- To determine if the population rate/proportion behind your data is significantly different from the specified rate/proportion
- To determine how compatible the sample rate/proportion with a population rate/proportion
- To determine the probability of success in a Bernoulli experiment

- Your data come from binomial distribution (the proportion of success)
- You know the whole sample and the number of specified events (the proportion of sub-group)
- You have a specified proportion (p
_{0})

- P Value < 0.05, then the population proportion/rate IS significantly different from the specified proportion/rate. (Accept the alternative hypothesis)
- P Value >= 0.05, then the population proportion/rate IS NOT significantly different from the specified proportion/rate. (Accept the null hypothesis)

- To determine if the population rate/proportion behind your 2 groups data are significantly different

- Your 2 groups data come from binomial distribution (the proportion of success)
- You know the whole sample and the number of specified events (the proportion of sub-group) from 2 groups
- The 2 groups are independent observations

**Data Table**

**Percentage Plot of**

**1. Case**

**2. Control**

- P Value < 0.05, then the population proportion/rate are significantly different in two groups. (Accept alternative hypothesis)
- P Value >= 0.05, then the population proportion/rate are NOT significantly different in two groups. (Accept null hypothesis)

- To determine if the population rate/proportion behind your multiple group data are significantly different

- Your group data come from binomial distribution (the proportion of success)
- You know the whole sample and the number of specified events (the proportion of sub-group) from each group
- The multiple groups are independent observations

**Data Table**

- P Value < 0.05, then the population proportion/rate are significantly different. (Accept the alternative hypothesis)
- P Value >= 0.05, then the population proportion/rate are NOT significantly different. (Accept the null hypothesis)

*In this default setting, we concluded that the probability of have cancer was significantly different in different age groups. (P < 0.001)*

- To determine if the population rate/proportion behind your multiple group data vary

- Your group data come from binomial distribution (the proportion of success)
- You know the whole sample and the number of specified events (the proportion of sub-group) from each group
- The multiple groups are independent observations

**Data Table**

**Cell-Column %**

- P Value < 0.05, then Case-Control (Row) is significantly associated with grouped Factors (Column) (Accept the alternative hypothesis)
- P Value >= 0.05, then Case-Control (Row) is not associated with grouped Factors (Column). (Accept the null hypothesis)

*In this default setting, we concluded that the proportion of cancer varied among different ages. (P = 0.01)*