All the tests we’ve done so far have involved sets of data for which we could find the mean and standard deviation. However, sometimes we only have frequencies or proportions. For example, let’s say that marketing researchers post an article about a new product on Facebook, Twitter, LinkedIn, and Instagram. They want to determine if followers are more likely to read the article from a particular social network.
The company has the following numbers of followers on Twitter, Facebook, and LinkedIn (in thousands):
Facebook: 1991
Twitter: 821
LinkedIn: 1733
After releasing the article, the marketing researchers found the following numbers of people clicked the link:
| Number of people who click link (in thousands) | |
| 19 | |
| 23 | |
| 15 |
z-tests and t-tests are parametric tests since they’re based on means and standard deviations. In this case, we need to do a non-parametric test to determine if the number of people who clicked the link to the article is what we would have expected based on the number of followers on each social network. This is the null hypothesis; the alternative hypothesis is that the number of people who clicked the link is different than what was expected.
In this case, we’ll do a chi-squared goodness-of-fit test (χ2) to test the “fit” between observed and expected values.
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Continue to Afterward, or select a lesson below.
Lesson 1: Introduction to Statistical Research Methods
Lesson 2: Visualizing Data
Lesson 3: Central Tendency
Lesson 4: Variability
Lesson 5: Standardizing
Lesson 6: Normal Distribution
Lesson 7: Sampling Distributions
Lesson 8: Estimation
Lesson 9: Hypothesis Testing
Lesson 10: t-Tests for Dependent Samples
Lesson 11: t-Tests for Independent Samples
Lesson 12: Intro to One-Way ANOVA
Lesson 13: One-Way ANOVA: Test significance of differences
Lesson 14: Correlation
Lesson 15: Linear Regression
Lesson 16: Chi-Squared Tests
Afterward
Index