Stats midterm two

z-test formula

5-step procedure

• 1) State the null and alternative hypotheses

• 2) Pick a level of alpha (probability criterion)

• 3) Set the decision stage (greater likelihood of rejection with 0.05)

  • A. Choose a test statistic

  • B. Locate rejection region in the sampling distribution 

  • C. Identify critical limits

  • D. Clearly state the value of the observed statistic necessary to reject the null

• 4) Collect sample data and compute the test statistic

• 5) Make a decision 

Type 1 alpha error

Rejected the null hypothesis, when you shouldn't have. The null is true.

Type II error

failed to reject the null, when you should have. Null is false

One sample t-test formula

One sample t-test Cohen’s d formula

One sample t-test Eta square formula

One sample t-test omega square formula

One sample t-test 95% and 99% certainty for t given df

One sample t-test confidence interval on the difference of means

Two-sample t-test for independent groups formula

Footnote in the denominator of the two sample t-test ind

Pooled variance formula for two-sample t-test ind

two sample t-test ind Cohen’s d formula

two sample t-test ind Eta square d formula

two sample t-test ind omega square formula

2 sample t-test ind confidence interval on the difference of means

Two sample t-test for related groups formula

Standard error of the difference between pairs of scores formula (2-sample t-test related denominator)

2 sample t-test related Cohen’s d formula

2 sample t-test related eta square formula

2 sample t-test related omega square formula

Confidence interval on the difference between means from related samples

ANOVA formula (s)

Squared sums formula

Post Hoc comparison Tukey’s HSD

Anova eta square formula

Anova omega square formula

How do you increase power?

We increase power by increasing absolute value of the test statistic. The larger the absolute value, the more likely it will fall in the rejection region.

How do you increase absolute value

• Increase numerator, decrease denominator

• Increase the mean difference/strength of Iv manipulation

• Decrease standard error estimate: increase sample size or decrease stdv

How does t-test for related scores increase power

• decreases the denominator of the test statistic

• decreases the variability of scores (decreases stdv)

Hypothesis for z-test and 1 sample t-test

Hypothesis for 2 sample t-test ind and 2 sample t-test rel

Anova hypothesis

Synonyms for statistically significant

Real and reliable

2 characteristics of the null and alternative hyothesis

1) must be mutually exclusive

2) include all possible values

What is statistically significance?

1) observed value is large enough to fall in the rejection of the sampling distribution established by the alpha level and statistical hypothesis

2) value of test statistic is sufficiently rare to reject the null

To find the critical limit for 1 sample t-test, we need:

1) degrees of freedom

2) 1 or 2 tailed

3) alpha level for test (0.01 or 0.05)

What does cohen’s d measure

How many standard deviation units separate the means

What does eta square and omega square measure

• The percentage of variance in the DV that can be predicted from the IV. In other words, by knowing what treatment a participant got, how well can you predict their score.

• Omega square is a corrected measure of eta square to account for the bias of overestimation

What does omega square measure

A corrected ver

Mean Square (MS) is synonymous with what

Variance (ss/df)

3 assumptions of an F-test

1) each participant is randomly and independently chosen from the population

2) scores are distributed normally in the population

3) the variances of scores in the population are equal