In statistical hypothesis testing, the level of significance (α) is a critical concept that determines how much evidence is required to reject the null hypothesis. It defines the probability of making a Type I error—rejecting a true null hypothesis. The selection of α depends on the nature of the data and the type of test being applied, whether parametric or non-parametric.
Meaning of Level of Significance
The level of significance (commonly 0.05 or 0.01) represents the maximum allowable probability of concluding that a difference exists when it does not. It provides the threshold for deciding whether results are statistically significant.
Common Values of α
- 0.05 (5%) – Most widely used in biomedical research.
- 0.01 (1%) – Used when a higher degree of accuracy is required.
- 0.10 (10%) – Rare in medical and pharmaceutical research.
Understanding Parametric and Non-Parametric Data
1. Parametric Data
Parametric data follows a known distribution—usually the normal distribution. These tests assume that data is continuous, numerical, and meets specific statistical assumptions.
Characteristics of Parametric Data
- Normally distributed.
- Equal variance across groups (homogeneity).
- Measured on interval or ratio scale.
- Sample size is generally moderate to large.
Common Parametric Tests
- Student’s t-test (paired and unpaired)
- One-way and Two-way ANOVA
- Pearson correlation
- Regression analysis
Level of Significance in Parametric Tests
Parametric tests rely heavily on the assumptions of normality. Therefore, α is generally set at 0.05 unless more stringent evidence is required. A small p-value (≤ α) indicates that the observed differences are unlikely due to chance alone.
2. Non-Parametric Data
Non-parametric data does not follow a normal distribution. These tests are used for ordinal data, ranked data, small samples, or when assumptions of parametric tests are violated.
Characteristics of Non-Parametric Data
- Does not assume normal distribution.
- Can be used for nominal, ordinal, or skewed interval data.
- Suitable for small sample sizes.
Common Non-Parametric Tests
- Chi-square test
- Sign test
- Wilcoxon signed-rank test
- Mann–Whitney U test
- Kruskal–Wallis test
Level of Significance in Non-Parametric Tests
Non-parametric tests are less powerful than parametric tests because they use fewer assumptions. Therefore, α is usually set at 0.05. However, interpretation relies heavily on sample size and ranking rather than means.
Choosing α for Parametric vs. Non-Parametric Tests
| Type of Data | Common Tests | Typical α |
|---|---|---|
| Parametric | T-test, ANOVA, Pearson correlation | 0.05 or 0.01 |
| Non-Parametric | Chi-square, Sign test, Wilcoxon test | 0.05 |
Importance of Level of Significance
- Determines strictness of statistical decisions.
- Controls Type I error rate.
- Ensures reliability of conclusions in biomedical research.
- Helps interpret p-values objectively.
Example to Illustrate α
A researcher tests whether a new treatment reduces pain better than placebo.
- If p = 0.03 and α = 0.05 → Reject H₀ (significant effect).
- If p = 0.07 and α = 0.05 → Fail to reject H₀ (not significant).
Detailed Notes:
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