Hypothesis testing: the Framework

What is statistical hypothesis testing?

Decision making process for evaluating claims mathematically

Distinguish between results that easily occur or are unlikely

What is a hypothesis

Claim or conjecture that may or may not be true

Two types of hypotheses in a test

Null and alternative

Null hypothesis

Always =, no difference, no change, status quo, written first (on top), H0

Alternative hypothesis

Inequality: not equal, difference or change written second, Ha

Example of null

Drug does not work

Example of alternative hypothesis

Drug works, does decrease level of depression!

do we like null or alt hypothesis in real world?

Alt because we want to see changes

Setup for proportions

H0: p=#

Ha: p=/ #

**number should be the same

what test is used for setup for proportions

Two tailed test

Two possible decisions

Reject the null hypothesis or fail to reject the null hypothesis

reject the null hypothesis

Not the same (significant difference)

fail to reject null hypothesis

Data is not convincing, no sig difference

Testing hypothesis using confidence intervals

Confidence interval: 95% sure real result will be captured in interval

So if result is within confidence interval, null hypothesis is TRUE (fail to reject)

Decision errors

Hypothesis tests are NOT flawless

Type 1 error

Reject null hypothesis when H0 is true

Type 2 error

Failing to reject null hypothesis when it is false

Alpha

probability of making a type 1 error (reject null when it is true)

If making type 1 error, choose

Small significance level (a=0.01) and be careful about rejecting null hypothesis aka demand strong evidence before rejecting null

If type 2 error, choose

Higher significance level (0.10) and be cautious about failing to rject H0 when null is actually false

Hypothesis testing using z score and p value

1. identify parameter, list hypothesis, identify significance level, identify p-hat and n

2. check conditions

3. calculatse z score and identify p value

4. conclusion (compare p value to alpha)

P value

Probability value is z-score area TIMES 2 because it is on both left and right side

If p value < a

Reject a

If p value > a

Fail to reject H0

Let alpha be ___ if not given

.05

why should we use p-value to test hypothesis instead of CI

CI is not always sustainable cuz confidence interval cannot always be constructed