Chapter 1: Statistical Analysis Command Term to Master

Worksheet 1.2

Chapter 1: Statistical analysis – command term to master

DeduceReach a conclusion from the information given.

Example

Assessment Statement 1.1.5Deduce the significance of the difference between two sets of data using calculated values for t and the appropriate tables.

Author’s comment

Because the command term is deduce, a conclusion must be reached here. You must conclude if the difference between two sets of data is significant. You will use the calculated value for t and the tables you have already practised using in the worked example in your text. The bottom of the table will tell you how significant the difference is.

Example question

The question will probably be asked in the short answer section of the test. This is the way the question may be written:

Two groups of barnacles were living on a rocky shore. One group lived above the water level and one group lived below the water level. Are the shell sizes of the barnacles significantly different depending on where they live in relation to the water level? 15 barnacles were sampled from each area. The Student t-test was used to determine if the differences in the shell sizes was significant. The t value was found to be 2.25. Deduce the significance of the difference between the two sets of data using the calculated values for t.

You will be given a t table (or partial t table) to use to find the significance. First look under ‘Degrees of freedom’ and find 28 (15 + 15 = 30 – 2 = 28). Move to the right under t values and find the number closest to 2.25. Notice that it is 2.05. Below 2.05 at the bottom of the table, you will find the probability that chance alone could produce this difference. It is 0.05.

So, your answer is: The probability that chance alone could produce this difference is 0.05. This means that there is a 5% probability that chance alone can make this difference. Therefore, the difference is significant since there is a 95% chance that where the barnacles live in relation to the water does make a difference in the size of their shells.

If the t value given had been 1.65 for the same example, your answer would be: The probability that chance alone could produce this difference is 0.10 or 10%. Therefore, the difference is not significant, since there is only a 90% chance that where the barnacles live in relation to the water makes a difference in the size of their shells. Scientists must be 95% certain of their finding before they can draw a conclusion that two sets of data are significantly different.