Answer to Question #266588 in Operations Research for Jess

Question

Describe how you would conduct Hypothesis testing in detail. Include the information that you need in order to conduct the hypothesis test and give as many examples of the different situations/questions you can have.

Answer 1

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

1. State your research hypothesis as a null (H_o) and alternate (H_a) hypothesis.
2. Collect data in a way designed to test the hypothesis.
3. Perform an appropriate statistical test.
4. Decide whether to reject or fail to reject your null hypothesis.
5. Present the findings in your results and discussion section.

for example:

You want to test whether there is a relationship between gender and height. Based on your knowledge of human physiology, you formulate a hypothesis that men are, on average, taller than women.

To test this hypothesis, you restate it as:

H_o: Men are, on average, not taller than women.

H_a: Men are, on average, taller than women.

To test differences in average height between men and women, your sample should have an equal proportion of men and women, and cover a variety of socio-economic classes and any other variables that might influence average height.

There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).

If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p-value. This means it is unlikely that the differences between these groups came about by chance.

Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p-value. This means it is likely that any difference you measure between groups is due to chance.

Your choice of statistical test will be based on the type of data you collected.

Based on the type of data you collected, you perform a one-tailed t-test to test whether men are in fact taller than women. This test gives you:

• an estimate of the difference in average height between the two groups.
• a p-value showing how likely you are to see this difference if the null hypothesis of no difference is true.

Your t-test shows an average height of 175.4 cm for men and an average height of 161.7 cm for women, with an estimate of the true difference ranging from 10.2cm to infinity. The p-value is 0.002.

Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.

In most cases you will use the p-value generated by your statistical test to guide your decision. And in most cases, your cutoff for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.

In your analysis of the difference in average height between men and women, you find that the p-value of 0.002 is below your cutoff of 0.05, so you decide to reject your null hypothesis of no difference.

In our comparison of mean height between men and women we found an average difference of 14.3cm and a p-value of 0.002; therefore, we can reject the null hypothesis that men are not taller than women and conclude that there is likely a difference in height between men and women.