PSYCH 248 Chapter 9: Introduction to the t Test Statistic

What is a t-test?

Group of statistical tests that allows you to determine if TWO MEANS are significantly different.

When must we use a t-test?

When the population mean and standard deviation are unknown.

What is a one-sample t-test?

Single-sample t-test is used when you have a single-sample experiment; it compares:

Why is a t-test called an estimated z-score?

We do not know the variance (or SD) of the untreated (KNOWN) population

we can only estimate what it is

When is t a good estimate of the z score?

When the sample size is large

In the formula for the one-sample t-test, what is in the numerator? In the denominator?

Mean difference / estimated difference

M - μ / SEM
where SEM = s / √n

What is sampling error?

Difference between sample statistic and population parameter

Define estimated standard error how is it different from previous chapters?

The standard deviation of the sampling distribution of the means.

Define degrees of freedom. How is it calculated?

How many values are free to vary
df = n - 1

Be able to find t-critical, given the following information: one-tailed vs. two-tailed, α, and n

1. Calculate degrees of freedom
2. Determine if it is one-tailed or two-tailed
3. Alpha level usually 0.05 or 0.01

What happens to tcritical as df increases?

Increases

What happens to tcritical as df approaches infinity?

Decreases

How does the amount of variability in the data impact the t-test?

Variability = eSEM
A higher variability decreases the t-test
A lower variability increases the t-test

How does the sample size impact the t-test?

A higher sample size decreases the t-test
A lower sample size increases the t-test

What would a large value for t suggest?

A large value for t suggests that the obtained mean difference is much greater than would be expected (REJECT)

Hypothesis testing with single-sample t-test:

1. State the hypotheses
2. Locate the critical region
3. Calculate the t-test
4. Make a decision

Step 1 of a single sample t-test: Hypothesis

Nondirectional:
H0 = µ1 = µ2
H1 = µ1 ≠ µ2

Directional:
H0 = µ1 > µ2
H1 = µ1 < µ2

Step 2 of a single sample t-test: Find your critical region

1. Find df = n - 1
2. Know the alpha level that is given, usually 0.01 or 0.05
3. Determine if its one-tailed or two-tailed

Step 3 of a single sample t-test: Calculate the single sample t-test

1. sample SD (s) = √ (SS/df)
2. Estimated standard error (SEM) = s /√ n
3. T-statistic = M - u / SEM

Step 4 of a single sample t-test

Make a decision
1. If your calculated t-test is GREATER than your t-critical then REJECT the NULL because it indicates a SIGNIFICANT DIFFERENCE p < .05, .01
2. If your calculated t-test is SMALLER than your t-critical then RETAIN the NULL because it DOES NOT indicate a SIGNIFICANT DIFFERENCE p > .05, .01

Cohen's d for one-sample t-test

M - μ / σ

Sample APA Conclusion for one-sample t-test:

In this study using a two-tailed one-sample t-test, between the sample light truck model ( M = 20, SD = 3) and the population light truck model (μ = 22) there was a significant difference and we reject the null hypothesis, (t(15) = 2.67, p<0.05, d = 0.667).