Descriptive Statistics

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The Objectives:

• What is descriptive statistics?


• Descriptive statistics and inferential statistics – What makes them different?

Descriptive Statistics

Through Descriptive statistics, the main features of the collected data are described quantitively. For the data under study statistical procedure are used in descriptive statistics. Data are organized and described with the help of descriptive statistics where data is collected from a population or a sample. However, the group which is being studied is the only thing that can be described through descriptive statistics, these results cannot be generalized.

So, descriptive statistics can be used only when one is not required to extend the results or generalize it to a much larger group. Descriptive statistics summarizes the dataset; the measures include the measure of central tendency and dispersion. Measures of central tendency are- Mean, Median and Mode and the measures of dispersion are- Range, Mean deviation about the mean or median, standard deviation or variance, skewness and kurtosis. Frequency distributions are also an example of descriptive statistics. It gives a simple summary of the observations in the sample or the population under consideration

Summaries may be either visual or quantitative, the graphical representation is the visual summary and summary statistics is the quantitative one. To describe the data at the initial stage of statistical analysis, we use summary statistics, or sometimes they are sufficient to describe the data set. The history of the use of summary and descriptive statistics is quite extensive, statistics first appeared in tabulating economic data and populations. The technique of summarization has recently been formulated under exploratory data analysis. Example of this technique is box plot. Descriptive statistics deal with returns in the business world where historical behavior of return is done through it. However past information is useful for analysis, expectations of the future or forecasting is also essential.

Difference between Descriptive and Inferential Statistics:

The aim of descriptive statistics and inferential statistics are different. While the former describes or summarizes the sample itself the latter uses data to know about the whole population. So this makes them different. Inferential statistics considers probability theory; on the other hand descriptive statistics doesn’t consider probability theory. In spite of the fact that inferential statistics helps in drawing the main conclusions in analysis of data, descriptive statistics are also presented.

Predictions and inferences regarding the population from analyses of a sample and observations are done with the help of inferential statistics. Unlike the descriptive statistics the analysis’s result of inferential statistics using sample can be generalized to a larger population which is represented by the sample. However, the sample should be the representative of the group that is generalized. Generalization is done through tests of significance. For example a t-test or a chi-square test or normal test can be used to know that whether the probability that the results of the analysis of the sample are representatives of the whole population. Such test of significance gives us an idea of the probability that the analysis’s result could have occurred by chance at the time when there no relationship between the studied variables in the population. Some of the examples of inferential statistics are-ANOVA, Regression Analyses- Linear, Logistic, structural equation modeling, correlation analyses, survival analysis, etc.

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