Analyzing Quantitative Data: Inferential Statistics

In a prior post, we looked at analyzing quantitative data using descriptive statistics. In general, descriptive statistics describe your data in terms of the tendencies within the sample. However, with descriptive stats, you only learn about your sample but you are not able to compare groups nor find the relationship between variables. To deal with this problem, we use inferential statistics.

Types of Inferential Statistics

With inferential statistics, you look at a sample and make inferences about the population. There are many different types of analysis that involve inferential statistics. Below is a partial list. The ones with links have been covered in this blog before.

  • Pearson Correlation Coefficient–Used to determine the strength of the relationship between two continuous variables
  • Regression Coefficient-The squared value of the Pearson Correlation Coefficient. Indicates the amount of variance explained between two or more variables
  • Spearman Rho–Used to determine the strength of the relationship between two continuous variables for non-parametric data.
  •   t-test-Determines if there is a significant statistical difference between two means. The independent variable is categorical while the dependent variable is continuous.
  • Analysis of Variance-Same as a t-test but for three means or more.
  • Chi-Square-Goodness-of-Fit-This test determines if there is a difference between two categorical variables.

As you can see, there are many different types of inferential statistical test. However, one thing all test have in common is the testing of a hypothesis. Hypothesis testing has been discussed on this blog before. To summarize, a hypothesis test can tell you if there is a difference between the sample and the population or between the sample and a normal distribution.

One other value that can be calculated is the confidence interval. The confidence interval calculates a range that the results of a statistical test (either descriptive or inferential) can be found. For example, If we that the regression coefficient between two variables is .30 the confidence interval may be between .25 — .40. This range tells us what the value of the correlation would be found in the population.


This post serves as an overview of the various forms of inferential statistics available. Remember, that it is the research questions that determine the form of analysis to conduct. Inferential statistics are used for comparing groups and examining relationships between variables.

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