Question

The test which is used to determine the difference between the observed frequencies and expected frequencies in one or more than one categories is

• A. Z - test
• B. t - test
• C. Chi - square test
• D. ANOVA

Hint:

In genetics, the Chi-square test is the standard tool used to evaluate whether observed offspring phenotypic ratios significantly deviate from expected Mendelian ratios, such as $3:1$ or $9:3:3:1$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Statistical tests are selected based on the type of data (continuous or categorical) and the research question being evaluated.
When analyzing categorical data, researchers compare observed frequencies with expected frequencies calculated from a theoretical model (such as Mendelian inheritance ratios).
Key Formula or Approach:
The test statistic used for this comparison is the Chi-square ($\chi^2$) goodness-of-fit test, calculated as:
\[ \chi^2 = \sum \frac{(O - E)^2}{E} \]
where $O$ represents the observed frequency and $E$ represents the expected frequency for each category.

Step 2: Detailed Explanation:
Let us analyze the applications of the listed statistical tests:
The Z-test is a parametric test used to compare the means of two groups when the population variance is known and the sample size is large ($n > 30$), matching Option (A).
The t-test is a parametric test used to compare the means of two groups when the population variance is unknown and the sample size is small ($n < 30$), matching Option (B).
ANOVA (Analysis of Variance) is a parametric test used to compare the means of three or more independent groups, matching Option (D).
The Chi-square ($\chi^2$) test is a non-parametric test designed specifically for categorical data.
It evaluates how well an observed distribution of frequencies matches an expected theoretical distribution (goodness-of-fit), or whether two categorical variables are independent of each other.
This matches the requirement of comparing observed and expected frequencies across categories.

Step 3: Final Answer:
The Chi-square test is used to compare observed and expected frequencies in categorical data.
This corresponds to Option (C).