Hypothesis testing - populations
Hypothesis testing is a fundamental statistical approach to determine the probability that an hypothesis is true. In ENGN2226, we will look at how to complete hypothesis testing on data about a population (R09) and on categorical data (R10). The broad principles of the approach for hypothesis testing between the two is, however, the same.
Example applications
Population data can be any sort of data that is sampled across a population (here, a population is not just ‘people’). It must have a continuous quantitative variable of concern. Examples of quantitative data include: height, weight, salary, age, and so on, but could also include data like time, cost, speed, etc, sampled across a population of results.
Steps
In this instance, we are concerned with data that is approximately normally distributed. For our purposes, you can examine the plot visually. If the two data sets are from samples that are approximately normally distributed, you can then conduct a hypothesis test using the
Student’s T-test.
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1.State the null and alternative hypothesis - typically the null hypothesis is that there is no difference between the samples
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2.Calculate the test statistic - in this case, the Student’s T-test
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3.Determine the p-value associated with the test statistic
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4.Determine whether the null hypothesis is accepted or rejected
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5.Provide a conclusion on what that means
Key concepts
- an explanation of how the null and alternative hypotheses are formed
- an example that walks through how to conduct a t-test, and then the p-value
- advice on whether to reject or accept the null hypothesis
- advice to the student engineer on when to use hypothesis testing
Core resources
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Khan Academy have a series of videos on Hypothesis testing, and solve using a t-statistic (7 videos){: .link-ext target=”_blank” }
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RStudio has an active help community, R-Bloggers. See their example of conducting a t-test if you’re planning on using RStudio: https://www.r-bloggers.com/two-sample-students-t-test-1/
Extra resources
Note, a T-test can be undertaken manually, or very easily using a spreadsheet. A T-test is built in to most spreadsheet packages - usually in the form TTEST(Data1; Data2; Mode; Type)[Libreoffice]. If you’re looking for something more powerful, then using the open source statistical software RStudio could be useful.