Recalling Words

Wilcoxon Test

Background

Many teachers and other educators are interested in understanding how to best deliver new content to students. In general, they have two choices of how to do this.

1. The Meshed Approach
   • Deliver new content while simultaneously reviewing previously understood content.
2. The Before Approach
   • Deliver new content after fully reviewing previously understood content.

A study was performed to determine whether the Meshed or Before approaches to delivering content had any positive benefits on memory recall.

The Experiment

Individuals were seated at a computer and shown a list of words. Words appeared on the screen one at a time, for two seconds each, until all words had been shown (40 total). After all words were shown, they were required to perform a few two-digit mathematical additions (like 15 + 25) for 15 seconds to avoid immediate memory recall of the words. They were then asked to write down as many of the 40 words as they could remember. They were given a maximum of 5.3 minutes to recall words.

The process of showing words and recalling words was repeated four times with the same list of words each time (four chances to get it right). The presentation of the first trial was the same for all treatment conditions. However, trials 2, 3, and 4 were slightly different for each treatment condition.

The SFR group (the control group) stands for Standard Free Recall. In all four trials the same list of 40 words was presented, in a random order each time.

The Before group also used the same 40 words during each trial. However, any words that were correctly recalled in a previous trial were presented first, or before the words that were not recalled in the last trial. After all the correct words were presented in random order, the non-recalled words were presented in a random order.

The Meshed group also used the same 40 words during each trial. However, words that were correctly recalled in a previous trial were alternated with a missed word during the next presentation order.

The data records the number of correctly recalled words (out of the 40 possible) from the fourth trial. Results were obtained for 30 students, 10 in each of the three treatment groups: SFR, Before, and Meshed.

The Data

The results from the study can be found in the Friendly data set in R after loading library(car).

Click the “Code” button to see the data.

datatable(Friendly, options=list(lengthMenu = c(3,10,30)))

Questions and Hypotheses

What type of learning is a better method, Meshed or Before? I think that Meshed learning is better compared to Before learning.

\[ H_0: \text{Before} = 0 \]

\[ H_a: \text{Meshed} > 0 \]

Data Analysis

friendly <- dplyr::filter(Friendly, condition %in% c("Meshed", "Before"))

friendly %>% 
    group_by(condition) %>% 
    summarise(minimum = min(correct),
              average = mean(correct),
              median = median(correct),
              maximum = max(correct)) %>% 
    pander()

condition	minimum	average	median	maximum
Before	24	36.6	39	40
Meshed	30	36.6	36.5	40

First step in analysis is analyzing number. This is done by Numerical Summaries. First filter to the condition of learning. Then create a table with the minimum, average, median, and maximum. These numbers help figure out the values for recalling information.

Graphical Summaries

ggplot(friendly, aes(x = condition, y = correct)) + geom_boxplot() + theme_bw()

The graph shows us that the recall rate is higher with before method then meshed. Although there are more outliers when using the Before method.

Interpretation

wilcox.test(correct ~ condition, data = friendly, mu = 0, alternative = "greater", paired = TRUE, conf.level = 0.95) %>% 
    pander()

Wilcoxon signed rank test with continuity correction: correct by condition

Test statistic	P value	Alternative hypothesis
18	0.528	greater

According to the Wilcoxon test my hypothesis was correct that using the meshed method is better compared to the before method. My P-value is 0.528 which is greater than the confidence interval which is .05. So We will fail to reject the null hypothesis.

We can conclude that meshed learning can be proven more useful compared to before learning. The Numerical and Graphical Summaries conclude that the methods are closely related that statistical tests have to determine the better learning method.