Hypothesis Testing: P-values

Hypothesis

-declarative sentence NOT A QUESTION

-describes a relationship between 2 or more variables

-must be testable

a process that guides decisions based on data collected from a sample

What is hypothesis testing?

hypothesis testing steps

1) Making an initial assumption

2) Collecting evidence (sample data)

3) Based on the available evidence (sample data), deciding whether to reject or not reject the initial assumption

Null hypothesis (Ho)

-currently accepted value for a parameter

-Generally formulated as no relationship between variables or no difference between groups on some variable

Alternative hypothesis (Ha)

-also called research hypothesis that involves the claims to be tested

-Generally formulated as the opposite of the null hypothesis (there is a relationship or a difference)

null

What hypothesis do we test?

two-tailed

Tests of ___________ hypotheses are more common in the biomedical literature.

Type I error (alpha error)

•Rejecting the null hypothesis when the null hypothesis is actually true

•"a false positive decision"

Type II error (beta error)

•Failing to reject the null hypothesis when the null hypothesis is actually false

•"a false negative decision"

Type I error

A fire alarm ring when there is no fire

Type II error

An alarm fails to sound when there is a fire

Type I error

the defendant is innocent, but they are convicted and sentenced

Type I error

Drug X does not relieve condition and is not eliminated as a treatment option

Type II error

The defendant is guilty, and they are not sentenced or convicted

Type II error

Drug X relieves condition and is eliminated as a treatment option

traditional approach to hypothesis testing

1) convert your RQ into Ho and Ha

2) Select the appropriate stats test

3) Select the desired level of significance and critical value for test stat

4) Calculate the test stat

5) Compare the test stat to the critical value and draw conclusions

P-value

are the actual probabilities calculated from a statistical test, and are compared against a to determine whether to reject the null hypothesis or not

reject null hypothesis

If your alpha is greater than your p value what do you do?

fail to reject null hypothesis

If your alpha is less than your p value what do you do?

true

P value is the probability of obtaining, When Ho is _________, a value of the test stat as extreme or more extreme than the one actually computed. (it doesnt tell us Ho is true)

statistical incompatibility

The smaller the p value, the greater the _____________ of the data with the null hypothesis.

stronger

The smaller the p value, the ___________ the evidence for rejecting the null hypothesis.

0.05

What is alpha that we need to memorize?

-probability of Ho being true

-size of the effect

-whether something is practically, economically, scientifically, or clinically significant

P value does NOT tell us:

reject Ho

If alpha is 0.05 and the P value is 0.053 what do we do?

fail to reject Ho

If the alpha is 0.05 and the p value is 0.361 what do we do?

reject Ho

If the alpha is 0.05 and the p value is 0.005 what do we do?