P Score Calculator 2 Prop Z Test TI 84

Two Proportion Z-Test Formula:

\[ z = \frac{(\hat{p}_1 - \hat{p}_2)}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1} + \frac{1}{n_2})}} \] \[ P = 2 \times (1 - \text{normcdf}(|z|)) \]

P-value (two-tailed):

Z-score:

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1. What is the Two Proportion Z-Test?

The two proportion z-test compares proportions from two independent groups to determine if they are statistically different. The P-value calculated represents the probability of observing such a difference if the null hypothesis (no difference) were true.

2. How Does the Calculator Work?

The calculator uses the two proportion z-test formula:

\[ z = \frac{(\hat{p}_1 - \hat{p}_2)}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1} + \frac{1}{n_2})}} \] \[ P = 2 \times (1 - \text{normcdf}(|z|)) \]

Where:

\( \hat{p}_1 \) — Sample proportion of group 1 (x1/n1)
\( \hat{p}_2 \) — Sample proportion of group 2 (x2/n2)
\( \hat{p} \) — Pooled proportion ((x1+x2)/(n1+n2))
\( n_1, n_2 \) — Sample sizes of each group
normcdf — Standard normal cumulative distribution function

Explanation: The z-score measures how many standard deviations the observed difference is from zero. The P-value is calculated as the two-tailed probability from the standard normal distribution.

3. Interpretation of Results

Details: A small P-value (typically ≤ 0.05) suggests strong evidence against the null hypothesis, indicating a statistically significant difference between the two proportions.

4. Using the Calculator

Tips: Enter the number of successes (x1, x2) and sample sizes (n1, n2) for both groups. The calculator will compute the z-score and two-tailed P-value.

5. Frequently Asked Questions (FAQ)

Q1: When should I use this test?
A: Use when comparing proportions from two independent groups with sufficiently large sample sizes (n*p and n*(1-p) > 5 for each group).

Q2: What's the difference between one-tailed and two-tailed tests?
A: This calculator provides two-tailed P-values. For one-tailed tests, divide the P-value by 2 if your alternative hypothesis is directional.

Q3: How does this relate to TI-84 calculations?
A: The formula matches the 2-PropZTest function on TI-84 calculators, which computes P-values using normcdf.

Q4: What are common significance levels?
A: Typical thresholds are 0.05, 0.01, or 0.001, depending on the field of study and desired confidence level.

Q5: Can I use this for small sample sizes?
A: For small samples (n < 30) or when expected counts are <5, consider Fisher's exact test instead.