When do you use Hypothesis Tests for Proportions?

You would use a Hypothesis test for proportion when you’re asked about the difference between two variables.

What is Needed to Run a Hypothesis Test for Proportions?

• Simple, random sampling
• Just (2) possible outcomes.
• Label 1 outcome a success, the other a failure.
• Have at least 10 successes and 10 failures
• Finally, the population is 20 times as large as the sample size.

How to do a Hypothesis Test for Proportions

Step 1: Write the Hypothesis and decide which type of tailed test you need.

We’ve covered hypothesis writing earlier. It’s very easy when writing Proportion tests.

Just remember that the null hypothesis ALWAYS includes some kind of equals. (Ex =, <=, or >=)

Furthermore, an alternative hypothesis is a statement that there is a relationship between two variables, a difference between two groups, or a difference from a previous or existing standard.

Let’s move on to the kind of tailed test.

One tail

If you want to reject if something is too small or too big, you’re doing a one-tail test.

But which tail?

Left tail vs. Right tail

Left tail: alternative hypothesis expresses ‘less than.’

Right tail: alternative hypothesis expresses “greater than”

Two tail

For example, If the alternative hypothesis has l=

Step 2: Compute the Standard Deviation (of the sample!)

σ = sqrt[ P *(1 – P)/n]

where P is the hypothesized value of population proportion in the null hypothesis, and n is the sample size.

Step 3: Compute the test statistic

The test statistic is a z-score (z) defined by the following equation.

z = (p – P)/σ

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and σ is the standard deviation of the sampling distribution.

Step 4: Find the P value

The P-value is the probability of observing a sample statistic as extreme as the test statistic. Since the test statistic is a z-score, use that process to assess the probability associated with the z-score.

Step 5: Interpret your results

Given the null hypothesis, the researcher rejects the null hypothesis if the sample findings are unlikely. Typically, this involves comparing the P-value to the significance level and rejecting the null hypothesis when the P-value is less than the significance level.

Hypothesis Tests Master Index

Helpful Links:

Statistics References
IASSC Equation Guide

Distribution Test Hubs

• General Z
• T
• General F
• General Chi (x)

Hypothesis Tests Listing

• Means Test
  • One Sample
    • Students t (test 2 tail, left, right)
    • One Sample z (test 2 tail, left, right)
  • Two Samples
    • Paired t (test 2 tail, left, right)
    • Two Sample Z Tests
      • Equal Variance
        • 2 Mean, Equal Variance (discuss pooled s) z (test 2 tail, left, right)
      • Unequal Variance
        • 2 Mean, Unequal Variance z (test 2 tail, left, right)
    • Two Sample T-Tests
      • Equal Variance
        • 2 Mean, Equal Variance (discuss pooled s) z (test 2 tail, left, right)
      • Unequal Variance
        • 2 Mean, Unequal Variance z (test 2 tail, left, right)

• Variance Tests
  • Continuous Data
    • Population
      • Chi-Square Hypothesis Tests
        • The Chi-Square Test (Variance, not Proportions)
        • Chi-Square Test of Independence (Comparing observations)
    • Samples
      • F-Test

• Proportion Tests
  • Discrete Data
    • BinomialP-Test
  • Continuous Data
    • Single Sample Test Of a Given Proportion
    • Two Sample Tests of Proportions
  • Other
    • Observational Frequency
      • Chi-Square Test of Proportion

• Goodness of Fit (all using Chi-Square)
  • Normal Goodness of Fit
  • Poisson Goodness of Fit
  • Binomial Goodness of Fit
  • Uniform Goodness of Fit

• Confidence Intervals
  • Confidence Interval for Variation
    • Chi-Square
  • Confidence Interval for
    • Means
    • Proportion
    • Proportion (Interval for two Proportions)
  • p test using Z

Additional Helpful Hypothesis Testing Study Guide Videos

Introduction to Hypothesis Testing

How to Choose Which Hypothesis Test to Use

Beyond Normal: Non-Parametric Hypothesis Tests

Finally, Black belt candidates are widely expected to be conversant in non-parametric hypothesis testing across all three types; Means, Variance, and Proportion.

Here are the specific requirements for each:

Six Sigma Green Belts

Also see, IASSC Six Sigma Green Belt BOK requires:

3.5 Hypothesis Testing with Non-Normal Data
3.5.1 Mann-Whitney
3.5.2 Kruskal-Wallis
3.5.3 Mood’s Median
3.5.4 Friedman
3.5.5 1 Sample Sign
3.5.6 1 Sample Wilcoxon

Six Sigma Black Belts

The ASQ Six Sigma Black Belt BOK requires:

Also see Non-parametric tests
Select, develop and use various non-parametric tests, including Mood’s Median, Levene’s test, Kruskal-Wallis, and also Mann-Whitney, etc. (Evaluate)

The IASSC Six Sigma Black Belt BOK requires:

Hypothesis Testing with Non-Normal Data
3.5.1 Mann-Whitney
3.5.2 Kruskal-Wallis
3.5.3 Mood’s Median
3.5.4 Friedman
3.5.5 1 Sample Sign
3.5.6 1 Sample Wilcoxon

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