Testing Hypotheses about Proportions

To make informed decisions from data..

we test hypotheses to convince that there’s been a difference

Null Hypothesis (H0)

Starting hypothesis to be tested; null because it assumes nothing has changed and it specifies a parameter

Alternative Hypothesis (HA)

Range of values that contains all the other values of the parameter that we’d consider plausible if we reject the null hypothesis

If we have reasonable doubt..

we reject the null hypothesis and say there’s evidence of the alternative hypothesis

If we don’t have enough evidence to reject our null hypothesis in favor of the alternative..

we FAILED TO REJECT the null

P-Value

Value which we base our decision (probability of seeing unlikely data given that the null hypothesis is true)

Low P-value

Reject null hypothesis in favor of alternative hypothesis, null isnt false, just that we have evidence that suggests that

High p-value

Data are consistent with the model from null hypothesis, no reason to reject it

One sided alternative

having only a single sided inequality p>H0 and/or p< H0

Double-sided alternative

only care that p is different (p doesnt equal H0)

To run a Hypothesis Test (PHANTOMS)

• P: state your parameter of interest

• H:State your Hypotheses (H0 and HA)

• A: Assumptions and Conditions

• N: Name your test and model used

• T: Obtain test statistic

• O: Obtain p-value

• M: Make a decision to reject H0 or not

• S: State your conclusion in context (There is/not strong evidence that % of… does not = start %)

one-proportion z-test

Use when assumptions and conditions are met to use a Normal Model for sampling distribution of proportions)

6 Principles of underlying the proper interpretation of p-values

1. P-values can indicate how incompatible data are with a specified statistical model

2. P-values dont measure the probability that the studied hypothesis is true or the probability data were produced by random chance alone

3. Scientific conclusions and business or policy decisions shouldnt be based only on whether a p-value passes a specific threshold

4. Proper inference requires full reporting and transparency

5. A p-value or statistical significance doesnt measure the size of an effect or the importance of a result

6. By itself, a p-value doesnt provide a good measure of evidence regarding a model or hypothesis

What can go wrong?

• Dont base H0 and HA on what’s seen from data

• Dont make H0 what you want to be true

• Dont forget to check your conditions

• Dont say that your proved the HA

• Dont think a larger sample will cause a previously not reject H0 to be rejected