An overview page for t-tests

T-tests - An overview

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Ed 510 Applications of Educational Research

The basic logic of a t-test

Two groups are compared
These can be two classrooms, two treatment groups, two interventions, or a single group to a population
The differences between groups are tested
The test is based on group means
Either as Mean 1 - Mean 2 (Sample means for groups 1 and 2 respectively)
Or as Mean sample - population mean (Population mean is always 0)

The purpose of the analysis to to be able to show that the differences between means is greater than a mathematical difference that could have occurred by chance alone.

The differences between the means is adjusted for sample size and errors of sampling.

The two equations below reflect these ideas

Example 1: X₁ - X₂

Example 2: X - m

These expressions give the differences between means. In Example 1, the means of two independent samples are compared by subtraction. In Example 2, a sample mean is compared to the mean of the population from which the sample was drawn. Again this comparison is by subtraction.

The correction for sample size and sampling errors is reflected in the following expression.

S²
(N) ^1/2

Thus the equation to find the t-ratio for differences in 2 independent sample is

X¹ - X²
____________
(s²)^1/2
____
(N-2)^1/2

The equation to test the difference between a sample mean and it population mean is

X-m
_______
(s²)^1/2
____
(N-2)^1/2

Let's consider the following examples:

1. A special education teacher wants to know if the performance of her class on the Seashore Coordination Battery is comparable to what should be the expected average score for his 4th graders based on national norms.

He will use a test that compares __________________________________.

2. A principal wants to know if the use of spelling lists or spelling context is more effective. She compares the performance of two second grade classrooms after 5 weeks of instruction in each method. Class A uses spelling lists and Class B uses spelling in context.

She will compare the average spelling test scores for the two classes using _______________________.

Keep in mind

Once a researcher has completed the calculations for the t-ratio, all that is known is that the differences between two means exceed 0.

What remains to be known is if the differences are greater than chance differences.

That leads the researcher to consult a table of critical values of t.

This table provides randomly calculated t-values for a range of sample sizes and at various levels of probability.

As sample size increases a smaller t-ratio is needed to demonstrate that differences between group means would have occurred by chance. Why?

As the level of probability (likelihood of chance differences) decreases, a smaller t-ratio is needed to demonstrate that differences between group means would have occurred by chance. Why?

Summarizing questions

How might you apply some of the concepts in this lesson to statistical comparisons in your own teaching?