RM2 Exam 3

Quasi Experiment

similar to experiment but researchers do not have full experimental control

ex. cant randomly assign Ps to IV

has at least 1:

• quasi IV: resembles true IV but researchers do not have full control

• DV

threats to internal validity- can we be sure our result is due to quasi IV?

potential issues: selection effects, design confounds, etc

Why Use Quasi Experiment

real world opportunities

external validity

ethics

Construct and statistical validity

Small n Design

a study where researchers gather alot of info from just a few cases

benefits= higher experimental control, studying special cases

cons= internal validity, external validity (fix by triangulating)

triangulating: comparing a case study’s results to research using other methods

Independent Samples T Test

comparing means of 2 independent samples/groups

degrees of freedom- n1+ n2 -2

ex. Compare exam scores between students who studied with music and students who studied in silence

Independent Samples T Test Formula

how likely is a sample t exist at the pop level?

t= mean of sample 1- mean of sample 2/ estimate of pop SD of mean differences

Null and Alternative for Independent Samples T test

null- 2 pop means do not differ

alternative- 2 pop means do differ

Effect Size for Independent Samples T test

measure of absolute magnitude of observed effect/difference

independent of sample size

estimated d= observed effect/ estimated pop SD

Denominator is difference between the t formula

Guidelines= .2- small, .5- medium, .8-large

asses how large effect is after removing any effects that are due to sample size

Paired Samples T test

comparing means from related groups (same group at different times/matched pairs)

within subjects design

Counterbalancing

in repeated measures, present levels of IV to Ps in different sequences to control order effects

Paired Observations

Yields 2 observations from each P

as many pairs of observations as Ps

different data structure than a between subjects design which assumes samples of unrelated

(for paired samples- Ps are not related)

Different Score

change in our DV from one condition to another for a single P

paired samples t test

ex. difference between pain level with swear word and neutral word

• P1- D1= X1swear- X1neutral

• P2- D2= X2swear- X2neutral

• then calculate mean different score

_

D = D/ n

Paired Samples T test Formula

t= mean difference score/ standard error (same denominator as one sample t test)

one sample t test and paired samples t test have same formula

One Way Between Subjects ANOVA

use when: 3 or more unrelated means and want to compare them

(comparing means of 3+ independent groups)

factor= IV

one IV= 1-factor experiment/design

use because more than 2 levels creates inflation of P/type 1 error

Analysis of Variance

does not compare specific levels (is omnibus)

Null for Paired Samples T test

null: mean difference score in pop is zero (does not differ)

alternative: difference score in pop is not zero (does differ

Types of 1 way (1-factor) ANOVA

samples independent

• between subjects design- non matched

• 1 way ANOVA for independent groups

samples not independent

• within subjects design or matched groups

• 1-way ANOVA for dependent groups/ related samples/ repeated measures

1 Way ANOVA

H0 and H1 look different (have more than 2 conditions)

for 3 conditions

• H0: u1=u2=u3

• H1: HoFalse

at least one of pop means different from otheers

not all the same

Procedures for 1 way between subjects ANOVA

same for all hypothesis tests

get calc value of test stat

get critical value and compare

use f statistics

calculate F statistic from data

determine F crit

ANOVA Logic

Individuals vary naturally

Determine if variation is systematic and meaningful or not (by using hypothesis test)

within group variability and between group variability

One Way Between Subjects ANOVA Formula

F= variability between groups/ variability within groups (chance/error)

top and bottom will always be positive

calculate F in terms of pieces of variance= F ratio

F= MS between/ MS within

degrees of freedom

• between K-1

• within n-K

K= number of groups in IV

Mean Square (One Way Between Subjects ANOVA)

estimate of variance of something

for One Way Between Subjects- variability between groups (MS between)

for within groups (MS within) (also called MS error)

F= MS between/ MS within

Null and Alternative for ANOVAs

null- the pop means Mu1, Mu2, Mu3 do not differ

Alternative= the pop means are not all the same (at least one mean is different)

Post Hoc Tests

for ANOVA

when we reject null (if statically significant)

is a follow up test (similar to t test but testing multiple groups at multipl times

• alpha inflation- why we cant use t tests, increased risk of type 1 error

corrections= bonferoni and tukey tests

Type 1 Error

Saying theres a significant result when there is not one

Bonferoni Correction

series of t tests

divide desired alpha by the number of follow up tests, then process as normal with t test (will sum back up to our original type 1 error rate)

once we have new significance level, run independent samples t test to look for differences between our pairs of groups

pros= easy to calculate

cons= overly conservative (increased risk. of type 2 error) (give small alpha level)

use when: small number of planned comparisons

ex. a=.05, running 3 post hoc comparisons, each alpha= .017

Tukeys Honestly Significant Difference

compare difference between group means to a cutoff number that ensures a honestly significant difference

makes adjustments to test statistic (not alpha)

gives estimate of the difference between the groups and a CI

pros= reduces type 2 error

cons= hard to calculate by hand

compares the mean difference to new test statistic

yields a p value

One Way Repeated Measures ANOVA

comparing the means of 3+ related means

hypotheses are same as one way between ANOVA

Procedure is the same

One Way Repeated Measures ANOVA Formula

F= MS condition/ MS error

MS condition= variability between conditions

MS error= variability within groups after removing individual differences

Individual differences are identifiable and removable

benefit= greater power (if F calc is large) (more likely to detect significant effect)

denominator is smaller

Degrees of Freedom for One Way Repeated Measures ANOVA

df condition= k-1

• (k= number of conditions)

df error= (k-1) (n-1)

How to Use Tukeys Post Hoc

look at table (Ptukey)

compare numbers to alpha level (.05)

if < .05= significant

if not significant= did not detect any significant pairwise comparisons