Question

Discuss the following course elements:

• Descriptive statistics
• Inferential statistics
• Hypothesis development and testing
• Selection of appropriate statistical tests
• Evaluating statistical results.

Answer 1

Descriptive Statistics:

Descriptive statistics are the statistics which summarizes the data of a sample. These statistics are of two types:

(a) Quantitative Statistics:

This kind of statistics provides the quantitative summary of the data which is sufficient to understand the sample information.

For Example, let us consider we are given with the sleeping hours of five students, and we have to find the quantitative statistics for them.

Sleeping Hours

8

7.5

7

7.5

7.5

Quantitative statistics will be:

	Sleeping Hours
count	5
mean	7.500
sample standard deviation	0.354
sample variance	0.125
minimum	7
maximum	8
range	1
1st quartile	7.500
median	7.500
3rd quartile	7.500
interquartile range	0.000
mode	7.500
low extremes	0
low outliers	0
high outliers	0
high extremes	0

(b) Visual Statistics:

This kind of statistics provides the data in the simple graph form which is a very quick way to understand the data.

Consider the sample example as above and let us analyze the data will the help of a box plot.

Inferential statistics:

Inferential statistics are the statistics which allows us to make the predictions from the sample data and help in making rough conclusions about a population.

Considering the example of sleeping hours of 5 students, we have the sample data of the students and now, we can try to determine if the data can predict whether the sleeping hours will work for everyone (population). We can do this by using the Z-score or hypothesis testing.

Hypothesis development and testing:

Hypothesis testing is performed to determine the likelihood that a population parameter, such as mean, is likely to be true.

There are four basic steps for hypothesis testing:

1. Stating the hypothesis:

We will state the null and alternative hypothesis for our claim assuming the hypothesis or claim we are testing is true.

2. Criteria for a decision:

Criteria of a decision is to introduce the level of significance in our test. Level of significance is the probability of a false rejection of a null hypothesis.

3. Calculating the test statistic:

Test statistics helps us to know how many standard deviations, a sample mean is from the population mean.

4. Reaching to the conclusion:

The value of the test statistic is used to make a conclusion about the null hypothesis.

Selection of appropriate statistical tests:

Selection of the appropriate statistical tests depends on the three factors:

1. What is our type of data?

We have to check under the four categories of data, namely, interval data, ratio data, ordinal data, and nominal data and decide their type accordingly.

2. Is the data normal distributed or not?

When the data is normally distributed, a parametric statistical test is used and if the data is not normally used, a nonparametric test is used.

3. Wha is the aim of the study?

What do we want to compare? We want to compare the two samples or paired data?

Thus, these are the factors for the selection of the appropriate statistical tests.