+
+
+
+
+
```{r} #| echo: FALSE # The content of this code block will not be
+shown when rendered #| output: FALSE # Output from this code block will
+not be shown when rendered
+
+
+
Compute the height difference score
+
df_wide <- df_wide %>% mutate( height_diff = Height_Year_1 -
+Height_Baseline )
+
+
+
Calculate summary statistics for the difference score
+
summary(df_wide$height_diff)
+
+
+
Compute summary statistics for Height by eventname
+
summary <- df_long %>% group_by(event) %>%
+get_summary_stats(height, type = “mean_sd”)
+
data.frame(summary)
+
+The summary statistics provide insights into participant's height across two annual assessments. At baseline, the average height is 55.24 inches (sd = 3.33). Over the year, there is an increase of 2.35 inches in average height to 57.59 inches at the time of the 1-year follow-up.
+
+### Conduct t-test on Difference Score
+A one-sample t-test is computed on the difference scores to examine whether there is evidence of change in participant's height between the two timepoints.
+```{r}
+# Perform a one-sample t-test on the difference scores for height
+model <- t.test(df_wide$height_diff, mu = 0)
+model
+
+
The results from the one-sample t-test conducted on the height
+difference scores reveals an increase in height from Baseline to Year 1.
+The t-test yields a t-value of 98.86 with a p-value less than <.001,
+indicating that the average height increase of 2.36 inches is
+significantly different from zero. Additionally, the 95% confidence
+interval indicates that the true mean difference score in the population
+lies between approximately 2.31 to 2.41 inches.
+
+
Model Plots
+
```{r} # Scatterplot to compare height differences across two events
+ggplot(df_wide, aes(x = Height_Baseline, y = Height_Year_1)) +
+geom_point(aes(color = Height_Baseline), alpha = 0.6) + # Color points
+by event type, adjust for your data labs( x = “Height at Baseline”, y =
+“Height at Year 1”, title = “Scatterplot of Heights at Baseline and Year
+1”, subtitle = “Each point represents a participant” ) + theme_minimal()
++ geom_smooth(method = “lm”, se = FALSE) + # Add a regression line
+without confidence interval theme(legend.position = “bottom”)
+
```
+
The scatterplot visually depicts the relationship between
+individuals’ heights at baseline and their heights at year 1. Each point
+on the plot represents an individual, with their baseline height plotted
+on the x-axis and their year 1 height on the y-axis. A noticeable
+positive linear trend can be observed, as highlighted by the blue
+regression line, indicating that those who were taller at baseline
+generally remained taller at year 1. The strength and direction of this
+relationship suggests a strong positive association between baseline and
+year 1 height values.
+
+
+
Wrapping Up
+
This analysis examined difference scores of participant’s height
+using a one-sample t-test. Findings showed a significant increase in
+height values over the one-year interval of 2.36 inches, with confidence
+intervals ranging from 2.31 to 2.41 (t = 98.864, df = 11135, p-value
+< 2.2e-16). Further, a scatterplot visualizing the relationship
+between baseline and Year_1 weights showed a strong positive linear
+trend. This suggests that participants who were taller at baseline
+generally remained taller at Year_1, reaffirming the consistent growth
+trend observed in the data.
+
This difference score approach used in this example quantifies the
+change in height values over time within a single group and uses a
+one-sample t-test to test whether this value differs significanctly from
+0. More generally, this approach is often implemented when data used to
+evalaute change is only available at two timepoints, as more flexible
+approaches are typically implemented when data from additional (>2)
+time points is available.
+
+
+
+
+
+
+
