PSYCH STATS EXAM 3

Four Steps of Hypothesis Testing

Four Steps of Hypothesis Testing

1. state hypothesis

2. critical values

3. Collect and calculate data

4. make decisions

what must one always remember when writing their hypothesis statement

always write it in terms of the population

anti-hypothesis; no treatment effect or significant differences took place

null hypothesis (Ho)

treatment will cause a change or significant difference; there can be multiple

alternative hypothesis (H1)

looking for values that fall into the extreme 5%,1, or .1% of scores

alpha level

composed of the extreme values that are very unlikely to be obtained if the null hypothesis is true

critical region

what happens when critical region becomes smaller

values are more towards extreme ends of distribution

what happens as alpha level decreases

probability of type I error happening decreases

two tailed vs one tailed

two tailed is a nondirectional test because it doesn't tell us what direction the difference is

one tailed is directional test because it tells us whether there is an increase or decrease

Standard Error Formula

Om = o/√n

Z Score formula for sample mean

Z= m-M/Om

what do we do when we answer yes to step four of the hypothesis method

reject the null

what do we do when we answer no to step four of the hypothesis method

fail to reject null

as sample size increases

standard error (Om) decreases

Cohen's D

mean difference/ standard deviation

small Cohen's D

d ≤ .2

medium Cohen's D

.2 ≤ d .≤ 8

large Cohen's D

d ≥ .8

explain the term most conservative

-score that is furthest from the mean -by choosing z score that farther from mean, you're reducing likelyhood of committing type I error

when you have a one tailed directional test you're more likely to

reject the null

when given the opportunity, one should more likely pick a

one tailed test bc you're less likely to commit a type II error

Type I Error

-determined by ALPHA LVL -considered worst type of error -incorrectly rejected a true null -when one claims there's a treatment effect but in reality there is not -ex. sending an innocent person to jail

Type II Error

-failed to reject a true null -we thought there was not treatment effect but there was -determined by calculating BETA, works w/ Power -ex. setting a guilty person free

tells one the likelihood that one will correctly reject a false null

Power

how do we determine Beta

1-Power= Beta

as mean difference increases

test statistic and rejecting the null both increase

as mean difference decreases

test statistic and rejecting the null both decrease

as standard deviation(o) and standard error (Om) both increase

test statistic and rejecting the null both decrease

as standard deviation(o) and standard error (Om) both decrease

test statistic and rejecting the null both increase

as sample sizes increases

standard error (Om), test statistic, and rejecting the null all increase

Assumptions of Z Score Testing

1. Random Sampling: independent random sampling & random sampling with replacement

2. Independence of Observations: each individual's score is independent of each other, it doesn't impact the other

3. Value of Pop. Standard Dev. isn't changed by treatment: how we calculate error

4. Normal distributions: is sample size is 30 or greater or if it comes from normal distribution population

reporting results for a z statistic

"In a sample, n=6, it was found that (fancy words), z= +3.40, p<.05".

Single Sample T test

when we don't have population variance we use sample variance

estimated standard error formula

Sm= √ s2/n

Formula for Single Sample T test

t= m-M/Sm

When do we use a Z score and when do we use a T test

-if you have population standard dev -> Z score -if you don't have population standard dev. & working with single sample -> T test

when sample statistic doesn't accurately affect population parameter

biased statistic

Larger the sample size and degrees of freedom

more closely proportionationated will those scores math to the Unit Normal Table

smaller the sample size and degrees of freedom

more flattened out the t distribution will be

sample variance formula

s2= ss/df

percentage of variance explained

-r2 -percentage of variance due to treatment

r2 formula

r2= t2/ t2 + df

small r2

0.01 < r2 < 0.09

medium r2

0.09 < r2 < 0.25

large r2

r2 > 0.25

results statement for a single sample t test

" The participants averaged m=5 with a SD=4 on the happiness scale. Statistical analysis found that (more fancy words I should be asleep right now rrrriiiiiipppppppp), t(8-df)=3.00, p<0.5, r2= 24.56%'.

Assumptions about single sample t test

1. independence of observations: scores are independent thus they don't affect each other

2. normal population distributions: sample size of 30+ or comes from normal population distribution

Independent measures of between subjects t test

-two separate samples and we're comparing the means together -big clue if you have two different data sets ( n1,n2,SS1,SS2)

stating the hypothesis for a Independent measures of between subjects t test

null: M1-M2 = 0 alt: M1-M2 ≠ 0

DF for Independent measures of between subjects t test

since you have two samples, you add the two DF DF= df1 + df2

Pooled Variance Formula

S2p= SS1 + SS2 / df1 + df2

estimated standard error formula that we learned for CH10 when we have two samples and two sample means

Sm1-m2= √ S2p/n1 + S2p/n2

Formula for Independent measures of between subjects t test

t= m1-m2/ Sm1-m2

effect size => estimated Cohen's D

when the mean difference is negative, you take the absolute value ex. -7.5 becomes I 7.5 I

when we state with a certain degree of assurance that the actual population mean difference fall within a certain range

confidence interval

confidence interval percentages can be

50%, 80% or 90%

confidence interval formula

M1-M2= m1-m2 ± (tCI)(Sm1-m2)

result statement for Independent measures of between subjects t test

"Have you drank water today, didn't think so go do it, t(3)=2.50, p<.05, d=56.7, r2= 56.64%, CI=[ 2.14, 9.18]".

Assumptions of Independent measures or between subjects t test

1. independence of observations: scores independent of each other, they don't affect each other

2. normality: sample size of 30+

3. Homogeneity of variance: variance of population from which samples occur are the same ;Levine statistic; Hartley's Fmax

test to asses and make sure population from which samples come from have the same variance

Levine statistic

requires us to have equal sample sizes

Hartley's Fmax

Repeated Measures T Test

-we have one sample but experiment the same sample under two separate conditions -remove all individual differences thus makes it easier to pinpoint the actual cause of change -comparing different scores -ex. taking a test one day in a 60degrees room vs another day we take it in a 90degrees

Matched Subjects design

-we have two samples but try to make them as identical as possible -ex. matching up the kids with similar characteristics taking a test and grouping them together to make it look we have one sample but we really have two

difference of scores formula

X2-X1

mD formula

sum of difference of scores/ sample size

writing a hypothesis for a repeated measures or matched subjects design

null: mD= 0 alt: mD ≠ 0

estimated standard error with a D subscript formula

SmD= √ s2/n

Formula for repeated measures or matched subject design t test

t = mD/SmD

we use the ≤ or ≥ symbol when

we have one tailed

we use the = or ≠ when

we have two tailed

confidence interval formula for MD

MD= mD ± (tCI)(SmD)