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Chapter 4: Problem 148

Do iPads Help Kindergartners Learn: A Series of Tests Exercise 4.147 introduces a study in which half of the kindergarten classes in a school district are randomly assigned to receive iPads. We learn that the results are significant at the \(5 \%\) level (the mean for the iPad group is significantly higher than for the control group) for the results on the HRSIW subtest. In fact, the HRSIW subtest was one of 10 subtests and the results were not significant for the other 9 tests. Explain, using the problem of multiple tests, why we might want to hesitate before we run out to buy iPads for all kindergartners based on the results of this study.

Short Answer

Expert verified
Despite the result of HRSIW subtest showing a significant difference at 5% level in favor of the iPad group, one should hesitate before concluding that iPads help kindergartners learn. This is because out of 10 tests, it is statistically likely that one may show significance purely by chance at a 5% level. These results should be verified through more stringent methods correcting for multiple tests or by replicating the study before making such decisions.

Step by step solution

01

Understanding the problem

In the given exercise, a study is described in which iPads were given to half of the kindergarten students. This is a common setup for an experimental study where one group (the treatment group) gets a specific intervention (iPads in this case) and another group (the control group) does not. The result is deemed significant if the mean of the treatment group (students with iPads) is significantly higher than the control group (students without iPads). The HRSIW, one of the 10 subtests conducted, showed significant results favouring the iPad group. However, the other 9 tests did not show significant results.
02

Explain the problem of multiple tests

The problem of multiple tests also known as the multiple comparisons problem arises when a series of statistical tests are performed. If we perform multiple tests, the likelihood of encountering a significant result just by chance, even when there is no true effect, increases.
03

Applying the concept of multiple tests to the given problem

In the given scenario, 10 tests were conducted. Even if iPads had no effect on learning, at a significance level of 5%, we would expect 1 out of 20 tests (5% of 20) to be significant purely due to random chance. In other words, the single significant result might be a statistical artefact rather than a real effect of the iPads.
04

Conclusion

Given this, it should be hesitated before making a decision to provide iPads for all kindergartners based solely on these results. More robust statistical methods that correct for multiple testing, should be used to verify these results or the experiment should be replicated before making such decisions.

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Most popular questions from this chapter

Figure 4.25 shows a scatterplot of the acidity (pH) for a sample of \(n=53\) Florida lakes vs the average mercury level (ppm) found in fish taken from each lake. The full dataset is introduced in Data 2.4 on page 71 and is available in FloridaLakes. There appears to be a negative trend in the scatterplot, and we wish to test whether there is significant evidence of a negative association between \(\mathrm{pH}\) and mercury levels. (a) What are the null and alternative hypotheses? (b) For these data, a statistical software package produces the following output: $$ r=-0.575 \quad p \text { -value }=0.000017 $$ Use the p-value to give the conclusion of the test. Include an assessment of the strength of the evidence and state your result in terms of rejecting or failing to reject \(H_{0}\) and in terms of \(\mathrm{pH}\) and mercury. (c) Is this convincing evidence that low \(\mathrm{pH}\) causes the average mercury level in fish to increase? Why or why not?

Using the definition of a p-value, explain why the area in the tail of a randomization distribution is used to compute a p-value.

Euchre One of the authors and some statistician friends have an ongoing series of Euchre games that will stop when one of the two teams is deemed to be statistically significantly better than the other team. Euchre is a card game and each game results in a win for one team and a loss for the other. Only two teams are competing in this series, which we'll call team A and team B. (a) Define the parameter(s) of interest. (b) What are the null and alternative hypotheses if the goal is to determine if either team is statistically significantly better than the other at winning Euchre? (c) What sample statistic(s) would they need to measure as the games go on? (d) Could the winner be determined after one or two games? Why or why not? (e) Which significance level, \(5 \%\) or \(1 \%,\) will make the game last longer?

A confidence interval for a sample is given, followed by several hypotheses to test using that sample. In each case, use the confidence interval to give a conclusion of the test (if possible) and also state the significance level you are using. A \(99 \%\) confidence interval for \(\mu: 134\) to 161 (a) \(H_{0}: \mu=100\) vs \(H_{a}: \mu \neq 100\) (b) \(H_{0}: \mu=150 \mathrm{vs} H_{a}: \mu \neq 150\) (c) \(H_{0}: \mu=200\) vs \(H_{a}: \mu \neq 200\)

Significant and Insignificant Results (a) If we are conducting a statistical test and determine that our sample shows significant results, there are two possible realities: We are right in our conclusion or we are wrong. In each case, describe the situation in terms of hypotheses and/or errors. (b) If we are conducting a statistical test and determine that our sample shows insignificant results, there are two possible realities: We are right in our conclusion or we are wrong. In each case, describe the situation in terms of hypotheses and/or errors. (c) Explain why we generally won't ever know which of the realities (in either case) is correct.
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