Descriptive Statistics, Inferential Statistics and Hypothesis Tests

What is descriptive Statistics?

Descriptive Statistics refers to a discipline that quantitatively describes the important characteristics of the dataset. For the purpose of describing properties, it uses measures of central tendency, i.e. mean, median, mode and the measures of dispersion i.e. range, standard deviation, quartile deviation and variance, etc.

The data is summarized by the researcher, in a useful way, with the help of numerical and graphical tools such as charts, tables, and graphs, to represent data in an accurate way. Moreover, the text is presented in support of the diagrams, to explain what they represent.

·       Organize

·       Summarize

·       Simplify

·       Presentation of data

What is  Inferential Statistics?

Inferential Statistics is all about generalizing from the sample to the population, i.e. the results of the analysis of the sample can be deduced to the larger population, from which the sample is taken.

It is a convenient way to draw conclusions about the population when it is impossible to query every member of the universe.

The sample chosen is representative of the entire population; therefore, it should contain important features of the population.

Inferential Statistics is used to determine the probability of properties of the population based on the properties of the sample, by employing probability theory.

 The major inferential statistics are based on statistical models such as Analysis of Variance, chi-square test, student’s t distribution, regression analysis, etc.

 What is a t-test?

A t-test is a statistical test that is used to compare the means of two groups. It is often used in hypothesis testing to determine whether a process or treatment actually has an effect on the population of interest, or whether two groups are different from one another.

In the following table, some types of inferential tests and their purpose and SPSS command are shown.

Test	Purpose	SPSS command
Chi-squire	Association between variables	Analyze->Descriptive Statistics->crosstab
t	The one sample t-test compares the mean of your sample data to a known value. For example, you might want to know how your sample mean compares to the population mean.	Analyze->Compare Means->One-Sample T Test
t	Independent (or unpaired two sample) t-test is used to compare the means of two unrelated groups of samples. As an example, we have a cohort of 100 individuals (50 women and 50 men). The question is to test whether the average weight of women is significantly different from that of men? In this case, we have two independents groups of samples and unpaired t-test can be used to test whether the means are different.	Analyze->Compare Means->Independent Sample T Test
Regression	How independent variables control or influence the dependent variable. Multiple Linear Regression (MLR)	Analyze-Regression->Linear
Regression	How independent variables control or influence the dependent variable. Here dependent variable will two states (binary) like Yes or No etc.	1.     Analyze-Regression->Binary Logistic   2.     Make a dummy variable for dependent variable Transform->Recode into different variables

 What is the P value?

P value-

The p-value or probability value is, for a given statistical model, the probability that, when the null hypothesis is true, the statistical summary (such as the sample mean the difference between two groups) would be equal to, or more extreme than, the actual observed results.

a)     Concept is used in inferential statistics i.e., at t-test and also at regression analysis.

b)     P value <. 05 then we can say that population means are equal.

c)     P value <.05 tells that null hypothesis H_o is rejected and alternative hypothesis Ha is accepted.

d)     Researcher will try to reject the null hypothesis. In this case, p<.05

e)     If p < .05 then strong evidence against null hypothesis H_o.

f)      A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis H_a.

What is Hypothesis testing?

A type of statistical inference called hypothesis testing uses data from a sample to make inferences about a population parameter or population probability distribution. First, a cloudy assumption is made on the parameter or distribution.

Steps of Hypothesis test-

1.     Design your question in such a think that collected data can be tested.

2.     Assumption first, alternative hypothesis (Denoted by H_a )

3.     Assumption second, null hypothesis (Denoted by H_o)

4.     Perform an appropriate statistical test ( Can be use SPSS software)

5.     If the p value is < 0.05 then Ha is accepted and Ho rejected

6.     If the p value is > 0.05 then Ho is accepted and Ha is rejected

Example-

NAPD Case study-

There is a national leading training organization in Bangladesh that was established in 1980. The name of the organization is National Academy for Planning and Development (NAPD).  Every year, more than 2000 trainees are trained here to enhance capacity. NAPD provides different services like a modern classroom, breathing space, cafeteria, dormitory, prayer room, modern computer labs, modern language lab, modern auditorium support etc.

At the end of the training course, every training course is evaluated by trainees. Is NAPD a good training organization?  The answer to this question is difficult. You can infer that NAPD is a good training organization. Trainees will see NAPD from a different perception. So it is very difficult to infer.

What is the actual answer? How it can be obtained?

Design questioner for hypothesis test and get SPSS solution.

Let get a hypothesis test,

H_a  NAPD is a good training organization

H_o NAPD is not a good training organization

Result Case 1

From the SPSS test p= 0.03

Here p is less than .05 hence, H_a  accepted  and H_o is rejected

So inferential analysis proves that NAPD is a good training organization.

Result Case 2

From the SPSS test p= 0.08

Here p is greater than .05 hence, H_o is accepted and H_a  rejected

So inferential analysis proves that NAPD is not a good training organization.

Engr. Md. Abdur Rashid

Director  (Admin & Finance)

NAPD

Reference:  https://www.scribbr.com/statistics/statistical-tests/