T-Score and P-Value Calculator
Here’s a concise overview of T-scores and P-values, presented in a table format:
| Aspect | T-Score | P-Value |
|---|---|---|
| Definition | Number of standard deviations from the mean in a t-distribution | Probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true |
| Purpose | Measures the size of the difference relative to variation in sample data | Indicates the strength of evidence against the null hypothesis |
| Range | Can be positive or negative; typically between -3 and +3 | Always between 0 and 1 |
| Interpretation | Larger absolute values indicate greater difference from null hypothesis | Smaller values indicate stronger evidence against null hypothesis |
| Calculation | (Sample statistic – Hypothesized value) / Standard error | Derived from t-score and degrees of freedom using t-distribution |
| Relationship | As absolute t-score increases, p-value decreases | As p-value decreases, absolute t-score increases |
| Usage | Used to calculate confidence intervals | Used to determine statistical significance |
| Critical values | Determined by degrees of freedom and significance level | Typically compared to predetermined significance level (e.g., 0.05) |
Key Points
- T-scores measure the difference between observed and expected values in units of standard error.
- P-values represent the probability of obtaining results as extreme as observed, assuming the null hypothesis is true.
- A larger absolute t-score corresponds to a smaller p-value, indicating stronger evidence against the null hypothesis.
- T-scores can be converted to p-values using t-distribution tables or statistical software.
- Both t-scores and p-values are essential in hypothesis testing and statistical inference.
Remember that interpreting these values requires consideration of the context, sample size, and chosen significance level for your specific statistical test.