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Hypothesis Testing and T-tests

Decision Errors

There's an inverse relationship b/t the levels of the 2 errors

Type II

Fail to reject the null when it is false

Type I

Reject the null when its true

Effect size

Importance of:

It standardizes the difference b/t means (like a Z score) so that comparisons can be made to other scales, and even other studies (meta-analysis)

Conventions

Large = .8

Overlap of 53%

Medium = .5

Overlap of 67%

Small = .2

Overlap of 85%

Based on:

Population SD

Estimate of the sample mean

The amount that 2 populations do not overlap, or how much they are separated

Statistical Power

Power should be at least 80%

Depends on:

Significance level chose, type of test (1 or 2-tailed, etc.)

Effect size (sample size and SD)

Helps determine the real world significance of marginally significant findings

Helps determine how many participants are needed

The probability that the study will produce a significant result if H1 is true

one-tailed vs. two-tailed tests

two-tailed is non-directional

more stringent criteria

cutoff points must be cut in half

for p<.05 Z scores are +-1.96

one-tailed is directional

Sampling distributions

Confidence intervals

Results from a replicated experiment will fall in this interval 95% of the time

To find a score confidence interval, change the Z-scores to raw score by:

Multiply the SD by the Z score for each confidence interval and then add the mean

(1.96)(15)+100 = upper limit

Example: (-1.96)(15)+100 = lower limit

99% is b/t -2.57 and 2.57

95% is b/t -1.96 and 1.96

upper and lower ends are confidence limits

Based on the central limit theorem

The shape of a dist. of means is about normal if:

or the pop. distribution is normal

each sample has an N of 30 or more

The SD of a dist. of means is the sqroot of the variance of the dist of means

Also known as standard error (SE)

The variance (S^2) of a dist. of means is the S^2 of the pop divided by N

The mean of a distribution of means is the same as the mean of the population

you can figure out its characteristics by knowing:

the # of scores in each sample

the characteristics of the dist. of the pop of individuals

Shape - approximately normal

Spread - less than the spread of the real population

Mean - about the same as the mean of the real population

The process of hypothesis testing often involves determining whether to reject a null hypothesis (H0) based on sample data. Two types of t-tests are commonly used: one-tailed and two-tailed tests.