exam 3

define hypothesis testing

inferential statistic method that uses sample data to evaluate assumptions about a population parameter

Hypothesis Testing Steps

1. specify null and alternative
2. specify the significant level (A) (.05)
3. test statistic
4. decision

define null hypothesis (H0)

there is no significant difference; true effect in population, effect due to sampling error

Define alternative hypothesis (H1)

true effect in population, there is a diff

which hypothesis is being tested?

H0 (null)

define significance level

The probability of a Type I error. A benchmark against which the P-value compared to determine if the null hypothesis will be rejected. See also alpha.

Define p-value

The probability that data were obtained by random error or chance. e.g. p<0.05= less than 5% chance.

define alpha

probability of making type 1 error (level of significance)

define Beta

probability of making a type II error

define critical value

The dividing point between the region where the null hypothesis is rejected and the region where it is not rejected.

list error types

1) type I error
2) type II error

define: type 1 error (alpha)

reject H0 (null) when it is right (AKA false pos/lie)

type 1 error (alpha) ex

doctor looks at old man & says he is pregnant

define: type 2 error (beta)

accept H0 when it is wrong/fail to find existing effect (AKA false neg/dummy)

type 2 error (beta) ex

doctor tells woman who is about to give birth that she is not pregnant

fail to reject H0 (null) when p-value is?

p>0.05=no sig diff

reject H0 (null) when p=value is?

p<0.05=sig diff

2 tailed t test

Non-directional, 2 ends of distribution, 5%/2=2.5% on each on end of curve (tails)
-problem asks "was there a diff?"

list 3 ways to find significance

1) test (z/t value) is bigger than critical value
2) probability is less than alpha value (p<0.05)
3) confidence interval does not contain H0 (null) value (95% confidence interval around mean diff excludes null)

statistically not significant/ keep H0 (null) when....?

1) t/z <critical value
2)p-value>0.05
3) 95% confidence interval includes H0 (null)

statistically significant/ reject H0 (null) when....?

1) t/z >critical value
2)p-value<0.05 (in tails/extreme score)
3) 95% confidence interval excludes H0 (null)

define power

the probability of correctly rejecting the null hypothesis
-(p=1-beta)

what is power increased by?

-increase sample size
-increase alpha but can't go higher than 0.05

assumptions in z test

-random sampling
-independent observations
-sampling distribution must be normal
-data being measured must be in interval or ratio form.
-n is very large (30 ish) or population standard deviation is known

define effect size

measure of how large effect of diff is

define significance

says effect was not due to chance (real)

list measures for effect size

1) cohen's d (most common)
2)eta squared (n^2)
3) omega squared (w^2)

is eta-squared (n^2) or omega squared (w^2) better?

omega squared (w^2) > eta-squared (n^2)

- eta-squared (n^2) overestimates true effect size

Cohen's d small effect size

Cohen's d medium effect size

0.2-0.8

Cohen's d large effect size

>0.8

What's wrong w/ z-tests?

need to estimate population standard deviation cuz it's not known

compare z & t distribution

both symmetrical bell shaped & mean=0
-but t-distribution-more flat, spread out, heavier in tails

2 independent sample t test

compare 2 sample means to see if they are diff
-score=quantitative
-group-nominal

What are the three assumptions of the one-sample t test?

Normality, random sampling & independence

between subjects/independent samples

compare 2 groups that get diff level of IV measured @ same time,

within subject/related samples

compare scores for same group that gets all levels of IV across time, get MD (mean of diff)

What are 4 assumptions for the two-independent sample t test?

Normality, random sampling, independence & equal variances

assumptions for related sample t test

random selection, sampling distribution for diff of means is normally distributed

related sample t test

test whether average diff (MD) between 2 measurements is diff from zero

sampling distribution

the distribution of values taken by the statistic in all possible samples of a given size
-never have all the data

Why is the sample mean an unbiased estimator of the population mean?

cuz is M is determined for all possible samples of a given sample size, M will population mean

standard error

the standard deviation of a sampling distribution

standard error of the mean

the standard deviation of the sampling distribution of sample means; estimate of the mean

confidence interval

a range of values so defined that there is a specified probability that the value of a parameter lies within it (95%)
-strategy when population SD is known
-set z=0 as middle interval

wider confidence interval...

more confidence