Hypothesis Testing. Applying the Concepts

Transcription

1 Hypothesis Testing Applying the Concepts

2 This video is designed to accompany Module 3 in Beyond the Numbers Student-Centered Activities for Learning Statistical Reasoning a publication of the Van-Griner Publishing Company

3 Multivitamins and Cancer

4 Article Analysis: Roll the DISE When you see statistically significant or not statistically significant you should assume a Type I error rate of 0.05 (unless told otherwise) and: 1. DESCRIBE the comparison being made. 2. IDENTIFY the null and an alternative hypotheses.

5 Article Analysis 3. STATE the outcome of the comparison. 4. EXPLAIN the risk associated with the decision made.

6 Multivitamins and Cancer 1. DESCRIBE: Number of cancers seen in group taking multivitamins and the number of cancers seen in group taking placebo. 2. IDENTIFY: In terms of H0 and HA: a) H0: Number of cancers in vitamin group is same as in placebo group. b) HA: Number of cancers in vitamin group is less than in placebo group.

7 Multivitamins and Cancer 3. STATE: Results were statistically significant so you know that the decision was to accept HA, that multivitamin usage reduces cancer risk. 4. EXPLAIN: There is always a chance that this was the wrong decision, that the multivitamins are not effective at reducing cancer risk. We know that this risk is quantified by the Type I error rate.

8 Subway versus McDonalds

9 Subway Versus McDonald s 1. DESCRIBE: Calories consumed by teens at Subway and those consumed by teens at McDonald s. 2. IDENTIFY: In terms of H0 and HA: a) H0: Number of calories consumed by teens at Subway is the same as at McDonald s. b) HA: Number of calories consumed by teens at Subway is less than at McDonald s.

10 Subway Versus McDonald s 3. STATE: Results were NOT statistically significant so you know that the decision was to not accept HA, so no evidence that Subway is a practically healthier food choice for teens. 4. EXPLAIN: There is always a chance that this was the wrong decision. But the preset Type I error rate of 0.05 helps to quantify that risk.

11 Mental Illness and Obesity

12 Mental Illness and Obesity 1. DESCRIBE: Weight before and after patients complete fitness program for mentally ill. 2. IDENTIFY: In terms of H0 and HA: a) H0: Weight before fitness program is no different than weight after fitness program b) HA: Weight before fitness program is less than weight after fitness program.

13 Mental Illness and Obesity 3. STATE: Results were statistically significant so you know that the decision was to accept HA, that the fitness programs to lead to weight loss. 4. EXPLAIN: There is always a chance that this was the wrong decision, that the fitness programs are not effective at reducing weight in the larger population. We have set this risk level to be 5 chances in 100.

14 Presidential Payment

15 Presidential Pay 1. DESCRIBE: Presidential pay at low achieving universities and Presidential pay at high achieving universities 2. IDENTIFY: In terms of H0 and HA: a) H0: There is no correlation between Presidential pay and Performance of a University. b) HA: There is a positive correlation between Presidential pay and the Performance of a University.

16 Presidential Pay 3. STATE: Results were NOT statistically significant so you know that the decision was to not accept HA, so no evidence that universities that pay their Presidents more get better results in terms of performance. 4. EXPLAIN: The risk of going with HA when H0 might have been true was estimated to exceed the preset Type I error rate of 5 chances in 100. So HA was not chosen.

17 Streaks and Basketball

18 Streaks and Basketball 1. DESCRIBE: Streaks of free throw successes versus what player would make at random. 2. IDENTIFY: In terms of H0 and HA: a) H0: Streaks ( Runs ) are no longer than would be expected by random chance. b) HA: Streaks ( Runs ) are longer than would be expected by random chance.

19 Streaks and Basketball 3. STATE: Results were statistically significant so you know that the decision was to accept HA, that there is evidence streaks are longer than expected by random chance. 4. EXPLAIN: There is always a chance that this was the wrong decision, that the streaks are not longer than random chance in the larger population. We know that in this case that risk was set to be 5 chances in 100 and the study data met that requirement.

20 One-Sentence Reflection To understand the usage of statistical significance in the media, always DESCRIBE what is being compared, IDENTIFY the null and alternative, STATE how the comparison turned out, and EXPLAIN what risks were involved in the decision that was made.