Hypothesis Testing

Students T-Test

Most experiments in biology, or science in general, require a statistical analysis of the collected data. This usually falls into two broad categories of statistical procedures; descriptive and hypothesis testing. Descriptive statistics paint a numerical picture of the data in terms of the mean (average) and variance of the samples. Statistics used for testing hypotheses come in a wide variety of types, but all are used to evaluate the difference between the observed results and expected results based on an a priori hypothesis. In this lesson you will take random samples from a population of different beans, use descriptive statistics to characterize the samples and then use the Student's T-test to evaluate hypotheses about the differences in the mean mass of the different beans in your sample.
Lesson 1: Random Samples

There are few situations when an experimenter can measure every individual in a population. Therefore taking samples becomes the only option. The assumption is that a sample is a representative picture of the entire population. In order to meet that assumption samples must be obtained by some process of random selection (or as close to it as possible).

You will be presented with a population that contains several different kinds of dried beans. Your challenge in this lesson is to devise a method for obtaining a representative random sample of this population. Describe this sampling procedure in the Methods section of your lab report.

In the sample there will be several types of beans. We are going to focus on three of them: the Kidney, Pinto, and Black Eyed beans. Separate these beans from the other beans in your sample. From your observation during this sampling procedure formulate two hypotheses.
  1. Comparing the Kidney bean to the Pinto bean, which one has the greater average mass?
  2. Comparing the Kidney bean to the Black Eyed bean, which one has the greater average mass?
Lesson 2: Mean and Variance

 In this lesson you are going to describe the samples of these three beans in terms of their mean and variance. The mean (or average) is a measure of the "central tendency" of the sample; that is what is the one number that will represent the value where most individuals in the sample fall (or near to it). By itself the mean gives a very limited picture of the sample. The variance measures the amount of "spread" in the sample on both sides of the mean.

  1. Measure the mass of each bean to the nearest tenth of a gram and record the values in your note book.
  2. Enter these values in an Excel spread sheet.
  3. Use the spread sheet to calculate the sample mean and variance for each kind of bean.
  4. In Excel create a bar graph of the mean values along with the 95% confidence intervals.

The spread sheet will automatically calculate the number of individuals in each sample, the mean, and variance. It will create a bar graph of the means. The expanded spread sheet will also calculate the critical numbers for the T-Test. 
In addition to this spread sheet, you should also fill in the spread sheet that summarizes the mean and variance measurements of the other groups in the class. Use this to compare your samples with those of your classmates.

Lesson 3: The Student's T-Test

You need to use the data and calculations you have done in Lesson 2 to evaluate your two hypotheses with the Student's T-test. The Excel spread sheet will do most of these calculations for you. 

It is important to understand that you should only enter data into the shaded cells of this spread sheet. The other cells are used to calculate important values for the T-Test. 

Below the first page are 3 columns for entering data for the mass of Kidney, Pinto, and Black Eye beans. Once you have done this, you should see numbers for sample size, mean, and variance appear on the chart on the first page as well as a bar graph of the means. This page represents the Results section of your lab report. 

 Now you need to copy these values into the corresponding shaded cells on the page to the right of the first page. Finally select a "P" or "alpha" value (usually .05) and use the link to the T-test table to find the critical tabulated T value with your P value and the degrees of freedom (df) calculated on page 1.

All these calculations will become part of your Results section in your lab report. Your interpretation of these tests will form the basis of your Conclusion section. Remember, in the Conclusion you must use specific examples from the Results to explain how you came to the decision to either support or reject your hypotheses.