Hypothesis testing Hypothesis tests are most often used to make a - - PowerPoint PPT Presentation

Hypothesis testing

Hypothesis tests are most often used to make a statement about superiority, inferiority or equality of treatments. Confidence intervals do contain this information also, but the conclusion is a bit more difficult to extract. The most difficult step in a hypothesis test is setting up the hypothesis.

Thomas Jaki Statistical methods in health research

Innocent until proven guilty

A hypothesis is a statement about a parameter of interest. The null, H0, and the alternative hypothesis, HA, are competing. The null hypothesis is the current believe. The alternative hypothesis reflects what you want to show.

Thomas Jaki Statistical methods in health research

Example

You developed a new migrane pill, you believe relieves more people than the currently used products. Extensive studies on the currently used products show that they help 55% of the patients with migrane. What should your hypothesis be?

Thomas Jaki Statistical methods in health research

Hypothesis testing step by step

1

State the null hypothesis.

2

Decide what test to use and check the assumptions of the test.

3

Calculate the test statistic.

4

Find the probability of observing the test statistic if the null hypothesis is in fact true (p-value).

5

Decide whether this is enough evidence to reject (or not reject) the null hypothesis.

6

State the conclusions and interpretation of the results.

Thomas Jaki Statistical methods in health research

χ2-test - Example

If you have 2 (categorized) variables that you believe are related a Chi-square (χ2) test can be used. A study at the University of Texas Southwestern Medical Center examined 626 people to see if there was an increased risk of contracting hepatitis C associated with having a tattoo. If the subject had a tattoo, researchers asked whether it had been done in a commercial tattoo parlor or elsewhere.

Thomas Jaki Statistical methods in health research

Example - cont.

Observed values Tatoo Hepatitis C Comm Parlor Elsewhere None Total Yes 17 8 18 43 No 35 53 495 583 Total 52 61 513 626

Thomas Jaki Statistical methods in health research

Example - cont.

Expected values Tatoo Hepatitis C Comm Parlor Elsewhere None Total Yes

43∗52 626 = 3.57 43∗61 626 = 4.19

35.24 43 No

583∗52 626

= 48.43

583∗61 626

= 56.81 477.76 583 Total 52 61 513 626

Thomas Jaki Statistical methods in health research

Example - cont.

X2 =

• cells

(observed − expected)2 expected χ2 = (17 − 3.47)2 3.47 + · · · + (495 − 477.76)2 477.76 = 67.43

Thomas Jaki Statistical methods in health research

Example - cont.

The degrees of freedom (df) are (# rows − 1)(# cols − 1) = (2 − 1)(3 − 1) = 2 From the χ2-calculator we find the the cut-off value for 99.9% is 13.82. Since this is much smaller than the calculated value, we can conclude that tatoos and hepatitis are related with 99.9% certainty.

Thomas Jaki Statistical methods in health research

A confidence interval approach

For a 2x2 table, we can also use a confidence interval to test for a difference. Observed values Tatoo Hepatitis C Yes No Total Yes 25 18 43 No 88 495 583 Total 113 513 626

Thomas Jaki Statistical methods in health research

A confidence interval approach - cont.

ˆ p1 = characteristic present group 1 total group 1 = 25 113 = 0.221 ˆ p2 = characteristic present group 2 total group 2 = 18 513 = 0.035

Thomas Jaki Statistical methods in health research

A confidence interval approach - cont.

ˆ d = ˆ p1 − ˆ p2 = 0.221 − 0.035 = 0.186 SE =

• ˆ

p1(1 − ˆ p1) n1 + ˆ p2(1 − ˆ p2) n2 =

• 0.221(1 − 0.221)

113 + 0.035(1 − 0.035) 513 = 0.040

Thomas Jaki Statistical methods in health research

A confidence interval approach - cont.

A 95% confidence interval then is: ( ˆ d − 2 ∗ SE, ˆ d + 2 ∗ SE) (0.186 − 2 ∗ 0.040, 0.186 + 2 ∗ 0.040) (0.106, 0.266) Since zero is not included, we are at least 95% confident that there is a relationship between tattoos and hepatitis.

Thomas Jaki Statistical methods in health research