# Sample size for Chi-square

## Effect size is the difference in proportions between two groups on the outcome

In order to conduct an

When running a sample size calculation for chi-square, it is best to use an evidence-based measure of effect size yielded from a published study that is conceptually or theoretically similar to the study being conducted. Use the reported proportions in a published article to calculate the sample size needed for a chi-square analysis.

For example, let's say that researchers find quality evidence that 85% of people that receive a treatment will have a positive outcome and 70% of people that do not receive the treatment will have a positive outcome. They now have an evidenced-based measure of effect of 15% (85%-70% = 15%). Researchers could enter these values into G*Power and know exactly how many observations of the outcome they would need to collect in order to detect the 15% treatment effect.

*a priori*sample size calculation for a chi-square, researchers will need to seek out evidence that provides the**proportion of people in the treatment group**and**the control group that had the categorical outcome of interest**. The**absolute****difference between these two proportions**is the effect size.When running a sample size calculation for chi-square, it is best to use an evidence-based measure of effect size yielded from a published study that is conceptually or theoretically similar to the study being conducted. Use the reported proportions in a published article to calculate the sample size needed for a chi-square analysis.

For example, let's say that researchers find quality evidence that 85% of people that receive a treatment will have a positive outcome and 70% of people that do not receive the treatment will have a positive outcome. They now have an evidenced-based measure of effect of 15% (85%-70% = 15%). Researchers could enter these values into G*Power and know exactly how many observations of the outcome they would need to collect in order to detect the 15% treatment effect.

### The steps for calculating sample size for a chi-square in G*Power

1. Start up G*Power.

2. Under the

3. Under the

4. Under the Type of power analysis drop-down menu, select

5. If there is a

6. If there is a

7. In the

8. In the

9. Leave the alpha value at

10. Enter

11. If researchers have exactly

2. Under the

**Test family**drop-down menu, select**z test**.3. Under the

**Statistical test**drop-down menu, select**Proportions: Difference between two independent proportions**.4. Under the Type of power analysis drop-down menu, select

**A priori: Compute required sample size - given alpha, power, and effect size**.5. If there is a

**directional hypothesis**, under the**Tail(s)**drop-down menu, select**One**.6. If there is a

**non-directional hypothesis**, under the**Tail(s)**drop-down menu, select**Two**.7. In the

**Proportion p2**box, enter the**proportion of people in the treatment group that will have the outcome**. Example:**".85"**8. In the

**Proportion p1**box, enter the**proportion of people in the control group that will have the outcome**. Example:**".70"**9. Leave the alpha value at

**0.05**, unless researchers want to change the alpha value according to the current empirical or clinical context.10. Enter

**"****.80"**into the**Power (1-beta err prob)**box, unless researchers want to change the power according to the current empirical or clinical context.11. If researchers have exactly

**equally**sized groups, then leave the**Allocation ratio N2/N1**value at**"1."**If researchers have**unequally**sized groups, then divide the sample size of the treatment group by the sample size of the control group and enter that**value**into the box.Using the proportions from the example and the 11 steps above, a two-tailed 15% effect size at an alpha of .05 and 80% with equal sample sizes yields a sample size of

**242**with 121 participants in each group to be able to detect that effect.Click on the

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