[L8] Relationship between Variables Correlation and Regression

Question 1

We are interested in finding a way to represent ___
between scores.

Answer 1

association

Question 2

Types of Correlation

Answer 2

Bivariate; Multivariate Correlation

Question 3

Correlation does not prove __

Answer 3

Causality

Question 4

Multivariate Correlation have more ____ Validity

Answer 4

Ecological

Question 5

IGT & RMT = test of difference
Correlation = test of _
_

_

Answer 5

correlation/association

Question 6

___ – first and most obvious way to summarize
data where we are examining the relationship between
two variables

Answer 6

Scatterplot

Question 7

We put one variable on the x-axis and another on the yaxis,
and we ___for each person showing their
scores on the two variables.

Answer 7

draw a point

Question 8

test of correlation involved administering ___ tests in the same group of participants

Answer 8

2 or more different

Question 9

When we want to tell people about our results, we ____

Answer 9

don’t
have to draw a lot of scatterplots.

Question 10

__
_
_Children were asked to listen
to a word and repeat it. They were then asked which of
these 3 words started with the same sound.

Answer 10

Initial phoneme detection.

Question 11

____reading score, a standard
measure of reading ability.

Answer 11

British Ability Scale (BAS)

Question 12

We usually summarize and represent the relationship
between two variables with a ___
__
_
_

Answer 12

number (correlation
coefficient).

Question 13

We also calculate the ____ for this
number, and we want to be able to find out if the
relationship is ___

Answer 13

Confidence Intervals; statistically significant

Question 14

Thus, we want to know what is the probability of finding
a relationship at least this strong if the ____ that
there is no relationship in the population is true.

Answer 14

null hypothesis

Question 15

– a best fitting line
used for prediction

Answer 15

Line of best fit or Regression Line

Question 16

Predicting the variation in Y as a __
_

Answer 16

function of the variation
in X.

Question 17

– how steep the line
*

Answer 17

Slope

Question 18

___ – the position or height of the line.

Answer 18

Intercept

Question 19

By convention we give the height at the point where the
line ___

Answer 19

hits the y-axis.

Question 20

The
height is called the____or often just the
intercept

Answer 20

y-intercept ; (or sometimes the constant)

Question 21

The intercept represents the ___of a person
who scored _
_ on the x-axis variable.

Answer 21

expected score ; zero

Question 22

y=b0+b1X

Answer 22

regression expression, predicting behavior of y as function of x

useful for raw scores

Question 23

It is often the case that the intercept __. After all, __no one_usually scores ___

Answer 23

doesn’t make any
sense; 0 or close to 0.

Question 24

We can use the ___of slope and __ to
calculate the expected value of any person’s score on Y,
given their score on X.

Answer 24

two values, intercept

Question 25

y = β0 + β1x (sometimes it is y = a + bx or y = mx + c)
Where x is the x-axis variable. This equation is called the
___

Answer 25

regression equation.

Question 26

We can make a _
__ about one score from the
another score

Answer 26

prediction

Question 27

Problem: if we don’t understand the ___, regression
lines and equations are ___.

Answer 27

scale(s), meaningless

Question 28

thinking about the relationship between two variables can
be very useful

Answer 28

Making Sense of Regression Lines

Question 29

When there is a relationship between two variables, we
can ___ one from the other.

Answer 29

predict

Question 30

We can not say that one __ the other,

Answer 30

explains

Question 31

We need some way of making the scales have some sort
of meaning, and the way to do this is to
__ the data
into __

Answer 31

convert; standard deviation units.

Question 32

Talking in terms of SDs means that we are talking about
_
__

Answer 32

standardized scores.

Question 33

Because we are talking about standardized regression
slopes, we call it “___

Answer 33

standardized slope.

Question 34

___ – a more important name for the
standardized slope.

Answer 34

Correlation coefficient

Question 35

In order to convert the units, we need to know the ___

Answer 35

SD of
each of the measures.

Question 36

If we know the ___, we can calculate the correlation
using the formula: r = β x σx / σy

Answer 36

slope

Question 37

The letter r actually stands for ___, but most people
ignore that because it is confusing

Answer 37

regression

Question 38

Thus, if we know the _
__ we can calculate the correlation

Answer 38

slope

Question 39

3 ways to calculate for the correlation coefficient”r”

Answer 39

1. regression line
2. standardized slope
3. proportion of variance

Question 40

In correlation, we want to know how well the regression
line ___

Answer 40

fits the data.

Question 41

That is, how
___the points are from the line.

Answer 41

far away

Question 42

The __ the points are to the line, the stronger the
relationship between the two variables.

Answer 42

closer

Question 43

When we had one variable and we wanted to know the
spread of the points around the mean, we calculated the
_
_

Answer 43

SD (σ).

Question 44

The square of the SD is the _
__.

Answer 44

variance

Question 45

We can do the same thing with our regression data, but
instead of making d the difference between the mean and
the score, we can make it the difference between the value
that we would expect the person to have, given their score
on the x-variable, and the score they actually got. We can
calculate their ___

Answer 45

predicted scores,

Question 46

the difference between their
predicted score and their actual score. The difference is
called
_–.

Answer 46

Residual

Question 47

Their ____ (the difference between the score they
got and the score we thought they would get based on
their initial phoneme score)

Answer 47

residual score

Question 48

if we want to calculate the equivalent of the
variance, we need to ___ each person’s score

Answer 48

square

Question 49

___ = d squared

Answer 49

Residual squared

Question 50

The value of the standardized slope and the value of the
square root of the proportion of variance explained will
___ be the same value.

Answer 50

always

Question 51

We therefore have ___of thinking about
correlation.

Answer 51

two equivalent ways

Question 52

The first way is the ___
It is the expected
increase in one variable, when the other variable increases
by 1 SD.

Answer 52

standardized slope.

Question 53

The second way is the __
__ If you
square a correlation, you get the proportion of variance in
one variable that is explained by the other variable.

Answer 53

proportion of variance.

Question 54

A correlation is both ___statistics.

Answer 54

descriptive and inferential

Question 55

We can find the
____and we can also use
it to describe the ___

Answer 55

probability estimate ; strength of the relationship

Question 56

• __ – strength of relationship
  _

Answer 56

Magnitude

Question 57

___ – positive, negative, curvilinear etc.

Answer 57

Direction

Question 58

Cohen’s effect size:

Answer 58

• r = 0.1 = small correlation
• r = 0.3 = medium correlation
• r = 0.5 = large correlation

Question 59

Note that these only really apply in what Cohen, called
___

Answer 59

Social and Behavioral sciences.

Question 60

Common mistake

Answer 60

• A correlation around 0.5 is a large correlation.
• A correlation does not have to exceed 0.5 to be large.
• If you have a correlation of r = 0.45, you have a
  correlation which is approximately equal to a large
  correlation.
• It’s not a medium correlation just because it hasn’t quite
  reached 0.5

Question 61

Pearson Correlation Coefficient
* Also known as ___

Answer 61

Pearson Product moment correlation.

Question 62

Pearson Product moment correlation developed by

Answer 62

Karl Pearson

Question 63

Pearson Correlation Coefficient
is a _____ and makes the ___
made by other parametric tests.

Answer 63

Parametric correlation; same assumptions

Question 64

level of measurement for Pearson Correlation Coefficient

Answer 64

Continuous and normally distributed data

Question 65

to determine r

Answer 65

1. standardized slope
2. proportion of variance
3. pearson product moment correlation

Question 66

Optional Extra: Product Moments
* ___: the moment is the __ from the fulcrum
multiplied by the weight on the lever.

Answer 66

Physics; length

Question 67

___ the total moment is equal to the length
from the center, multiplied by the weight. The same principle applies with ___.

Answer 67

Seesaw analogy: correlation

Question 68

The same principle applies with correlation: needs to be balanced (raw to standard score) to be
_-
_

Answer 68

comparable

Question 69

• We find the _
  __ for each of the
  variables. In this case the center is the
  __.

Answer 69

length from the center; mean

Question 70

So, we calculate the difference between the score and the
mean for each variable (these are the ___) and then
we multiply them together (this is the ___).

Answer 70

moments; product

Question 71

Because this value is dependent on the ___
we need to divide it by N.

Answer 71

number of people,

Question 72

And because it is related to the ___, we
actually divide by N-1.

Answer 72

standard deviation

Question 73

This is called ___, and if we call the two variables
x and y,

Answer 73

covariance

Question 74

Just as before, we need to __ this value by
dividing by the ___

Answer 74

standardize; standard deviations.

Question 75

Calculating the Correlation
Coefficient:

we need to divide by ___, so we
multiply them together

Answer 75

both SDs

Question 76

So instead of finding the square roots and then
multiplying them together, it is easier to multiply the two
values together, and then find the ____

Answer 76

square root.

Question 77

Importance scattergraph or plot:
*

Answer 77

It will show us approximately what the correlation should
be.

It will help us detect any errors in our data, for example
data entry errors.

It will help us get a feel of our data.

Question 78

The confidence intervals for a statistic tell us the likely
___

Answer 78

range of a value in the population.

Question 79

Sampling distributions of correlation is ___. It is not __
_, which means we can’t add and
subtract CIs in the usual way.

Answer 79

tricky; symmetrical

Question 80

___transformation used which
makes the distribution symmetrical.

Answer 80

Fisher’s z transformation –

Question 81

Used to calculate the CIs and then transform back to
correlations.

Answer 81

Fisher’s z transformation –

Question 82

It is called a ____, because it makes the
distribution of the correlation into a z distribution which
is a normal distribution with a mean of 0 and SD of 1.

Answer 82

z transformation

Question 83

There are ___ to find the p-value associated with a
correlation.

Answer 83

2 ways

Question 84

Calculating the p-value

Answer 84

1. Use table in Appendix 3.

Question 85

If we really want to know the p-value, then we can
convert the value for r into a ___

Answer 85

value for t.

Question 86

We can use this t-value to obtain the __using
a __

Answer 86

exact p-value, computer program

Question 87

When we know the __ we can also calculate the
___ of the regression line

Answer 87

correlation; position

Question 88

We can use the two values ___ to create
a regression equation which will allow us to predict y
(display behavior); (). from x desirability

Answer 88

(slope and intercept);

Question 89

We can use the
___ to draw a graph with the line
of best fit on it

Answer 89

predictions

Question 90

we have extended the line to __ – we would not
normally do this.

Answer 90

zero

Question 91

If variables are both dichotomous (for example, yes/no,
top, bottom) we can use the ___

Answer 91

Pearson correlation formula.

Question 92

Dichotomous Variables - A much easier way is to calculate the value of__
and then use the ___, which will
give the same answer as using the r correlation.

Answer 92

chi-square; phi ( ф ) correlation formula

Question 93

The p-value of the correlation will be the same as the pvalue
for the ___because the two tests are just
different ways of thinking about the same thing.

Answer 93

chi-square test

Question 94

If one of your variables is continuous and the other is
dichotomous we can use the ___

Answer 94

Point Biserial Formula:

Question 95

*These formulae give exactly the same answer as the
__
_, but they just easier to use.

Answer 95

Pearson Formula

Question 96

On special occasions we can correlate using a
__ This is when one variable is categorical and has just two
all-inclusive values.

Answer 96

dichotomous variable.

Question 97

Here, we may give an ___according to
membership of the categories, e.g. 0 for female and 1 for
male.

Answer 97

arbitrary value

Question 98

Dichotomous Variables- We then proceed with the ___ as usual.

Answer 98

Pearson Correlation

Question 99

The Point Biserial is written as

Answer 99

rpb.

Question 100

This value can be turned into an ordinary___

Answer 100

t-value.

Question 101

This may sound like a cheat because the Pearson’s was a
____ type of statistic and that the level of
measurement should be at least interval.

Answer 101

parametric

Question 102

This is true only if we want to make ___
from our results about underlying populations

Answer 102

certain assumptions

Question 103

• Used when the data do not satisfy the assumptions of the
  Pearson Correlation because they are not normally
  distributed or are only ordinal in nature

Answer 103

Non-Parametric Correlations

Question 104

Non-Parametric Correlations (2)

Answer 104

Spearman Correlation
Kendall Correlation

Question 105

Two ways to find the Spearman Correlation.

Answer 105

calculate the Spearman correlation

Question 106

steps of spearman correlation

Answer 106

1. Draw a scatterplot
2. Rank the data in each group separately
3. Find the difference between the ranks for each
   person. Which we call d.
4. use the Formula for Spearman

Question 107

The first way to calculate the Spearman correlation is just
to calculate a (Pearson) correlation, using the ___

Answer 107

ranked data.

Question 108

The problem is that the Pearson Formula is a bit __,
especially if a computer is not used.

Answer 108

fiddly

Question 109

A simplification of the Pearson Formula is available,
developed by Spearman, which works in the case where
there are ___.

Answer 109

ranks

Question 110

Find the __ for each
person. Which we call d.

Answer 110

difference between the ranks

Question 111

The ____ is on a scale, however it is not on a scale
we understand

Answer 111

d-score total

Question 112

We need to convert the scale into one that we do
understand such as the
____, which goes from
-1.00 to +1.00.

Answer 112

correlation scale

Question 113

However, there is a slight complication because the
formula as we have given it is only valid when there are
___

Answer 113

no ties in the data.

Question 114

Three ways to deal with this problem:

Answer 114

1. Ignore it. It does not make a lot of difference.
2. Use the Pearson Formula on the ranks (although the
   calculation is harder than the Spearman formula).
3. Use a correction. (book suggests a site)

Question 115

We calculate the significance of the Spearman in the same
way as the significance of the __ Correlation.

Answer 115

Pearson

Question 116

___– not at all straightforward or easy to
calculate.

Answer 116

Confidence Intervals

Question 117

If we use a non-parametric test, such as a __
correlation, we tend to lose power.

Answer 117

Spearman

Question 118

By converting data to ___ information about the actual
scores are thrown away

Answer 118

ranks

Question 119

Although we could be strict and say that rating data are
strictly measured at an ordinal level, in reality when there
isn’t a problem with the distributions, we would always
prefer to use a ___

Answer 119

Pearson Correlation.

Question 120

A ___ correlation gives a better chance of a
significant result

Answer 120

Pearson

Question 121

A curious thing about the Spearman is ___

Answer 121

how to interpret it.

Question 122

We can’t say that it is the +____, that is the
relative difference in the SDs, because the SDs don’t
really exist as there is not necessarily any relationship
between the score and the SD.

Answer 122

standardized slope

Question 123

We also can’t say that it is the ___
explained, because the variance is a ___ term, and
we are using ranks

Answer 123

proportion of variance; parametric

Question 124

All we can really say about the Spearman is that it is the

___

Answer 124

Pearson correlation between the ranks.

Question 125

Non-Parametric Correlations

Answer 125

Spearman Rank Correlation Coefficient

Question 126

Spearman Rank Correlation Coefficient - shows how closely the ___ are related.

Answer 126

ranked data

Question 127

___ – alternative nonparametric
correlation, which does have a more sensible
interpretation. (advantage: meaningful interpretation)

Answer 127

Kendall’s Tau-a (τ – Greek Letter)

Question 128

Very rarely used however.

Answer 128

Kendall’s Tau-a

Question 129

Kendall’s Tau-a is rarely used for two reasons:

Answer 129

1. Difficult to calculate if you do not have a computer.
2. It is always lower than a spearman correlation, for the
   same data (but the p-values are always exactly the same).

Question 130

Kendall’s Tau-a - Because people like their correlations to be ___, they
tend to use it less.

Answer 130

high

Question 131

The fact that two variables correlate does not mean there
is a ___ relationship between them.

Answer 131

causal

Question 132

Correlation does not mean causality, but ___ does
mean correlation.

Answer 132

causality

Question 133

Correlation when one variable is categorical

Answer 133

Chi-square test

Question 134

In general, if one variable is a purely category-type
measure, then correlation cannot be carried out, unless
the variable is ___.

Answer 134

DICHOTOMOUS

Question 135

• We can however use the Chi-square test since it is called
  a ____

Answer 135

test of association.

Question 136

___ is also a measure of ___ between two
variables

Answer 136

Correlation; association

Question 137

What we can do with a nominal/categorical data is
reduce the measured variable to ___ level and
conduct a ___ test on the resulting frequency
table.

Answer 137

nominal; chi-square

Question 138

This is only possible, however, where you have gathered
several ___ in each category.

Answer 138

cases

Question 139

We can find the ___ for the measured data and
record how many responses/frequencies were ___

Answer 139

overall mean; above and
below this mean

Question 140

*Typical variables that cannot be correlated (unless a
rational attempt to order categories is made) are: marital
status, ethnicity, place of residence, handedness,
sexuality, degree subject and so on.__

Answer 140

*Typical variables

Question 141

A lack of relationship is signified by a value __
_

Answer 141

close to
zero.

Question 142

A value of zero however could occur for a___

Answer 142

curvilinear
relationship.

Question 143

___ is a measure of the correlation.

Answer 143

Strength