Psyc 305

Front 1

basic stats lecture

Back 1

..

Front 2

population

Back 2

The entire set of things of interest

Front 3

parameter

Back 3

property descriptive of the population
ex) pop mean

Front 4

sample

Back 4

part of the population
typically this provides the data we will look at

Front 5

estimate

Back 5

property of a sample
ex) sample mean

Front 6

descriptive stats

Back 6

Summarize/describe the properties of samples (or populations when they are completely known)

Front 7

inferential stats

Back 7

Draw conclusions/make inferences about the properties of populations from sample data

Front 8

variable

Back 8

-varies
-condition or characteristic that can have different values

Front 9

types of variables (6)

Back 9

can classify as:nominal, ordinal, interval, ratio
or classify as: dependent, independent

Front 10

categorical (discrete/qualitative) variables (2)

Back 10

nominal and ordinal

Front 11

numerical (cont/quantitative) variables (2)

Back 11

interval
ratio

Front 12

dependent variables (Y)

Back 12

outcome/response
predicted variables
continuous (normally distributed)

Front 13

independent variables (X)

Back 13

factors in experiments
predictors/covariates
categorical/continuous

Front 14

(3) measures of central tendency

Back 14

mean
median
mode

Front 15

mean is affected by ___values

Back 15

extreme/outliers

Front 16

is median affected by outliers

Back 16

no

Front 17

is mode affected by outliers

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no

Front 18

can you have no modes

Back 18

yes

Front 19

can you have multiple modes

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yes

Front 20

mode used for ___or___data

Back 20

numerical
categorical

Front 21

(3) measures of variation

Back 21

range
variance
SD

Front 22

measures of variation give info about __or___

Back 22

spread or variability

Front 23

range

Back 23

simplest measure of dispersion
largest value-smallest

Front 24

average of squared deviations of values from the mean

Back 24

variance

Front 25

most commonly used measure of variation

Back 25

SD

Front 26

SD shows

Back 26

variation about the mean
has same units as original data

Front 27

shape of distribution

Back 27

describes how data distributed
symmetric or skewed

Front 28

left skewed (negatively skewed)

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median>mean

Front 29

right skewed (positively skewed)

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mean > median

Front 30

in most experiments Y(dependent variable) assumed to be continuous and

Back 30

normally distributed

Front 31

normal distribution

Back 31

-mean=median=mode
-mean(μ ) and SD(σ) sufficient to describe normal dist
-interval: μ ± 1σ contains 68% of the values
-interval: μ ± 2σ contains 95% of the values
-interval: μ ± 3σ contains 99.7% of the values

Front 32

session 2
hypothesis testing: comparing one/two means

Back 32

..

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hypothesis=

Back 33

Answer to a research question or assumption made about a population parameter

Front 34

step 1 for hypothesis testing

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make a null hypothesis (Ho): no effect
make alternative hypothesis (H1): some effect

Front 35

step 2 for hypothesis testing

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choose alpha (sig level)
use .05 (or .01 if told otherwise)

Front 36

cutoff sample score for α is called the

Back 36

critical value

Front 37

step 3 for hypothesis testing

Back 37

look at the data and compute test statistic:
-if you have one mean and σ is known use z
-if you have one mean and σ is UNknown use t
-if you have 2 means use t
-more than two means use ANOVA

Front 38

step 4 for hypothesis testing

Back 38

reject or not reject the null:
-Compare the calculated value of your test statistic to the (tabled) critical value for α
If your value is greater that the critical value,
reject Ho, otherwise accept Ho
-OR look at p value of test statistic value and if p value< .05 reject Ho

Front 39

if Ho is rejected you can conclude that

Back 39

there is a statistically significant effect in
the population

Front 40

does a significant effect indicate the effect is important or meaningful

Back 40

no
need to calculate effect size to do so

Front 41

Pearson’s correlation coefficient (r) (effect size
correlation)
Omega (ω)
Cohen’s d

Back 41

Commonly used measures of effect size

Front 42

r = ___ (small effect)
r = ___(medium effect)
r = ___ (large effect)

Back 42

.10
.30
.50

Front 43

z-test purpose

Back 43

test whether a sample mean significantly differs from a population mean (μ).

Front 44

Prior Requirements/Assumptions for z-test (3)

Back 44

􀂄 The population is normally distributed.
􀂄 The mean (μ) and standard deviation (σ) of the
population must be known.
􀂄 The sample must be a simple random sample of
the population.

Front 45

Technically, the z-test for a single mean is equivalent to calculating the ____of your sample mean

Back 45

z score

Front 46

can convert sample score to standard score (z) which follows___distribution

Back 46

standard normal (μ=0, σ=1)

Front 47

purpose of the z statistic is to

Back 47

transform any normal distribution to the standard normal distribution
*shape does NOT change just units

Front 48

z=+/-1.96

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alpha=.05

Front 49

z=1.96
z=-1.96

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2.5%
2.5%

Front 50

Hypothesis testing about a single mean with Z-test

Back 50

-if z-score in absolute value larger than 1.96 you may reject the null with sig level of .05

Front 51

limitations of z test
alternative?

Back 51

-Knowing the true value of the standard deviation (σ) of a population is unrealistic (unless entire pop. known)
-t-test

Front 52

purpose of t-test

Back 52

to test whether a sample mean significantly differs from a population mean (μ).

Front 53

Prior Requirements/Assumptions for t-test

Back 53

􀂄 The population is normally distributed.
􀂄 The mean (μ) of the population must be known.
􀂄 The sample must be a simple random sample of
the population.

Front 54

t-statistic is obtained by replacing σ with s (sample SD) this replacement causes what

Back 54

t-stat no longer follows standard normal dist but now follows a t-dist

Front 55

t-distribution varies in shape according to

Back 55

-degrees of freedom (DF= N-1)
*as DF increases t-dist approaches standard normal dist (DF=30 is basically standard normal dist)

Front 56

t approaches z as __increases

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N

Front 57

If your calculated t-value in absolute value is ___ than the critical value from the table, you may reject the null hypothesis with the significance level of .05
OR if p-value/sig level of t-value is____than .05

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larger
less

Front 58

purpose of t-test for 2 means
2 samples may be either __or___

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-test whether two unknown population means (μ1 and μ2) are different from each other based on their samples
-independent or correlated

Front 59

hypothesis for t-test with 2 means

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Ho: μ1 = μ2
H1: μ1 ≠ μ2

Front 60

t-test for two independent samples
Prior Requirements/Assumptions (3)

Back 60

􀂄 Both populations are normally distributed.
􀂄 The standard deviations (σ1 and σ2) of
the populations are the same.
􀂄 Homogeneity of variance (σ1 = σ2)
􀂄 Each sample must be a simple random
sample of the population.

Front 61

limitation of t-test
alternative?

Back 61

-only used for hypothesis testing one or 2 means
-ANOVA

Front 62

one-way ANOVA

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...

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factor=

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Independent variable

Front 64

different values or categories of the independent variable/factor=

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levels

Front 65

what experiment involves a single IV with two or more levels

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single factor

Front 66

(2) single factor experiments
difference between them

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One-way independent-groups design--> each group has different subject
One-way design with repeated measurements--> each group has same subjects

Front 67

factorial experiments

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Involve more than one independent variable with two or more levels.

Front 68

Two-way independent-groups designs:
if experiment has 2 factors with 2 levels each=

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2x2 experiment

Front 69

purpose of one way anova

Back 69

to test whether the means of k (≥ 2) populations significantly differ

Front 70

hypothesis of one way anova

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Ho : μ1 = μ2 · · ·= μk
H1 : Not all μ’s are the same (at least
one of the means is different)

Front 71

one way anova
Prior Requirements/Assumptions (3)

Back 71

􀂄 The population distribution of the
dependent variable is normal within each
group.
􀂄 The variances of the population
distributions are equal (homogeneity of
variance)
􀂄 Independence of observations

Front 72

2 sources of variance in anova

Back 72

Vb
Vw

Front 73

variance due to different treatments/levels of a factor across groups=

Back 73

variance between groups (Vb)

Front 74

random fluctuations of subjects within each group=

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variance within groups (Vw)

Front 75

F statistic/ratio

Back 75

-Vb/Vw
-When Ho is true, this ratio is expected to be equal
to 1
-When H1 is true, this ratio is expected to be greater than 1.

Front 76

F stat follows___dist
this dist varies in shape according to (2)

Back 76

F
DF (b) and DF(w)

Front 77

the F dist is a _____skewed distribution used most commonly in ANOVA

Back 77

right

Front 78

if your calculated F value is greater than the critical value you may reject the null at .05 OR look at p value of calculated F value and if ___than .05 reject the null

Back 78

less

Front 79

With only two groups, either a _____ or an F test can be used for testing the significance of the difference between means.

Back 79

t test
*both lead to same conclusions
In fact, when k = 2, t = ±√F

Front 80

in ANOVA
V=

Back 80

SS(sum of squares)/DF

Front 81

Total SS=

Back 81

variation
SS(T)= SS(B)+SS(W)

Front 82

Vt, Vb and Vw are often called the total, between group, and within-group Mean Squares, abbreviated
by

Back 82

MS(T), MS(B) and MS(W)

Front 83

The (overall) ANOVA test doesn’t tell which means are different so we perform _____test

Back 83

post hoc comparison

Front 84

____test gives a global effect of the independent variable (factor) on the dependent variable (omnibus or overall test)

Back 84

F-test

Front 85

Post hoc (a posteriori/unplanned) comparisons
done _____the experiment
used if

Back 85

after
3+means compared

Front 86

2 post hoc tests

Back 86

scheffe
Turkey HSD

Front 87

scheffe test

Back 87

use when groups have different sizes
most conservative test (unlikely to reject Ho)

Front 88

tukeys HSD test

Back 88

used if groups have equal sizes

Front 89

The minimum absolute difference
between two means required for a
significant difference.

Back 89

HSD

Front 90

Turkey-Kramer Test

Back 90

when sample sizes are unequal

Front 91

For Tukey:
observed Q compared against critical value of Q (CQ) for .05 and reject Ho when
OR

Back 91

-observed Q value is greater than the critical
value
-reject null if mean differences>HSD

Front 92

steps for Tukey HSD

Back 92

step 1: ANOVA
step 2: calc differences in means
step 3: CQ
step 4: calculate HSD
*when comparing HSD to mean differences , put mean differences into absolute values
reject the null if HSD less than mean differences between 2 groups

Front 93

(4) ways to assess normality

Back 93

-look at descriptive stats ie skewness
-construct charts/histograms/normal quantile plot
-K-S test
-Shapiro-Wilk test

Front 94

limitation of normality tests

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It is very easy to give significant results when sample size is large

Front 95

(2) ways to assess homogeneity of variance

Back 95

Fmax test of Hartley
Levenes Test

Front 96

Serious violation of homogenity of variance tends to
inflate the observed value of the_____

Back 96

F statistic ie) too many rejections of Ho (high Type I error)

Front 97

Fmax test of Hartley (3 steps)

Back 97

1) Calculate the sample variance for each group,
and find the largest and smallest variances
2) Fmax= max V/min V
3) observed Fmax value is compared against a critical value of this statistic (if the observed Fmax value exceeds the critical value, we may reject the null hypothesis that the variances are identical across groups)

Front 98

Tests the null hypothesis that the population
variances are equal

Back 98

Levene’s test

Front 99

If Levene’s test is significant (p < .05), then we may conclude that the variances are

Back 99

significantly different

Front 100

F-test is robust against the violation of this assumption, for homogeneity of variances, when samples are

Back 100

of equal size

Front 101

knowing the value of one observation gives no clue as to that of other observation=

Back 101

Independent observations

Front 102

the most crucial assumption underlying the F test

Back 102

independence of observations

Front 103

experiments should be carefully designed to avoid non-independent observations by random sampling&assignment, why?

Back 103

-no easy way to fix F test when assumption of independence violated
-no easy test for non-independence

Front 104

if 3 assumptions for ANOVA not met a _____may be useful

Back 104

data transformation

Front 105

data transformation makes data less____
makes heterogeneous variances more___

Back 105

skewed
homogeneous

Front 106

If data transformation doesn’t work, consider ____tests, i.e. Kruskal-Wallis ANOVA.

Back 106

nonparametric

Front 107

session 5 two way anova

Back 107

...

Front 108

in Two Way factorial experiments assume (2)

Back 108

 subjects serve only in one of the
treatment conditions (independent-groups
design)
 sample sizes are equal in each condition
(balanced design).

Front 109

Two Way factorial experiments

Back 109

-2 IV's (Row, Column)
-more than 2 means

Front 110

Two Way factorial experiments: when each factor has 2 levels we call it a _________design

Back 110

2 x 2 factorial design

Front 111

two-way factorial experiment contains information about (2)

Back 111

two main effects
interaction effect

Front 112

main effects

Back 112

-effect of one factor when the other factor is ignored (by averaging the means over all levels of the other factor) ie) 2 IV's effect on DV
-differences among marginal means for a factor

Front 113

interaction effect

Back 113

-extent which the effect of one factor depends on the level of the other factor ie) interaction between different levels of the 2 IV's

Front 114

An ____is present when the effects of one factor on DV change at the different levels of the other factor

Back 114

interaction

Front 115

presence of an interaction indicates that the main effects

Back 115

alone do not fully describe the outcome of a factorial experiment

Front 116

Two way ANOVA
Prior requirements/assumptions (3)

Back 116

 The distribution of observations on the
dependent variable is normal within each
group (normality).
 The variances of observations are equal
(homogeneity of variance).
 Independence of observations.

Front 117

hypothesis for main effects

Back 117

-row main effect
Ho: μR1 = μR2 = · · · = μRr (equal row marginal means)
H1R: Not all μR are the same
-column main effect
Ho: μC1 = μC2 = · · · = μCc (equal column marginal means)
H1C: Not all μC are the same

Front 118

hypothesis for interaction effect

Back 118

-HoRC: The interaction between R and C is
equal to zero (e.g., RC = 0)
-H1RC: The interaction between R and C is not
zero (e.g., RC ≠ 0)

Front 119

in Two Way ANOVA you partition SS(B) into (3)

Back 119

SS(R)=variation between row means
SS(C)=variation between column means
SS(RC)=variation between cell means

Front 120

when 2 way ANOVA results significant use ___tests to find significant main effect and ____analysis to determine significant interaction effect

Back 120

post hoc
simple effect

Front 121

simple effect analysis

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effect of one factor at each level of the other factor
-effects of rows at C1
-effects of rows at C2
-effects of columns at R1
-effects of column at R2

Front 122

calculating simple effects

Back 122

-we can apply a one-way ANOVA for one factor
repeatedly at each level of the other factor
-then when calculating F ratio use MS(W) from the two way ANOVA in the denominator

Front 123

session 7 one way repeated measures ANOVA

Back 123

..

Front 124

repeated measures design

Back 124

-measurements on single DV repeated a number of times within same subject
-ex) 2 conditions, before and after treatment
-N subjects measured on single DV under K conditions/levels of a single IV

Front 125

One-way repeated measures ANOVA used for (2)

Back 125

-examine effect of treatment (IV) (between group effects, Ho:μ1 = μ2 · · · = μk )
-test the effect of subjects (between subject effect, Ho: V=0)

Front 126

are we interested in effect of subjects or subject level variability

Back 126

-not really
-if effect it significant it just means subjects differ but has nothing to do with the IV

Front 127

prior assumptions (3) for one way repeated measures ANOVA

Back 127

-distribution of observations on the DV is normal within each level of the treatment
factor.
-variances of observations are equal
(homogeneity of variance) at each level of the
treatment factor
-population covariance between any pair of
repeated measurements is the same (homogenous
covariance)

Front 128

hypothesis in one way repeated measures ANOVA
for between group effect

Back 128

Ho: μ1 = μ2 · · · = μk
H1: Not all μ are the same

Front 129

hypothesis in one way repeated measures ANOVA for subject effect

Back 129

Ho: V=0
H1: V≠ 0

Front 130

in repeated measure designs is independence likely to hold

Back 130

nope

Front 131

when both homogeneity of variance (equal variance) and homogeneous covariance (equal covariance) assumptions are met we describe this as ____symmetry

Back 131

compound

Front 132

in one way repeated measures
k=
n=

Back 132

number of conditions/levels of IV
number of subjects

Front 133

One-way repeated measures ANOVA:
SS(B)=
SS(S)=
SS(T)=
SS(BS)=

Back 133

-Variation between group means (treatment)
-Variation between row means (= subject means)
-total sum of the squared difference between all observations and the grand mean
-SS(T) - SS(B) - SS(S)

Front 134

_____is a more general condition of CS

Back 134

Sphericity

Front 135

Mauchly’s W test

Back 135

determines if sphericity/CS has been violated
if p<.05 CS is violated

Front 136

When CS assumption is violated, the omnibus F tests in one-way repeated measures ANOVA tend to be inflated, leading to more

Back 136

false rejections of Ho

Front 137

how to deal with CS violations

Back 137

-use a conservative critical value based on the possible violation of CS
-inflation of the F test can be adjusted by evaluating it against a greater critical value, obtained by reducing the degree of freedom
*know as conservative F-test

Front 138

DF(B) = E(k-1) and DF(BS) = E(k-1)(n-1), E measures
when CS holds E=
when CS is violated E is___than 1

Back 138

extent to which CS is violated
1
less

Front 139

Geisser & Greenhouse & Huynh-Feldt estimates
which is smallest (more conservative)

Back 139

SPSS estimates of E
Geisser & Greenhouse

Front 140

DF (B) and DF (BS) are reduced when

Back 140

CS is violated

Front 141

when CS is violated get a ___critical value for F

Back 141

larger