RM2 Final

Frequency Claim

1 variable

percent

how often something happens

Association Claim

2 variables

link between them

does not argue causality

Pearsons r

Causal Claims

2 variables

strongest

what causes something

Nominal

Qualitative

yes or no questions

categories have no logical order

ex. eye color, drink size

Ordinal

quantitative

rank ordering

ex. race finish, sibling order, cup size

Interval

Quantitative

no true zero

ex. IQ, temp

Ratio

Quantitative

true zero

ex. age, cost, height, weight, time, income

Z score

how many SD away from the mean

allows us to compare across distributions, find probabilities, identify rare and common regions

mean of 0, SD of 1

follows same distribution as original set of data

Standard Normal Distribution

zscore of any and every normal distribution

mean=0, SD=1

xaxis= zscores

0=50th percentile

1= 84th percentile

Descriptive Stats

summarize, simplify, and better interpret data

mean= average

median= middle value

mode= most common

Inferential Stat

use sample data to make inferences about population

hypothesis testing, CI

Rare and Common Regions

tails= low prob/rare

middle= high prob/common

lowest and highest 2.5%=rare (5%0

Sampling Distribution

made up of all possible samples with the same sample size from our pop

Sampling Distribution of Sampling Means

plots means of our possible samples

Theoretical- not collecting all possible samples

helps us understand how samples would fall, compare scores and find percentiles

shape= unimodal, normal

center= mean

spread= use SE

Central Limit Theorem

SDSM will have a mean equal to underlying pop mean and SE

will become more normal as sample size increases

when normally distributed= underlying pop mean is or sample size greater than 30

means of SDSM= means of original distribution of individual scores

Standard Error

SD of sampling distribution

formula: pop SD/ square root of sample size

Effected by sample size and SD

greater SD= greater SE, larger sample sizes= smaller SE (more precise)

Standard Deviation vs Standard Error

SD= measure spread of individual data, remains stable as n increases, descriptive stat

SE= measures reliability of sample mean, decreases as n increases, inferential stat

Z test

one sample z test= evaluates if a mean of sample is different from a known pop mean

need: sample mean, pop mean, and SE

formula: sample mean- pop mean/ SE

Similarities of Z tests and Z scores

both use statistic table

similar equations

can calculate percentiles if normally distributed

Differences of Z tests and Z scores

zscores compare individual scores to pop mean

ztests compare sample mean to pop mean using SDSM

Hypothesis Testing Steps

1. state research question

2. formulate statistical hypothesis

3. formulate decision rule/ level of significance

4. make calculations

5. make decision

6. interpret

Factors Affecting Hypothesis Test

size of Z calc determined by: size of observed difference and size of SEM (more variable= wider and larger p value)

if inferential

Null Hypothesis

no effect/relationship

Alternative Hypothesis

there is an effect

Significance Level

most extreme 5%

defined by cutoff z values

size= alpha (a)

a=.05, critical value= ± 1.96

one tailed= .05 in one tail

two tailed= 2.5% in each tail

Rare Region

critical region

testing against this

if zcalc> zcrit= reject

rejecting means= observation does not come from H0 pop

one tailed= directional, less conservative, one end, easier to reject

two tailed= reject if in either tail, common, hard to reject null

P value

prob we get out result given null is true

p <.05

if less than .05= statically significant

Effect Size

measure of magnitude of observed difference

independent of sample size

use cohens d

.20=small, .50=medium, .80=large

formula: sample mean- pop mean/ pop SD

Type 1 Error

reject null when it is true

false alarm, more serious

fix with small alpha

saying there is a significant relationship when there is not

Type 2 Error

failing to reject when its false

miss

fix with increase power/sample size

saying there is not a significant relationship when there is

Power

prob that a test correctly rejects a false null

target= 80%

increased power= reduced chance of missing a true effect (lowers type 2 error rate), higher chance of detecting significant but meaningless effect

Factors Affecting Power

1. sample size (larger= more power)

2. effect size (larger= greater power/ less noise)

3. Significance level (bigger= greater power)

increased with: larger sample size, larger effect size, and larger a

Point Estimate

single value used to represent unknown pop mean

usually sample mean

Confidence Interval

range for which we are confident that the true pop lies within this range

want 95% (1.96) or 99% (2.58)

higher= wider, less precise

smaller SEM= narrower CI

width based on: pop SD, sample size, and how confident we are

larger the sample size, smaller the SE, and narrower the CI

One Sample T test

comparing sample mean to pop mean (pop SD unknown)

t crit depends on degrees of freedom

t calc> tcrit= reject

Design Confounds

something wrong with design of experiment

Experimenter’s mistake

could cause change in DV

effects internal validity

Selection Effects

kinds of Ps in one level are different than those in another level

occur when Ps choose own group or when researcher assigns one type of person to same group

effects internal validity

only for between subjects

prevent: random assignment, matching, do within subjects design

Order Effects

threat to internal validity

exposure to one condition change Ps responses to a later condition

for within subjects

fix with counterbalancing

Between Subjects Design

different Ps in different conditions of experiment

called independent groups

post test only (measure DV at end)

pre test/ post test (measure DV before and after IV)

Within Subjects Design

same subjects in all conditions

concurrent measures and repeated measures

condition order needs to be random

IV manipulated within a single group of subjects

Independent Samples t test

comparing means of two independent groups

null= 2 pop means do not differ

alternative= 2 pop means do differ

uses effects size

df= n1+n2-2

Paired Samples t test

comparing means from related groups

2 observations for each P

same formula as one sample t test

null= mean difference is zero

alternative= mean difference is not zero

df= n-1

One Way Between Subjects ANOVA

comparing means of 3+ independent groups

analysis of variance

does not compare specific levels

F statistic

top and bottom will be positive

df= between k-1, within n-k

MSbetween/ MSwithin

Null and Alternative for ANOVA

null= mean difference score in pop is zero

H0= u1=u2=u3

alternative= mean difference score in pop is not zero (at least one pop mean differs)

H1: HOFalse

ANOVA Logic

individuals vary naturally

within group and between group variability

Post Hoc Tests

for ANOVA

when we reject null (stat significant)

follow up test

cant use t test bc alpha inflation= increased risk of type 1 error

Bonferroni Correction

post hoc test

series of t tests

Divided desired a by number of follow up tests, then proceed as normal with t test

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

pros: easy to calculate

cons: conservative (increased risk of type 2 error)

Tukeys Honestly Significant Difference

post hoc test

compare difference between groups means to a cutoff

adjustments to test statistic (not alpha)

gives estimate of difference between groups and a CI

pros: reduces type 2 error

cons: hard to calculate by hand

How To Use Tukey Test

look at table (Ptukey)

compare numbers to alpha level (.05)

if <.05= significant

if not significant= did not detect any significant pairwise comparison

One Way Repeated Measures ANOVA

comparing means of 3+ related groups

MScondition/MSerror

benefit= greater power (more likely to detect significant effect)

df: condition k-1, error (n-1)(k-1)

Quasi Experiment

do not have full experimental control

cant randomly assign Ps

issues: selection effects and design confounds

why use: real world, external validity, ethics, construct and stat validity

Small n design

gather lost of info from a few cases

pro: higher experimental control, study special cases

cons: internal and external validity

Factorial Designs

manipulate more than one IV at once (2 or more IVs)

only one DV

examines more complex relationships

Simple Experiment

between subjects

2 levels of single IV

ex. laptop or by hand note method

Factorial Design Terminology

described with numbering system

2 times 2 (4 conditions)

2 times 3 (6 conditions)

indicates: number of factors and number of levels of each factor

conditions= crossing IV

Multiple IVs

can see whether and how they interact in their impact on DV

more similar to whats going on in real life

like multiple regression

2 times 4 times 3 Design

3 IVs

one has 2 levels, one has 4 levels, one has 3 levels

Main Effect

factorial design

impact of one IV on the DV averaging across levels

across rows or columns

Interaction

factorial design effect

when effect of an IV depends on the levels of another IV

how does one variable depend on another?

joint effect of IVs

difference between differences

in the cells of the design

interpret interaction first

Completely Parallel Lines

don/t have an interaction

Simple Effect

effect of one IV at one specific level of the other IV

look at if have significant result

Statistical Significance for Factorial ANOVA

2 factor experiment= 2 main effects= 1 interaction

Statistical significance for each= 3 F ratios (multiple nulls)

Multiple Null Hypothesis for Factorial ANOVA

Factor A (levels A1 and A2)

• uA1=uA2

Factor B (levels B1, B2, B3)

• uB1=uB2=uB3

H0= no interaction

HA= H0 not true

Calculating Variability Factorial ANOVA

mean square= estimate of variance

MS= SS/df

• SS= sums of squares

use relevant SS and relevant df

3 sources of variability

Further Analyses for Factorial ANOVA

only do if statistically significant

Analyze simple effects and effect size

if 3+ levels, pairwise comparisons and effect size

2 Factor ANOVA

3 F ratios

effect of Factor A

effect of Factor B

Interaction between A and B

Effect Size for Factorial ANOVA

partial eta squared

ranges from 0-1

n

only for significant results

.01=small, .09= medium, .25= large

Mixed ANOVA

one IV is between subjects, one IV is within subjects

ex. different Ps but all tested on same conditions

Jamovi- will give 3 F conditions

Replication

a study whose results have been reproduced when the study was repeated

types: direct, conceptual, replication + extension

Direct Replication

researchers repeat the original study as closely as possible to see if the original effect shows up

Conceptual Replication

researchers examine the same research question but test it differently (different procedures for operationalizing the variables)

Replication + Extension Replication

researchers replicate original study but add variables or conditions that tests additional questions

Meta Analysis

Mathematically averaging the effect size of all the studies that have tested the same variables

see what the overall effect and how strong the evidence is

helps our confidence

Questionable Research Practices

under-reporting null findings (need to include them)

HARKing- hypothesizing after results are known (changing hypothesis)

p-hacking- test data in many ways, report whats significant

all bad

Transparent Research Practices

open materials- all materials are posted, helps with replication, consistency of evidence

open data- full data set available, others can confirm results

preregistered- publish hypothesis and study design before data is collected, others will have more confidence in strength of evidence

External Validity and Sampling Reminders

refers to a broader population

comes from how not how many Ps

• better to have 200 randomly samples Ps

just bc a sample comes from a pop does not mean it generalized to that pop

Who Do Psychologists Study?

mostly convenience samples

most from North America (60%=US)

frequency claims must have external validity (random samples)

association and causal claims may not need it