Recalling Words

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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 (click to view)

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 (click to view)

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)))

Hypothesis

On paper, it appears as though there isn’t much of a logical reason as to why one of the two proposed approaches should differ in results from another. With that in mind, the following hypothesis has been made: There is not a significant difference in the results of the Before and Meshed categories.

\[H_0: \text{difference in medians of Before and Meshed approaches = 0}\] \[H_a: \text{difference in medians of Before and Meshed approaches} \neq 0\]

Data Analysis

By performing a Wilcoxon rank sum test, we can see if there is sufficent evidence to reject our hypothesis. The test will be preformed with a 0.95 confidence level (\(\alpha = 0.05\)).

wilcox.test(Friendly$correct[Friendly$condition == 'Meshed'], Friendly$correct[Friendly$condition == 'Before']) %>% 
  pander(caption="Wilcoxon rank some test with continuity correction (there are ties in the data)")

Wilcoxon rank some test with continuity correction (there are ties in the data)

Test statistic	P value	Alternative hypothesis
38	0.378	two.sided

The notches on the box plot below show the range of significance for the data; they act as a visual representation of where a p-value would be significant or insignificant.

ggplot(Friendly, aes(
  x= condition,
  y= correct,
  fill= condition)) +
  geom_boxplot(fill= c('cyan3', 'cyan', 'gray'), color= 'black',
               notch=TRUE, width= 0.4) +
  geom_dotplot(binaxis= 'y', position= 'dodge', stackdir='center',
               binwidth = 0.5) +
  scale_fill_manual(values=c("cyan", "cyan3", "lightgray")) +
  labs(title="Recalling Words Test",
       x= "Testing Methods",
       y= "Final Score") +
  theme_light() +
  theme(legend.position= 'none')

We can immediately see significant differences between the first two methods and SFR; however, the same can’t be said for our first two methods alone.

Numerical Summary

favstats(correct ~ condition, data = Friendly)[,-10] %>% 
  pander(caption= "Box-Plot Statistics")

Box-Plot Statistics

condition	min	Q1	median	Q3	max	mean	sd	n
Before	24	37.25	39	39.75	40	36.6	5.337	10
Meshed	30	36	36.5	38.75	40	36.6	3.026	10
SFR	21	25	27	38.5	39	30.3	7.334	10

Let’s look at our test results:

Conclusion

The Wilcoxon test resulted in a p-value of 0.378, which is more than our alpha value, 0.05. Thus there is insufficient evidence to reject our null hypothesis; there is no significant difference between using either the Before or Meshed learning methods. We can see that their median values are quite similar: \(\text{Meshed} = 36.5\) words correctly recalled, \(\text{Before} = 39\) words correctly recalled. Outside of that, it is clear that these two methods are superior to the SFR method \(\text{(median}=27\text{ words correctly recalled)}\) and at least one of them should be used in learning models as opposed to simply randomizing the order of learning material.