Descriptive statistics aim to summarize the characteristics of a given data set. In contrast, inferential statistics aim to use a sample of data to draw inferences about the whole population (i.e., hypothesis testing).
Types of Descriptive Statistics
1. Measures of Central Tendency
Central tendency is used to describe where the center of a dataset is located. Mean, median, and mode are commonly used statistics to measure central tendency.
2. Measures of Dispersion or Variation
Dispersion and variation describe how dispersed the distribution is for a set of data. Range, variance, and Standard Deviation are commonly used to measure dispersion and variation.
3. Measures of Frequency
You can sometimes understand how the data set looks by using frequency counts. A frequency count table can be useful to understand the characteristics of a dataset.
4. Measures of Position
You can use percentile ranks and quartile ranks to describe the relative position of where a data point or an individual is.
Inferential Statistics: Definition, Goal, and Examples
Inferential statistics are methods of using a sample of data to draw inferences about the whole population.
The goal of inferential statistics is to study a smaller group of people (i.e., a sample) in the hopes that the results from this sample can be generalized to the larger group (i.e., population).
For example, we may ask 200 students on campus their opinion about online classes. By using these 200 students’ opinions, we attempt to find out how the students from the whole university are viewing online classes.
In classic inferential statistics, we typically have two hypotheses (i.e., the null hypothesis and the alternative hypothesis). Below is a set of such hypotheses about online classes and in-person classes.
- Null Hypothesis: Students’ attitudes toward online and in-person classes are the same.
- Alternative Hypothesis: Students’ attitudes toward online and in-person classes are not the same.
The goal of classic inferential statistics is to find empirical evidence to prove the null hypothesis wrong. If we do a test (e.g., t-test or ANOVA) and find a low p-value (< 0.05), we can then reject the null hypothesis and conclude that students’ attitudes toward online and in-person classes are not the same.