Statistics are the arrangement of statistical tests which analysts use to make inference from the data given. These tests enables us to make decisions on the basis of observed pattern from data. There is a wide range of statistical tests. The choice of which statistical test to utilize relies upon the structure of data, the distribution of the data, and variable type.

1. Parametric statistical test

Parametric tests are used if the data is normally distributed .A parametric statistical test makes an assumption about the population parameters and the distributions that the data came from.

a) Z-Test

• Used when the sample size is large ($n\ge 30$).
• Assumes that the population variance is known.
• Common uses:
  • Testing the population mean ($\mu$) when the standard deviation ($\sigma$) is known.
  • Comparing two population means.

b) T-Test

• Used when the sample size is small (n < 30).
• Population variance is unknown.
• Types:
  • One-sample t-test: Compares the sample mean with the population mean.
  • Independent (two-sample) t-test: Compares means of two independent groups.
  • Paired t-test: Compares means of the same group before and after an intervention.

c) ANOVA (Analysis of Variance) (F-Test)

• Used to compare means of three or more groups.
• Assumes normal distribution and equal variances.
• Types:
  • One-way ANOVA: Compares one independent variable (e.g., effect of different teaching methods on student scores).
  • Two-way ANOVA: Examines two independent variables simultaneously.

2. Non parametric statistical test

Non parametric tests are used when data is not normally distributed. Non parametric tests include chi-square test.

a) Chi-Square Test (χ² Test)

• Used for categorical data (counts, proportions).

• Compares observed vs. expected frequencies.

• Common Uses:

  • Chi-square goodness-of-fit test: Checks if sample data fits a particular distribution.

  • Chi-square test for independence: Tests relationships between categorical variables.

b) Mann-Whitney U Test (Alternative to Independent t-test)

• Compares two independent groups when data is not normally distributed.

c) Wilcoxon Signed-Rank Test (Alternative to Paired t-test)

• Used for paired (dependent) samples when normality assumption is not met.

d) Kruskal-Wallis Test (Alternative to ANOVA)

• Compares three or more independent groups when data is not normally distributed.

e) Spearman’s Rank Correlation (Alternative to Pearson’s Correlation)

• Measures the strength and direction of association between two ranked variables.

f) Friedman Test (Alternative to Repeated Measures ANOVA)

• Used for analyzing repeated measures data that is not normally distributed.

📝 Note:

As the UGCNET Management exam questions are 2 marks based, whenever the question is asked in the exam about the statistical tests, it is only surface level. This table helps in solving such questions easily.

1. Memorize the below table by heart.
2. We have to determine which test is applicable based on the given parameters in the table below”