# PSYCH STATS EXAM 3

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Four Steps of Hypothesis Testing

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Four Steps of Hypothesis Testing

1. state hypothesis

2. critical values

3. Collect and calculate data

4. make decisions

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what must one always remember when writing their hypothesis statement

always write it in terms of the population

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

null hypothesis (Ho)

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

alternative hypothesis (H1)

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

alpha level

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

critical region

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what happens when critical region becomes smaller

values are more towards extreme ends of distribution

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what happens as alpha level decreases

probability of type I error happening decreases

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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

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Standard Error Formula

Om = o/√n

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Z Score formula for sample mean

Z= m-M/Om

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

reject the null

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

fail to reject null

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as sample size increases

standard error (Om) decreases

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Cohen's D

mean difference/ standard deviation

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small Cohen's D

d ≤ .2

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medium Cohen's D

.2 ≤ d .≤ 8

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large Cohen's D

d ≥ .8

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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

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

reject the null

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when given the opportunity, one should more likely pick a

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

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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

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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

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

Power

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how do we determine Beta

1-Power= Beta

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as mean difference increases

test statistic and rejecting the null both increase

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as mean difference decreases

test statistic and rejecting the null both decrease

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

test statistic and rejecting the null both decrease

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

test statistic and rejecting the null both increase

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as sample sizes increases

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

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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

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reporting results for a z statistic

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

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Single Sample T test

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

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estimated standard error formula

Sm= √ s2/n

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Formula for Single Sample T test

t= m-M/Sm

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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

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when sample statistic doesn't accurately affect population parameter

biased statistic

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Larger the sample size and degrees of freedom

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

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smaller the sample size and degrees of freedom

more flattened out the t distribution will be

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sample variance formula

s2= ss/df

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percentage of variance explained

-r2 -percentage of variance due to treatment

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r2 formula

r2= t2/ t2 + df

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small r2

0.01 < r2 < 0.09

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medium r2

0.09 < r2 < 0.25

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large r2

r2 > 0.25

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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%'.

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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

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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)

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

null: M1-M2 = 0 alt: M1-M2 ≠ 0

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DF for Independent measures of between subjects t test

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

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Pooled Variance Formula

S2p= SS1 + SS2 / df1 + df2

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

Sm1-m2= √ S2p/n1 + S2p/n2

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Formula for Independent measures of between subjects t test

t= m1-m2/ Sm1-m2

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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

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

confidence interval

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confidence interval percentages can be

50%, 80% or 90%

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confidence interval formula

M1-M2= m1-m2 ± (tCI)(Sm1-m2)

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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]".

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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

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

Levine statistic

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requires us to have equal sample sizes

Hartley's Fmax

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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

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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

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difference of scores formula

X2-X1

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mD formula

sum of difference of scores/ sample size

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writing a hypothesis for a repeated measures or matched subjects design

null: mD= 0 alt: mD ≠ 0

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estimated standard error with a D subscript formula

SmD= √ s2/n

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Formula for repeated measures or matched subject design t test

t = mD/SmD

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we use the ≤ or ≥ symbol when

we have one tailed

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we use the = or ≠ when

we have two tailed

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confidence interval formula for MD

MD= mD ± (tCI)(SmD)

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