Ch. 9 - t Statistic

Variance

r^2 = variability accounted for/ total variability (t^2/t^2 + df) r^2 = 0.01 small effect r^2 = 0.09 medium effect r^2 = 0.25 large effect

T Statistic

t = M - u/sM

Sample Mean Equations

t = M-u/sM or u = M + or - t*sM

Degrees of Freedom

- Computation of sample variance requires computation of the sample mean first df = n - 1

Estimated Cohen's d

- Estimated Cohen's d is computed using the sample standard deviation - Formula: estimated d = mean difference/sample standard deviation (M - u/s)

True or False: Sample size has a great influence on measures of effect size.

False - Measures of effect size are not influenced to any great extent by the sample size

True or False: By chance, two samples selected from the same population have the same size (n=36) and the same mean (M=83). That means they will also have the same t statistic.

False - The two t values are unlikely to be the same; variance estimates (s2) differ between samples

True or False: When the value of the t statistic is near 0, the null hypothesis should be rejected

False - When the value of t is near 0, the difference between M and u is also near 0

The results of a hypothesis test are reported as follows: t(21) = 2.38, p < .05. What was the statistical decision and how big was the sample?

The null hypothesis was rejected using a sample of n = 22

True or False: Compared to a z-score, a hypothesis test with a t statistics requires less information about the population

True - the t statistic does no require the population standard deviation; the z-test does

When n is small (less than 30) the t distribution...

is flatter and more spread out than the normal z distribution

Factors Affecting Width of Confidence Interval

- Confidence level desired - More confidence desired increases interval width - Less confidence acceptable decreases interval width - Sample size: Larger sample --> smaller SE --> smaller interval Smaller sample --> larger SE --> larger interval

Hypothesis Testing

- State the null and alternative hypotheses and select an alpha level - Locate the critical region using the t distribution table and df - Calculate the t test statistic - Make a decision regarding H0 (null hypothesis)

Influence of Sample Size and Sample Variance

- The larger the sample, the smaller the error - The larger the variance, the larger the error

Estimated Standard Error

- Use s2 to estimate σ2 - Estimated standard error is used as estimate of the real standard error when the value of σM is unknown

What is the t statistic?

- t might be considered an "approximate" z - Estimated standard error (sM) is used as in place of the real standard error when the value of σM is unknown