# Descriptive Statistics & Inferential Statistics: How to Answer to Statistical Exercise in five Steps

Statistical exercise is asked in Community Medicine practical exam. In this article, we will discuss how to attempt such an exercise in simple easy steps, which not only helps you to answer it correctly but also help you to remember how to solve it.

## Descriptive Statistics & Inferential Statistics:

Describing numbers using percentages and making comparative statements, like the majority of not attacked people were vaccinated against measles is Descriptive statistics.

Writing that the above comparison is statistically significant using the chi-square test is Inferential statistics.

## 1: Describe Null & alternate hypothesis(Descriptive Statistics)

Read carefully whatever is described in the exercise or given as a table.

Let us understand this with the help of the example given below.

Here, our hypothesis is the particular vaccine is effective against measles.

Null Hypothesis (Ho): There is no difference between the two groups(Vaccinated/Unvaccinated)

Alternate Hypothesis(H1): There is a difference between the two groups

## 2:Types of Data & Statistical Test

Types of data in the above example is Qualitative Data or Categorical data, as vaccinated not vaccinated, and attacked not attacked are characteristics(qualities) described here, which gives us an answer in yes or No.

On the other hand, if the quantity is measured then it will be Quantitative or Continous data, e.g. Height, weight, blood pressure, etc

Statistical test for Qualitative Data: Chi-square test,Z-test for proportions

Statistical test for Quantitative Data: Student’s t-test, Z-test using SE of difference between two means, ANOVA, etc.

for this example we can either use Chi-square or Z test for a proportion, We will use the chi-square.

## 3: Write Steps of Statistical Calculations

Formula for chi-suare test:

χ2 = ∑(Oi – Ei)2/Ei

where

• Oi = observed value (actual value)
• Ei = expected value.

Solving above the equation will give us a chi-square value of 8.6 at 1 degree of freedom(DF).

write χ2(DF,N)= 8.6 (1,200)

## Step 4: Write the Results of the Statistical Calculations.

The calculated value of chi-square in our example is χ2(1,200)=8.6, which is higher than the table value at a 95% confidence interval, So we can say that the p-value is less than .05 (p<.05)

## 5: Write the Conclusion from all Inferential & Descriptive Statistics

As the calculated value is higher than the table value, we reject the null hypothesis and conclude that the given vaccine is protected against measles and the difference is statistically significant(p<.05).

## FAQs

What is a statistical exercise?

A statistical exercise is a process of analyzing data using statistical methods to draw conclusions or make predictions about a population or phenomenon. It typically involves collecting data, cleaning and organizing the data, and using statistical techniques to analyze the data.

What are some common statistical techniques used in a statistical exercise?

Some common statistical techniques used in a statistical exercise include descriptive statistics (such as mean, median, and standard deviation), inferential statistics (such as hypothesis testing and regression analysis), and probability distributions (such as normal and binomial distributions).

What is the purpose of a statistical exercise?

The purpose of a statistical exercise is to use data to gain insights and make informed decisions about a population or phenomenon. It can be used to answer research questions, test hypotheses, identify patterns and trends, and make predictions about future events.

What are the assumptions of a statistical exercise?

Statistical techniques make assumptions about the data and population being studied. Some common assumptions include:
Independence of observations
Normality of the data
Constant variance
Random sampling

What are the limitations of a statistical exercise?

Statistical exercises have limitations that can affect the conclusions drawn from the data. Some limitations include:
Limited sample size
Selection bias
Measurement error
Confounding factors
It is important to consider these limitations when interpreting the results of a statistical exercise.