To Study Effectively, Test Yourself! Cognitive science...

To Study Effectively, Test Yourself! Cognitive science consistently shows that one of the most effective studying tools is to self-test. A recent study $^{10}$ reinforced this finding. In the study, 118 college students studied 48 pairs of Swahili and English words. All students had an initial study time and then three blocks of practice time. During the practice time, half the students studied the words by reading them side by side, while the other half gave themselves quizees in which they were shown one word and had to recall its partner. Students were randomly assigned to the two groups, and total practice time was the same for both groups, On the final test one week later, the proportion of items correctly recalled was $15 \%$ for the reading-study group and $42 \%$ for the self-quiz group. The standard error for the difference in proportions is about 0.07 . Test whether giving self-quizzes is more effective and show all details of the test. The sample size is large enough to use the normal distribution.

Key Concepts

P-value and Significance

The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the value obtained under the null hypothesis. It is used to decide whether the observed effect is statistically significant. A low p-value (below a predetermined significance level, such as 0.05) indicates that the observed difference is unlikely to have occurred by random chance, leading to the rejection of the null hypothesis in favor of the alternative hypothesis.

Z-Test for Proportions

A Z-test for proportions is used when the sample size is large enough for the normal approximation to the binomial distribution to be valid. In this question, the test compares the difference between two proportions (the fraction of correct recalls from each group) by calculating a Z statistic. This statistic quantifies how many standard errors the observed difference is away from the hypothesized difference under the null hypothesis.

Standard Error

The standard error is a measure of the variability or uncertainty in the estimation of a population parameter, in this case, the difference between two proportions. It helps determine how much the estimate is expected to fluctuate from sample to sample. In the problem, a standard error of 0.07 is provided, which is used in calculating the Z statistic by comparing the observed difference to this measure of sampling variability.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about population parameters based on sample data. In the context of this question, it involves formulating a null hypothesis, which typically represents no difference in effect between the two study methods (self-testing versus passive reading), and an alternative hypothesis, which asserts that one method (self-testing) is more effective. The process includes calculating a test statistic, comparing it to a critical value from the assumed distribution (in this case, the normal distribution), and determining whether to reject the null hypothesis.

Null and Alternative Hypotheses

The null hypothesis (H?) generally posits that there is no effect or no difference between two compared groups, meaning that the proportion of correct recalls would be equal for both groups. The alternative hypothesis (H?) specifies the condition under investigation – here, it is that the self-testing group’s proportion of correct responses is higher than that of the passive reading group. Clearly defining these hypotheses is a critical step in conducting a proper significance test.

Transcript

00:01 So we have cognitive science consistently shows that one of the most effective studying tools is to self -test.

00:08 So we had a recent study, and in that study there were 118 individuals involved, and they were split equally into two different groups.

00:21 So we had 59 in one group and 59 in another group.

00:27 And one of the groups self -quizzed, and the other group did reading and studying.

00:40 And it was determined that on the final test one week later, the proportion of items correctly recalled was 15 % for the reading study group.

00:54 So that would be our p hat.

00:59 And it was 42 % for the self -quiz group.

01:11 The standard error for the difference was 0 % percent.

01:22 0 .07.

01:25 And our question here is whether giving self -quises is more effective.

01:31 So we're trying to test the claim whether the proportion of individuals after self -quizzing was greater than if they just read and studied.

01:46 So we will have to write our null and alternative hypotheses.

01:53 And since our question that we are trying to run the hypothesis on is a greater than scenario.

02:03 That would be our alternative hypothesis because it does not have a statement of equality.

02:11 So our null hypothesis is that there's no difference between the two different techniques, reading, studying, or self -quizzing.

02:23 So as i look at this alternative hypothesis, i see a greater than symbol so i know that this is going to be a right -tailed test.

02:35 So the first thing i need to do is i need to calculate my standardized test statistic.

02:40 And i will do that by finding the difference between our sample proportions.

02:52 And then i'm going to subtract that from that the difference of our population proportions of the two groups.

02:58 And i'll divide it by the standard error of the difference.

03:07 So the values i have, i have the p hat for the self -quizzing group to be 0 .42.

03:17 I have the p hat for the reading study group to be 0 .15.

03:24 And if i were to look back at my null hypothesis, this says that they could be equal...

Please give Ace some feedback