Descriptive and inferential statistics

The descriptive statistics is the set of statistical methods that describe and / or characterize a group of data. The inferential statistics seeks to infer and draw conclusions about general situations beyond the set of data.

Statistics is a discipline that is responsible for processing and organizing data, data being any measure or value that can be obtained through experiments, surveys, censuses or other means. The analysis of the data usually begins with the application of descriptive statistics methods, and then continues with inferential statistics methods.

Descriptive statisticsInferential statistics
DefinitionMethods used to summarize the key characteristics of known data.Methods that involve the use of sample data to make generalizations or inferences about a population.
objectivesCharacterize a data group

Examine trends or distributions

Examine differences between groups.

Examine if variables are associated.

Compare averages between groups.

Predict one variable from another.

Analysis methodsMeasures of central tendency:

  • Media
  • Median
  • Fashion

Measures of variability:

  • Variance
  • Standard deviation
  • Rank
  • Frequency
  • t-test
  • Variance analysis
  • Correlation
  • Regression
Application areasNatural and social sciencesSocial and natural sciences
  • Characteristics of patients who are cared for in a hospital.
  • Average and distribution of the age, weight and height of the students of a school.
  • Predict the onset of dementia in people according to their cardiovascular status.
  • Prove that a medicine is used to treat a disease.

What is descriptive statistics?

The descriptive statistics is the part of statistical arranging data so that they can be analyzed and interpreted. Descriptive statistics methods allow us to:

  • Determine the central tendency of a variable : average or arithmetic mean, median or mode.
  • Determine the variability of a variable : standard deviation, variance, ranges.
  • Determine what the distribution of a variable is like : frequency histogram, normal distribution.

Descriptive statistics examples

When you want to characterize a group of individuals, you use descriptive statistics. For example, we have the following body temperature data for a group of men and women:


As they are presented, we cannot draw any conclusion, but when applying descriptive statistics techniques, we can then say that:

  • men in this group have an average temperature of 36.53ºC with a standard deviation of 0.45;
  • women in this group have an average temperature of 36.91 ºC, with a standard deviation of 0.36.

What is inferential statistics?

The inferential statistics or statistical inference is part of the statistic that seeks to predict or infer characteristics or expected results of a population based on data obtained from a sample of that population. Among the techniques applied in inferential statistics there are:

  • The t test: it is used to compare the arithmetic mean of two groups determining if the differences between the groups occur randomly or systematically indicating a real difference.
  • Analysis of variance or ANOVA : is applied to compare two or more groups of variables.
  • Correlation analysis : reveals whether the values ​​between two variables tend to change systematically. To make these determinations, the correlation coefficient r and the p- value or confidence interval IC are used.
  • Regression analysis : allows you to predict one value from another.

Examples of inferential statistics

If we want to determine if any behavior or biological state is associated with a disease, we use inferential statistical methods. For example, in a study conducted in Germany, 3109 people were evaluated for different health parameters for almost seven years. The results showed that high blood glucose levels (greater than 126 mg / dl fasting), smoking and physical inactivity were associated with the development of dementia.

When a new drug is discovered and its effectiveness is to be demonstrated in a certain disease, inferential statistics are used. In this case, the effects of one group treated with the drug and another group treated with a placebo or a control drug are compared.

Kelly et al’s group investigated endothelial function in 50 obese individuals before (Pre) and after (Post) three months of treatment with two drugs: exenatide and metformin (control). When analyzing the results with the ANOVA technique (P = 0.348; inferential statistics) they found that exenatide had no effect on endothelial function, compared to metformin.

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