Free · Probability and statistical models

Two Proportion Comparison with Pooled Z Score

Compare two independent observed conversion proportions using a pooled normal test.

  • Formula & worked example
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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

Twenty conversions in 100 versus forty in 100 give proportions 0.2 and 0.4 and pooled proportion 0.3.

z = (p1−p2)/√(p(1−p)(1/n1+1/n2))

Worked example

Enter these known values and leave the other values blank.

Sample size
100
# of positive results
20
Sample size
100
# of positive results
40
Conversion rate
20 %
Conversion rate
40 %
Z-score
-3.086
Alpha level's z-score
1.96

Assumptions and limitations

  • Groups are independent and assignments are fixed before observing the results.
  • The pooled normal test requires adequate expected successes and failures in both groups.
  • The comparative error is an unpooled normal margin in percentage points. Statistical significance does not measure practical benefit.

Common questions

What should I check before using this result?

Groups are independent and assignments are fixed before observing the results.

References

Enforce the mathematical input domain and include valid zero boundaries while preserving the captured arithmetic and control graph.

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