Descriptive vs Inferential Statistics: For Research Purpose

Descriptive vs inferential statistics is the type of data analysis which always use in research. Both of them have different characteristics but it completes each other.

As a researcher, you must know when to use descriptive statistics and inference statistics. Using both of them appropriately will make your research results very useful.

In this article, I try to elaborate and give a concrete example of how the two types of analysis should be used so that they do not touch each other.

Using descriptive statistics and inferential statistics properly will make your research outstanding!

Descriptive vs inferential statistics

First, let’s discuss the basic differences between these two types of analysis.

1. The difference of goal

Descriptive statistics and inferential statistics has totally different purpose.

Descriptive statistics goal is to make the data become meaningful and easier to understand.

Meanwhile inferential statistics is concerned to make a conclusion, create a prediction or testing a hypothesis about a population from sample.

To achieve the descriptive statistics purpose, there are two form of analyses which we could use:

1. Numerical analysis

2. Data visualization

These two types of descriptive analysis will help you generate a powerful insight from your dataset.

Remember, descriptive statistics could not be used to make a conclusion based on your dataset. It is only for describing the data and the characteristics.

Vice versa, by using inferential, we could generate an analysis to the population that the samples represent.

There are 4 types of inferential analysis which commonly used by the researcher:

1. Making inference

2. Hypothesis testing

3. Determining relationships

4. Making predictions

All these four analyses could be used if you want to make a conclusion based on your data.

2. Difference of numbers of variables

There are three types of data analysis based on the numbers of variables:

1. Univariate analysis

Univariate analysis is the examination of the distribution of only one variable

2. Bivariate analysis

Bivariate analysis is the examination of the two variables simultaneously.

3. Multivariate analysis

Multivariate analysis is the examination of more than two variables simultaneously.

Descriptive statistics is only used for univariate analysis. Which means, it is only could describe the characteristics for one variable only. It cannot be used to detect the relationship between more than one variable.

Vice versa, inferential analysis could be used for all of the three variables. You may use hypothesis testing for one or two variables, you could determine the relationship about variables, etc.

3. Difference of complexity

The truth is, descriptive analysis is simpler to use than inferential statistics.

As you know, descriptive statistics is only use basic formula such as mean, median, mode, variance, standard deviation, etc. It’s easy to use because you just need to put the value to the formula and see the results.

Otherwise, inferential statistics takes you a step forward to make an analysis which could be a conclusion for your research.

As I mentioned above, you may use hypothesis testing, determining relationship among variables through correlation and regression, or you may make a predictions through a statistical model.

It’s quite complex and take a lot of steps to inference a data.

Descriptive vs inferential statistics examples

We want to make a quantitative research find out if there is a relationship between the nutritional status of a child and the mathematical score obtained.

In this case, height is chosen as an indicator that shows a person’s nutritional status assuming the higher a child’s body, the better his nutrition.

Now, let’s take a look for these data to see the difference!

No.Height (cm)Math Score (points)
116675
216988
315867
415175
517072
616197
715465
815593
917698
1016188
1117767
1217784
1315169
1415173
1516395
1615780
1717792
1815781
1916590
2015662
2117994
2218099
2317485
2417889
2516273
2616994
2716095
2817099
2915169
3015760

I will make the descriptive analysis and inferential analysis so you’ll see the difference clearly!

Based on the table above, using descriptive statistics on SPSS, this is what we got!

frequencies-table

Let’s describe the height variable based on the summarize above!

  • The mean value based on our sample is 164 cm.
  • The standard deviation is 9.63 which means the data we use is spread out not too far from the mean value.
  • The mode value of student height is 151 cm.
  • The standard error value is 1.76, which means the sample that we are using has a very low error rate for the population.
  • The skewness value is 0.189 meaning that the data used tends to show right-skewed.
  • The value of kurtosis is -1,327 meaning it tends to be flat (platycurtic). The range between the tallest student and the shortest student is 29cm.

Now, make another descriptive analysis based on result above!

  • The mean of mathematical score of the 30 students is 82.27.
  • The median value is 84.5.
  • The mode value is 67.
  • The standard deviation is 12.35 which means the sample we use is quite close to the average value.
  • The skewness value is -0,347 which means that the data used tends to show left-skewed.
  • The value of kurtosis is -1.352 which means the data used tends to be flat (platycurtic).
  • The range between the highest students’ math scores and the lowest students is 39.

This is the most common thing which you could explain in descriptive statistics.

scatter-plot-of-descriptive-statistics

Take a look at the previous picture to see some insightful information

Based on the picture above, at a glance you will see that the higher a student is, the higher the math grade is. That is, there is a positive linear relationship between the two variables.

Not all data show this pattern, but in general, that is how it is seen.

To clarify it, we need to do a bivariate inference analysis to produce a more exact number.

First, we can use correlation analysis to quantitatively ascertain the relationship between height and mathematical values.

By using Pearson correlation coefficient and SPSS software, the following results are obtained.

correlation-analysis-for-bivariate

You can see the Pearson correlation coefficient from these two variables is 0.518. You can conclude that there is enough strong positive correlation between the two variables.

However, we cannot draw the conclusion that the student’s height is a factor that influences a child’s math score.

For this reason, it is necessary to do a simple linear regression analysis to prove whether height really has a significant influence on mathematical values.

If you use SPSS in conducting a simple linear regression analysis, this is the following output you will get.

simple-linier-regression-of-inferential-statistics

Based on the output, the best model we could make to analyze this research is:

y = -26.865 + 0.664 x1

Interpretation:

1. An increase in height of 1 cm will cause an increase in mathematical value of 0.664 point.

2. By ignoring all independent variables, a student’s math grade is -26,885 point.

For the interpretation of the second point, it is certainly not acceptable considering there is no way for students to have a height of 0 cm. So, it could be ignored!

Look at t the figure at number 1. Assuming a significance level of 5 percent, and the p-value produced is 0.03, then the p-value <significance level.

Based on these results, we can conclude that the height variable has a significant influence on a child’s mathematical value.

The higher a child is, the greater the mathematical score that will be obtained.

We can also see the coefficient of determination (R square) based on the output is 0.268.

This shows that height only affects a child’s math score of 26.8 percent. The rest (73.2 percent), a child’s mathematical value is determined by other variables not covered in this model.

Based on this fact, you can make a conclusion that student’s height has significant Impact to student’s math score. The higher, the better.

You could also give an advice for parents out there for always taking care their children nutrition to ensure the nutrition of their children so that they will grow up to be children who have good academic abilities.

Now, let we use inferential statistics for this example of research.

Above is the scatter plot of student’s height and their math score. What

Summary

The difference of descriptive statistics and inferential statistics are:

1. Difference of goal

2. Difference of numbers of variables

3. Difference of complexity.

Descriptive statistics are used to describe the general conditions and characteristics of the data while inferential statistics are used to draw conclusions for the population based on the sample we have.

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