JNTU B.Pharmacy IV BIOSTATISTICS AND RESEARCH METHODOLOGY Previous Question Paper (July-2021 - R17)

Measures of central tendency and dispersion are fundamental statistical tools used to summarize data distributions.

Mean is the arithmetic average calculated by summing all observations and dividing by the count. It is highly sensitive to outliers. Median is the middle value of an ordered dataset, providing a robust measure that is resistant to extreme values. Mode is the most frequently occurring value in a dataset, useful for nominal data.

Variance measures the average squared deviation of data points from the mean. Standard Deviation is the square root of the variance, representing the average distance of data points from the mean in the original units of measurement. Standard Error of Mean (SEM) estimates how far the sample mean is likely to be from the true population mean, calculated as the standard deviation divided by the square root of the sample size.

While standard deviation describes the spread of individual observations within a sample, the standard error describes the variability of the sample mean itself, serving as a measure of the reliability of the estimate of the population parameter.

Pearson's chi-square test is a non-parametric statistical test used to determine if there is a significant difference between the observed frequencies and the expected frequencies in one or more categories of a contingency table. It is primarily used to test the goodness of fit or the independence of two categorical variables.

The formula for the chi-square statistic is:

Where Oᵢ represents the observed frequency and Eᵢ represents the expected frequency for each category. The test follows a chi-square distribution with degrees of freedom calculated as (r-1)(c-1) for contingency tables, where r is the number of rows and c is the number of columns.

Example: Suppose a researcher wants to determine if a drug's efficacy is independent of the patient's gender. A sample of 100 patients is divided into two groups: 50 males and 50 females. The observed results are:

To perform the test:

1. State the null hypothesis: The drug's efficacy is independent of gender.
2. Calculate expected frequencies for each cell using the formula: (Row Total × Column Total) / Grand Total. For example, the expected frequency for 'Male-Effective' is (50 × 50) / 100 = 25.
3. Calculate the chi-square value by summing the squared differences between observed and expected frequencies divided by the expected frequencies for all four cells.
4. Compare the calculated χ² value against the critical value from the chi-square distribution table at a chosen significance level (e.g., 0.05) with 1 degree of freedom.
5. If the calculated χ² is greater than the critical value, reject the null hypothesis, indicating a significant association between gender and drug efficacy.