Ever got a question about “Which statistical test should I apply in this problem?”
It’s a fair question. With so many tests such as Z, T, ANOVA, Chi-square, non-parametric options the decision can feel overwhelming.
But the key is about clarity on understanding when a test is appropriate and why.
Parametric vs Non-Parametric Tests
Statistical tests are broadly grouped into two families:
- Parametric Tests: These assume that the data follows a particular distribution (usually normal). They’re more powerful when assumptions hold true.
- Non-Parametric Tests: These don’t rely on strict distributional assumptions. They work with ranks or categories, making them robust when data is skewed, ordinal, or when sample sizes are small.
Quick thought: If the data looks symmetrical and you know standard deviations, parametric tests shine. If not, non-parametric tests step in as reliable alternatives.
Z-test vs T-test
Both tests compare means, but the context differs:
- Z-test: Used when population variance is known and sample size is large (n ≥ 30). Example: Testing if the average height of 500 students differs from the national mean when variance is known.
- T-test: Applied when population variance is unknown and sample size is small (n < 30). Example: Comparing average marks of 20 commerce students to a hypothesized population mean.
The logic is similar. The difference lies in whether we know the population standard deviation. If we don’t, we rely on the t-distribution.
ANOVA vs Kruskal–Wallis
Suppose you want to compare more than two groups. Which tool do you use?
- ANOVA (Analysis of Variance): Parametric test comparing means across three or more groups. Assumes normality and equal variances.
- Kruskal–Wallis Test: Non-parametric alternative to ANOVA. Works on ranks instead of raw values. Ideal when the data is skewed or doesn’t meet ANOVA assumptions.
Example: A researcher comparing average test scores across three teaching methods would use ANOVA if scores are normally distributed, or Kruskal–Wallis if scores are not.
Pearson Correlation vs Spearman Rank Correlation
Both measure relationships, but the nature of data dictates the choice:
- Pearson Correlation: Measures the strength and direction of linear relationships between two continuous variables. Sensitive to outliers.
- Spearman Rank Correlation: Based on ranks. Suitable for ordinal data or non-linear monotonic relationships. Robust against extreme values.
Example: To check the relation between study hours and marks, Pearson is appropriate. To study the relation between job rank and satisfaction level, Spearman is better.
Choosing the Right Test
| Scenario | Parametric Test | Non-Parametric Alternative |
|---|---|---|
| Compare sample mean with population mean (large n, known variance) | Z-test | – |
| Compare sample mean with population mean (small n, unknown variance) | T-test | Mann–Whitney U (for two independent samples) |
| Compare means of more than two groups | ANOVA | Kruskal–Wallis |
| Association between two categorical variables | Chi-Square Test of Independence | Fisher’s Exact Test (for small samples) |
| Measure correlation (linear, continuous data) | Pearson Correlation | Spearman Rank Correlation |
Every statistical test is a tool, and like any tool, it must fit the task. Ask yourself: What kind of data am I working with? Do assumptions like normality hold? Am I comparing means, associations, or ranks?
Once you answer those questions, the choice of test almost reveals itself. The real skill lies in matching method with situation. So the next time you face a problem, pause for a second and think
“What story is my data trying to tell?”
Let the right test guide you to the answer.