Psychological Statistics Final

Front 1

statistics is

Back 1

a set of mathematical procedures used to summarize or draw conclusions from data.

Front 2

data are

Back 2

are values representing the measurement
of one or more variables.

Front 3

a variable is

Back 3

anything that varies, or changes.

Front 4

a score is

Back 4

is a particular person’s value on a variable.

Front 5

descriptive statistics are

Back 5

procedures used to summarize and present data

Front 6

inferential statistics are

Back 6

procedures used to draw conclusions about a
population based on data from a sample

Front 7

a population is

Back 7

is the complete set of all individuals
of interest in a study. Usually, it is too large.

Front 8

a sample is

Back 8

is a manageable subset of the population

Front 9

a parameter is

Back 9

is a value that summarizes a
characteristic of the entire population.

Front 10

a parameter is

Back 10

is constant
• Because all the data of interest is used to calculate
the parameter, there is no additional data that can
change its value.
– But parameters are typically unknown.

Front 11

a statistic is

Back 11

is a value that summarizes a
characteristic of a sample.
– It is typically used to estimate the parameter of
a real or hypothetical population.

Front 12

a statistic is

Back 12

is variable
• Because different samples may contain different
scores from the population, statistics of the same
variable may differ between samples.

Front 13

two types of categorical scales

Back 13

nominal and ordinal

Front 14

nominal scales are

Back 14

• values label or identify observations (e.g., male/female).
• mathematical operations: = and not equals

Front 15

ordinal scales are

Back 15

• values rank order observations (e.g., letter grades)
• mathematical operations: = , not equals , < , and >
• intervals are not necessarily equal

Front 16

two types of quantitative scales

Back 16

interval and ratio

Front 17

interval scales are

Back 17

• values order observations into equally spaced intervals
(e.g., degrees Fahrenheit).
• mathematical operations: = , not equals, < , > , + , and –
• * and / not meaningful because no true zero point

Front 18

ratio scales are

Back 18

• have a true zero point (e.g., inches).
• mathematical operations: = , not equals, < , > , + , - , *, and /

Front 19

discrete data are

Back 19

– there are not an infinite number of meaningful values that
exist between any two neighboring values
– All categorical scales produce discrete data.
– Quantitative scales may produce discrete or continuous
data.

Front 20

continuous data are

Back 20

– there are an infinite number of meaningful values that
exist between any two neighboring values
– possible values only limited by precision of measurement
instrument

Front 21

a real limit is

Back 21

– the range of values within which the true value
of a continuous value exists

upper real limit = value + ½(measurement unit)

lower real limit = value – ½(measurement unit)

Front 22

a measurement unit is

Back 22

the lowest measurable value greater than zero

Front 23

X and Y are

Back 23

the scores on each variable

Front 24

N is

Back 24

total number of participants in an
entire study or population

Front 25

n is

Back 25

number of participants in a condition
of a study or a single sample

Front 26

sigma is

Back 26

summation (add up all the scores)

Front 27

rules of priority

Back 27

• all operations
– inside parentheses
– in the numerator and denominator
– under a square root

• exponentiation
• negation
• multiplication and
division

• addition and
subtraction

Front 28

frequency (f)

Back 28

– the number of times a value of a particular
variable occurs in the data

Front 29

frequency distribution

Back 29

– the complete set of frequencies for each value
of a variable

Front 30

making a frequency table

Back 30

If the data are nominal,
the order of the
categories is up to you.

Otherwise, the values of
the variable should be
listed from highest ( top)
to lowest (bottom).

Front 31

cumulative frequency (cf)

Back 31

the frequency of scores less
than or equal to a given value

Front 32

proportion (p)

Back 32

p = f/N

Front 33

percentage (%)

Back 33

% = 100(p)

Front 34

cumulative percentage (c%)

Back 34

– the percentage of
scores less than or
equal to a given
value

c% = 100(cf/N)

Front 35

graphs

Back 35

– X axis (abscissa) = categories or values of the X variable
– Y axis (ordinate) = the statistic being presented

Front 36

bar graphs

Back 36

– for categorical (nominal or ordinal) data

Front 37

histograms

Back 37

– for quantitative (interval or ratio) data

Front 38

frequency polygons

Back 38

– for quantitative (interval or ratio) data

Front 39

normal distribution

Back 39

– a symmetrical “bell-shaped” distribution in which
frequency steadily increases as values approach the
midpoint of the distribution

Front 40

skew

Back 40

the degree to which the distribution is unsymmetrical

Front 41

positive skew

Back 41

• most scores are on the low
end of the distribution

Front 42

negative skew

Back 42

• most scores are on the
high end of the distribution

Front 43

modes

Back 43

– the number of distinct “peaks”
– one distinct peak = unimodal
– two distinct peaks = bimodal
– more than two = multimodal

Front 44

central tendency

Back 44

– the typical score

Front 45

mean

Back 45

• arithmetic average of the scores

Front 46

median

Back 46

• middle score

Front 47

mode

Back 47

the most frequent score

Front 48

notation for the mean

Back 48

– μ (mu) for the population mean (usually unknown)
– M for a sample mean

Front 49

mean is

Back 49

is the balancing point of
a distribution

Front 50

a deviation

Back 50

is each score minus the
mean (X – M).
• The sum of the deviations always
equals zero.

Front 51

The mean is sensitive to outliers

Back 51

– extreme scores that skew the
distribution

– the mean is a poor measure of central
tendency when there are outliers

Front 52

the median is not affected by

Back 52

outliers

Front 53

what do you do when the mean is sensitive to outliers?

Back 53

find the median

Front 54

the grand mean

Back 54

the mean of several
sample means.

Front 55

when to use the median instead of the mean

Back 55

– If the data include outliers
– If the data include undetermined values
– If the distribution is open-ended
– If the data are ordinal

Front 56

the mode is

Back 56

Only measure of central tendency for nominal data
• Otherwise, not a good measure because distributions can have more than one distinct
mode or no mode at all

Front 57

range

Back 57

– upper real limit of the highest score – the lower real
limit of the lowest score
– whole numbers: highest score – the lowest score + 1

Front 58

interquartile range

Back 58

– the difference between the the first and third
quartiles

Front 59

quartiles are

Back 59

are values that divide a distribution of
scores into four equal parts

first quartile (Q1) divides bottom 25% from top 75%
• second quartile (Q2) divides bottom 50% from top
50%; same as the median
• third quartile (Q3) divides bottom 75% from top 25%

Front 60

semi-interquartile range

Back 60

– half the interquartile range

SIQR = (Q3 – Q1)/2

Front 61

variance(σ2)

Back 61

the average squared deviation

Front 62

standard deviation(σ)

Back 62

– the square root of the variance

Front 63

populations vs. samples

Back 63

A sample tends to have less variability than the population from
which it was drawn.

Front 64

how is a statistic biased?

Back 64

A statistic is biased if, on average, it underestimates
or overestimates its corresponding parameter.

Front 65

how is a statistic unbiased?

Back 65

Dividing by n – 1 results in an unbiased
estimate of the population variance and
standard deviation.
– A statistic is unbiased if, on average, it equals its
corresponding parameter.

Front 66

degrees of freedom (df)

Back 66

– number of values that are free to vary in a sample
– for a single sample with one variable, df = n – 1

Front 67

what do the mean and standard deviation tell us?

Back 67

The mean (μ) and standard deviation (σ) tells us the position of a score relative to other scores in the population.

Front 68

raw scores

Back 68

are the data directly observed from
the measurements

Front 69

standardized scores

Back 69

indicate the relative position
of the raw scores in a distribution

Front 70

standardizing changes the scale how?

Back 70

Standardizing changes the scale into units of
variability (i.e., standard deviations)

Front 71

z-scores are what type of data?

Back 71

interval data

Front 72

problems with z-scores

Back 72

– large z-scores still appear small
– a z-score of zero is average
– negative values are confusing
• Solution: convert z-scores by changing the mean and standard deviation

Front 73

scatterplot

Back 73

– a two dimensional plot of each subject based on
their scores from two variables

Front 74

correlation

Back 74

the linear relationship between two variables

Front 75

positive correlation

Back 75

as one variable increases, the other variable tends
to increase

Front 76

negative correlation

Back 76

as one variable increases, the other variable tends
to decrease

Front 77

correlation direction

Back 77

Whether a correlation is positive or negative
is called its direction

Front 78

correlation magnitude

Back 78

The accuracy of one variable’s prediction of
the other variable is called the magnitude.

Front 79

Pearson product moment correlation
coefficient (r)

Back 79

– measures the degree to which the scatter plot
forms a straight line
– ranges from
• –1 (perfect negative correlation)
• to 0 (no correlation)
• to 1 (perfect positive correlation)
– the sign indicates direction
– the number indicates magnitude

Front 80

definitional formula of the pearson r

Back 80

– the average cross-product of the z-scores

Front 81

r 2 = coefficient of determination

Back 81

the proportion of variance in one variable (Y) that
can be predicted from the other variable (X).

Front 82

1 - r 2 = coefficient of nondetermination

Back 82

the proportion of variance in one variable (Y) that
cannot be predicted from the other variable (X).

Front 83

very strong pearson r means:

Back 83

r is > or equal to .70

r2 is > or equal to .49

Front 84

strong pearson r means:

Back 84

r is greater than or equal to .50 - .69

r2 is greater or equal .25 - .48

Front 85

moderate pearson r means:

Back 85

r is greater or equal .30 - .49

r2 is greater or equal .09 - .24

Front 86

weak pearson r means:

Back 86

r is greater or equal .10 - .29

r 2 is greater or equal .01 - .08

Front 87

very weak pearson r means:

Back 87

r is less than or equal to .10

r2 is less than or equal .01

Front 88

spurious correlations

Back 88

are correlation coefficients
that are artificially high or low

Front 89

outliers

Back 89

anyone who is more than 3 standard deviations away from the mean, if so you can remove them from your data but you must report it

Front 90

restricted range

Back 90

example: harvard cuts off at 1300 on SATs

Front 91

curvilinearity

Back 91

when the relation between two variablesis better described as a curve

Front 92

sample size

Back 92

the larger the sample, the more reliable the correlation

Front 93

n should be greater or equal to

Back 93

30

Front 94

Given any correlation, there are three
possible causal relationships.

Back 94

X ------> Y

Y------> X

3rd factor ----> X and Y

Front 95

in a standard normal distribution:

Back 95

Approx. 68% of the distribution is within 1 σ of μ.

Approx. 95% of the distribution is within 2 σ of μ.

Approx. 100% of the distribution is within 3 σ of μ.

Front 96

percentile rank (PR)

Back 96

– the percentage (%) of scores less than or equal to a
given score (X) rounded to the nearest whole
number.

Front 97

unit normal table

Back 97

lists the proportion
of the standard normal distribution less than
and greater than any given z-score

Front 98

Body p

Back 98

is the larger proportion of the
distribution associated with a given z-score.

Front 99

Tail p

Back 99

is the smaller proportion of the
distribution associated with a given z-score.

Front 100

percentile

Back 100

– the score (X) at which a given percentage (%) of
the distribution is equal to or less than that score.

Front 101

probability (p)

Back 101

– the frequency (f) of an outcome relative to all possible outcomes (N)
– probability = proportion
– probability ranges from .00 to 1.00
– assumes random sampling

p = f/N

Front 102

random sampling

Back 102

each outcome or individual has an equal chance of
occurring or being selected from the population

Front 103

sampling error

Back 103

the discrepancy between a sample statistic and
the population parameter

Sampling error causes
variability in the
sample means.

Front 104

sampling distribution (of the mean)

Back 104

– the theoretical distribution of sample means if
all possible samples of equal size were selected

Front 105

Mean of the sampling distribution
distribution

Back 105

• Mean of the sampling distribution
– the expected value of any given sample mean
– on average, the sample mean will equal the mean
of the sampling distribution

Front 106

standard error

Back 106

– the standard deviation of the sampling distribution
– standard error is a measure of sampling error

Front 107

as the standard error decreases

Back 107

so does the average discrepancy
between the sample mean and
the population mean

Front 108

central limit theorem rule 1

Back 108

1. the mean of the sampling distribution equals
the population mean

thus, on average the sample mean equals the population mean

Front 109

central limit theorem rule 2

Back 109

the standard error is equal to the population
standard deviation divided by the square root
of the sample size

Standard error is an index of sampling error.
– Thus, as sample size (n) increases, sampling
error decreases.
– Therefore, the law of large numbers:

Front 110

law of large numbers

Back 110

The larger the sample, the more likely the sample
mean will equal the population mean

Front 111

central limit theorem rule 3

Back 111

The shape of the sampling distribution
approaches normal as sample size (n)
increases.
– The sampling distribution is practically normal
when…
• the population distribution is normal,
or
• the sample size (n) is greater than 30

Front 112

research hypotheses

Back 112

– a statement that outlines the predicted relationship
between the variables of interest

– e.g., rewards for good grades affect students’ IQ

Front 113

statistical hypotheses

Back 113

– two mutually exclusive mathematical propositions
about the parameter(s) of an unknown population

Front 114

Null hypothesis (H0)

Back 114

– states the expected value of a parameter (e.g., μ)
if the treatment has no effect ( i.e., the research hypothesis is false)
– e.g., “rewards do not affect students’ IQ” would
be written like so...
H0: μ = 100
where μ is the hypothesized mean of the
unknown population

Front 115

Alternative hypothesis (H1)

Back 115

– states the opposite of the null hypothesis
– e.g., “rewards do affect students’ IQ” would be
students IQ written like so...
H1: μ ≠ 100

Front 116

hypothesis test

Back 116

– procedure for estimating the probability that a
sample was drawn from a population if the null
hypothesis is true
– test whether the null is false, not whether the
alternative is true

Front 117

deductive falsification

Back 117

• a procedure in which evidence is sought leading to the
conclusion that a hypothesis is incorrect
• based on the logic of modus tollens

Front 118

Modus tollens (denying the consequent)

Back 118

– If A, then B (If there is fire, then there is oxygen.)
– Not B (There is no oxygen.)
– Therefore, not A (Therefore, there is no fire.)
• Affirming the consequent is not valid.
– If A, then B (If there is fire, then there is oxygen.)
– B (There is oxygen.)
– Therefore, A (Therefore, there is fire.)

Front 119

Modus tollens applied to hypothesis testing

Back 119

– If the hypothesis is true, then a prediction follows
(If H, then P).
– If the prediction is not true (Not P), then the
hypothesis is not true (Therefore, not H)
– If the prediction is true (P), then stating that the
hypothesis is true (Therefore, H) is not valid.
• Because we can only falsify a hypothesis, we
either reject the null or fail to reject the null

Front 120

critical region

Back 120

– the extreme values that are
unlikely be obtained if the null is
true

Front 121

Alpha

Back 121

– the probability of obtaining a
sample from the critical region.
– in the behavioral sciences, alpha
typically equals .05

Front 122

the p-value

Back 122

– the probability of selecting a
sample more extreme than the
current sample if the null hypothesis is true.

Front 123

if p < a

Back 123

• then the sample is in the critical region
• reject the null hypothesis
• the result is significant

Front 124

if p > a

Back 124

• then the sample is not in the critical region
• fail to reject the null hypothesis
• the result is not significant

Front 125

two-tailed tests

Back 125

– p and α are divided between the two tails of the
distribution
– Used for nondirectional hypotheses

Front 126

non-directional hypotheses

Back 126

research hypotheses that do not specify the direction
of the relationship between the variables

Front 127

format for statistical hypotheses for two-tailed tests

Back 127

H0: μ = value and H1: μ not equal value

Front 128

one-tailed tests

Back 128

– p and α are in one tail of the distribution
– Used for directional hypotheses

Front 129

directional hypotheses

Back 129

research hypotheses that specify the direction of the
relationship between the variables
• keywords: greater, more, higher, better, increases,
less, lower, worse, decreases

Front 130

format for statistical hypotheses for one-tailed tests

Back 130

H0: μ < value and H1: μ > value
H0: μ > value and H1: μ < value

Front 131

research hypothesis for one-tailed test

Back 131

Research hypothesis:
– Rewards increase student’s IQ
• Statistical hypotheses:
H0: μ < 100
H1: μ > 100
• α and p are in right tail

Front 132

research hypothesis for one-tailed test

Back 132

• Research hypothesis:
– Rewards decrease student’s IQ
• Statistical hypotheses:
H0: μ > 100
H1: μ < 100
• α and p are in left tail

Front 133

Type I error

Back 133

– rejecting the null hypothesis when it is true
– alpha ( α) is the probability of a Type I error

Front 134

Type II error

Back 134

– failing to reject the null hypothesis when it is
false

– beta (β) is the probability of committing a Type II error

Front 135

power

Back 135

1 – β
• the probability of rejecting the null hypothesis if it is
false
• power should be > .80

Front 136

understanding power

Back 136

look at notes

Front 137

power increases as

Back 137

the effect size increases.

Front 138

effect size

Back 138

is the difference between the population mean
based on H0 (μ0) and the actual population mean (μ1) .

Front 139

power increases as

Back 139

the standard error decreases

Front 140

power increases as

Back 140

the standard error decreases
– the standard deviation decreases
– the sample size increases

Front 141

power increases as

Back 141

α increases

Front 142

power increases as

Back 142

α increases
– but increasing alpha also increases the probability
of a Type I error

Front 143

when sample sizes are small

Back 143

When sample sizes are small (n < 30), the
sampling distribution may not be normal

Front 144

when standard deviation is unknown

Back 144

When σ is unknown, the standard error
cannot be calculated

Front 145

student's t

Back 145

Uses the sample standard deviation (s) to
estimate the standard error

Front 146

using student's t

Back 146

When you use the estimated standard error
to standardize the sample mean, the statistic
is called t instead of z.

Front 147

t distribution

Back 147

a symmetrical distribution with a mean of zero
that gets wider and flatter as df decrease

– When df = infinity, the
distribution is
perfectly normal
and t = z.

Front 148

if |t| > tc then p < α

Back 148

then reject the null hypothesis

Front 149

Significance does not indicate ...

Back 149

Significance does not indicate effect size.
– Remember, effect size is the difference between
the actual population mean and the population
mean based on the null hypothesis.
– Small effects can be significant if sample size is
large enough because larger samples have less
sampling error and thus more power.

Front 150

estimating effect size

Back 150

If, on average, the sample mean equals the
actual population mean, then M – μ is an
estimate of the effect size (where μ is based on
the null hypothesis)

Front 151

cohen's d

Back 151

is the standardized estimate of
effect size

Front 152

large effect size (cohen's d)

Back 152

greater than .80

Front 153

medium effect size (cohen's d)

Back 153

.20 - .80

Front 154

small effect size (cohen's d)

Back 154

less than .20

Front 155

related samples t test

Back 155

Variation of the single sample t test used for:
– within-subjects
- matched-subjects

• Null hypothesis states that, on average, the
difference between the scores is zero.

Front 156

within-subjects (repeated measures) design

Back 156

• a research design in which the individuals of a single
sample are measured more than once

Front 157

matched-subjects design

Back 157

• a research design in which individuals from one sample
are paired with individuals from another sample based on
one or more variables that the researcher wants to control

Front 158

independent samples t test

Back 158

Used for between-subjects designs

• The samples are drawn from two theoretical
populations.
• Null hypothesis states that the difference
between the means of the two populations is
zero.

Front 159

between-subjects design

Back 159

a research design in which the means of different
unmatched samples are compared (e.g., an
experimental sample and a control sample)

Front 160

Sampling distribution of the difference
(between the means)

Back 160

– the distribution of all possible differences between the means of all possible samples of a given size

Front 161

the distribution of all possible differences between
– the mean of this distribution = 
1 - 
2
• if the null hypothesis is true, then the mean of this
distribution is equal to zero
– the standard deviation of this distribution is called
the standard error of the difference

Back 161

Sampling distribution of the difference
(between the means)

Front 162

Pairwise error rate (α)

Back 162

– the probability of committing a Type I error
when comparing two means

Front 163

Experimentwise (familywise) error rate

Back 163

– the total probability of committing a Type I
error when performing more than one pairwise
comparison
• equal to 1 – (1 – α)c, where c = no. of comparisons
• probability of committing at least one Type I error
increases as the number of comparisons increase

Front 164

Analysis of variance (ANOVA)

Back 164

Analysis of variance (ANOVA)
– determines whether the variance between
groups significantly exceeds the variance
within groups due to error

Front 165

Within-group variance (σ2
w)

Back 165

Within-group variance (σ2
w)
– the total variance within each group
– variability in subjects responses due to error
• extraneous variables other than the treatment or
independent variable that affect subjects’ scores

Front 166

Between-group variance (σ2
b)

Back 166

– the variance among the means of each group

Front 167

treatment variance (σ2t)

Back 167

refers to the variability
in people’s responses due to the treatment or
independent variable only

Front 168

Anova

Back 168

If treatment variance = 0, then F = 1
• We reject the null if F is significantly greater than 1.

Front 169

F distribution

Back 169

an unsymmetrical distribution that becomes more
and more positively skewed as the degrees of
freedom within and the degrees of freedom
between decrease

Front 170

total sum of squares (SST)

Back 170

is the SS of all the scores
across all groups

Front 171

total degrees of freedom

Back 171

(dfT) is the df of all the
scores across all groups

Front 172

Factorial design

Back 172

is a research design in which
the effects of more than one factor on the
dependent variable are examined.

Front 173

factor

Back 173

A factor is the same as the treatment or independent
variable, or any categorical variable (e.g., gender)
that may be related to the dependent variable.

Front 174

ANOVA is used to

Back 174

ANOVA is used to analyze factorial designs
– A two-way ANOVA analyzes two factors, a threeway
ANOVA analyzes three factors, etc.

Front 175

main effect of B

Back 175

– What is the effect of B ignoring A?
– Does the mean time following the “persist”
instructions differ from the mean time following
the “do not persist” instructions?

Front 176

Main effect of A

Back 176

– What is the effect of A ignoring B?
– Does the mean time for low SE people differ
from the mean time for high SE people?

Front 177

A x B interaction

Back 177

– Does the effect of B depend on A?
– Does mean time difference between instructions
for low SE people differ from the mean time
difference between instructions for high SE
people?

Front 178

Non-parallel lines usually
indicate ...

Back 178

Non-parallel lines usually
indicate an interaction.

Front 179

Parallel lines indicate...

Back 179

Parallel lines indicate no
interaction

Front 180

graphing factorial designs

Back 180

look over in notes

Front 181

Two-way ANOVA

Back 181

Two-way Analysis of Variance
• Also called a kA x kB ANOVA, where...
kA is the number of levels of factor A
kB is the number of levels of factor B
kAkB = # of groups/conditions in the experiment
– For example
• a 2 x 2 ANOVA has 4 groups
• a 2 x 3 ANOVA has 6 groups
• a 3 x 3 ANOVA has 9 groups
• a 3 x 4 ANOVA has 12 groups, etc.

Front 182

When reporting the results of an two-way ANOVA...

Back 182

When reporting the results of an two-way
ANOVA, state whether each main effect and
the interaction were significant or not.
• Example:
– The 2 x 3 ANOVA revealed a significant main
effect for anger, F (1, 54) = 5.00, p < .05. The
main effect for cues was not significant, F (2, 54)
= 3.00, p > .05. The Anger x Cues interaction
was significant, F (2, 54) = 6.00, p < .05.

Front 183

Parametric tests

Back 183

Parametric tests
– inferential statistics that assume certain
characteristics of the population are true
– t tests and ANOVAs are parametric

Front 184

Nonparametric tests

Back 184

Nonparametric tests
– inferential statistics that make few or no
assumptions about the characteristics of the
population

Front 185

Assumptions of parametric tests

Back 185

– normality
• the population distribution is normal
– homogeneity of variance
• when comparing two or more groups, the population
variances of each group are equal
– data are quantitative (interval or ratio)

Front 186

Why use parametric tests?

Back 186

– Parametric tests have more power than
nonparametric tests.
– Generally, if sample sizes are large (N > 30), t
tests and ANOVAs are robust against violations
of normality and homogeneity of variance.

Front 187

Robust

Back 187

means that the statistical tests still perform well,
even though certain assumptions may not be true.

Front 188

Why use nonparametric tests?

Back 188

– If parametric assumptions have been violated and
sample sizes are small (N < 30), then parametric
tests may lead to an inflated probability of a Type I
error.
– If the data are categorical (nominal or ordinal),
parametric tests should not be used.

Front 189

Chi-square Goodness of Fit Test

Back 189

• nonparametric test of whether the observed
frequencies in each category conform to
(i.e., “fit”) the frequencies expected based
on the null hypothesis.

Front 190

fo

Back 190

is the observed frequency

Front 191

fe

Back 191

is the expected frequency

Front 192

Is the x2 significant?

Back 192

the distribution is
positively skewed,
and becomes flatter
and longer as
degrees of freedom
increase.

Front 193

Chi-square Test for Independence

Back 193

• nonparametric test of whether the observed
frequencies associated with two variables
are independent (i.e., unrelated).

Front 194

Writing in APA Style

for chi-square test for independence

Back 194

Extroverts were significantly more likely to conform
than introverts, x2(1, N = 60) = 4.15, p < .05.