Calculate z-scores from raw values, find the area under the standard normal curve, determine p-values, and look up critical z-values for hypothesis testing.
Z = (X − μ) / σ
Find area from Z
| Metric | Value |
|---|
| z | .00 | .01 | .02 | .03 | .04 | .05 | .06 | .07 | .08 | .09 |
|---|
| Significance (α) | One-tailed z | Two-tailed z |
|---|---|---|
| 0.10 (90% CI) | ±1.282 | ±1.645 |
| 0.05 (95% CI) | ±1.645 | ±1.960 |
| 0.025 | ±1.960 | ±2.240 |
| 0.01 (99% CI) | ±2.326 | ±2.576 |
| 0.001 (99.9% CI) | ±3.090 | ±3.291 |
A z-score (standard score) tells you how many standard deviations a value is from the mean of a distribution. Z-scores allow comparison of values from different datasets.
| Range | % of data (approx.) |
|---|---|
| μ ± 1σ (z = ±1) | 68.27% |
| μ ± 2σ (z = ±2) | 95.45% |
| μ ± 3σ (z = ±3) | 99.73% |
Z-scores are used in ATAR (Australian Tertiary Admission Rank) scaling, where raw subject scores are scaled to a common distribution to ensure fairness across subjects with different levels of difficulty.
A p-value is the probability of observing results at least as extreme as those observed, assuming the null hypothesis is true. Australian statistical practice (following ABS and NHMRC guidelines) generally uses α = 0.05 as the threshold for statistical significance.