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YEAR 2 Stats > Correlation and Partial correlation > Flashcards

Correlation and Partial correlation Flashcards

1
Q

What does Bivariate Linear Correlation examine?

A

Examines the relationship between two variables

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2
Q

Examines the relationship between two variables

A

Bivariate Linear Correlation

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3
Q

Relationships between two variables may vary in…?

List 3 points

A
  1. Form
  2. Direction
  3. Magnitude/strength
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4
Q

How can relationships between two variables vary in form?

List 2 ways

A
  1. Linear
  2. Curvilinear
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5
Q

How can relationships between two variables vary in direction?

List 2 ways

A
  1. Positive
  2. Negative
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6
Q

How can relationships between two variables vary in magnitude/strength?

List 3 ways

A
  1. r = - 1 (perfect negative relationship)
  2. r = +1 (perfect positive relationship)
  3. r = 0 (no relationship)
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7
Q

What is considered a perfect correlation?

A

+/- 1

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8
Q

What is considered a strong correlation?

A

+/- 0.9, 0.8, 0.7

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9
Q

What is considered a moderate correlation?

A

+/- 0.6, 0.5, 0.4

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10
Q

What is considered a weak correlation?

A

+/- 0.3, 0.2, 0.1

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11
Q

What is considered zero correlation?

A

0

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12
Q

Linear correlation involves measuring …?

A

The relationship between two variables measured in a sample

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13
Q

Measuring the relationship between two variables measured in a sample

This is known as…?

A

Linear correlation

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14
Q

We use ______ to estimate the population parameters

A

Sample statistics

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15
Q

We use sample statistics to estimate the _______

A

Population parameters

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16
Q

True or False?

In hypothesis testing for correlation, we always start by assuming the null hypothesis is false

A

False

We always start by assuming the null hypothesis is true: there is no relationship between the population variables

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17
Q

Once we’ve determined the relationship in our sample, inferential analyses allow us to determine _________ when the null hypothesis is true

A

The probability of measuring a relationship of that magnitude

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18
Q

What is the chance of measuring a relationship of that magnitude when the null hypothesis is true?

How do we measure this?

A

p-value

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19
Q

The probability of measuring a relationship of that magnitude when the null hypothesis is true

This is known as…?

A

p-value

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20
Q

What is a p-value?

A

The probability of measuring a relationship of that magnitude when the null hypothesis is true

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21
Q

If the probability of measuring a relationship of the obtained magnitude is less than our threshold (0.05), we are prepared to …?

a. reject the null hypothesis
b. fail to reject the null hypothesis

A

a. reject the null hypothesis

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22
Q

What are the 5 parametric assumptions of correlations?

A
  1. Both variables should be continuous (level of measurement)
  2. Related pairs: Each participant (or observation) should have a pair of values
  3. Absence of outliers
  4. Linearity – points in the scatterplot should be best explained with a straight line
  5. Sensitive to range restrictions
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23
Q

If one or both variables are ordinal, do we use parametric (Pearson’s r) or non-parametric (Spearman’s rho) correlation?

A

We use a non-parametric alternative (Spearman’s rho)

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24
Q

What do outliers do?

A

They skew the results of the correlation

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25
Q

True or False?

Points in the scatterplot should be best explained with a curve

A

False

Points in the scatterplot should be best explained with a straight line

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26
Q

What is the non-parametric equivalent to Pearson’s r correlation?

A

Spearman’s rho

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27
Q

Spearman’s rho is the non-parametric equivalent to…?

A

Pearson’s r correlation

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28
Q

What is the non-parametric equivalent to Pearson’s r correlation when there are fewer than 20 cases?

A

Kendall’s Tau

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29
Q

Kendall’s Tau is the non-parametric equivalent to…?

A

Pearson’s r correlation when there are fewer than 20 cases

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30
Q

Pearson’s correlation coefficient investigates the relationship between…?

A

2 quantitative, continuous variables

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31
Q

The resulting correlation coefficient (r) is a measure of …?

A

The strength of association between the two variables

32
Q

The strength of association between the two variables is measured by

A

Pearson’s correlation coefficient (r)

33
Q

How do we calculate covariance?

List 4 points

A
  1. For each datapoint, calculate the difference from the mean of x, and the difference from the mean of y
  2. Multiply the differences
  3. Sum the multiplied differences
  4. Divide by N – 1
34
Q

What provides a measure of the variance shared
between our x and y variables?

A

Covariance

35
Q

Covariance provides a measure of the variance shared between …?

A

x and y variables

36
Q

What is a ratio of covariance (shared variance) to separate variances?

A

Correlation coefficient (r)

37
Q

What is the correlation coefficient (r)?

A

A ratio of covariance (shared variance) to separate variances

38
Q

How can we obtain a measure of separate variances?

A

Multiplying the standard deviation for x and y

39
Q

What is the formula for correlation coefficient (r)?

A

covariance (x, y) / SD x * SD y

40
Q

If the covariance is large relative to the separate variances, r will be

a. Exactly 0
b. Closer to 0
c. Further from 0
d. Negative

A

c. Further from 0

41
Q

If the covariance is small relative to the separate variances, r will be

a. Exactly 0
b. Closer to 0
c. Further from 0
d. Negative

A

b. Closer to 0

42
Q

When r is further from 0, this means that

a. The covariance is large relative to the separate variances

b. The covariance is moderate relative to the separate variances

c. The covariance is small relative to the separate variances

d. The covariance is negative relative to the separate variances

A

a. The covariance is large relative to the separate variances

43
Q

When r is closer to 0, this means that

a. The covariance is large relative to the separate variances

b. The covariance is moderate relative to the separate variances

c. The covariance is small relative to the separate variances

d. The covariance is negative relative to the separate variances

A

c. The covariance is small relative to the separate variances

44
Q

r reflects how well a straight line fits the data points

What does this mean?

A

r reflects the strength of the correlation

45
Q

If datapoints cluster closely around the line, r will be …?

a. Further from 0
b. Exactly 0
c. Exactly 1
d. Closer to 0

A

a. Further from 0

46
Q

If datapoints are scattered some distance from the line, r will be…?

a. Further from 0
b. Exactly 0
c. Exactly 1
d. Closer to 0

A

d. Closer to 0

47
Q

What is the df for r?

A

df = N - 2

48
Q

Why is the df for r = N - 2?

A

Because we estimate two population parameters (mean of x and mean of y, in order to calculate differences from those values)

49
Q

Should we report N or df when reporting r?

A

df

50
Q

How do we report r?

A

r(df) = r value, p = p-value

51
Q

True or False?

If we were to calculate the correlation using data measured with another sample from the same population the r-value we would obtain is likely to be the same

A

False

If we were to calculate the correlation using data measured with another sample from the same population the r-value we would obtain is likely to be different

52
Q

If we were to calculate the correlation using data measured with another sample from the same population the r-value we would obtain is likely to be different

What does this difference reflect?

A

Sampling error

53
Q

Imagine if we obtained r for all possible samples
drawn from the population of interest

What would the mean of the resulting distribution look like?

A

The mean of the resulting distribution would be
equivalent to the true population correlation
coefficient

54
Q

The null hypothesis (H0) states that there is no
relationship between the population variables (i.e. r
= 0)

So, under the null hypothesis, the sampling
distribution of correlation coefficients will have a
mean of …?

A

Zero

55
Q

The r-distribution has a mean of …?

A

Zero

56
Q

The extent to which an individual sampled
correlation coefficient (r) deviates from 0 can be
expressed in…?

A

Standard error units

57
Q

Standard error units are used to express…?

A

The extent to which an individual sampled
correlation coefficient (r) deviates from 0

58
Q

True or False?

Our obtained r-value is just a point estimate of the underlying population r-value

A

True

59
Q

True or False?

Our obtained r-value is not subjected to sampling error

A

False

Our obtained r-value is subjected to sampling error

60
Q

What is the formula for shared variance?

A

Shared variance = r^2

61
Q

Expresses the proportion of the separate variances that are shared

This is known as…?

A

Shared variance = r^2

62
Q

Calculate the shared variance between the two variables when:

r = .8

A

r = .8
r^2 = .64

Variables share 64% of variance

63
Q

True or False?

r =.8 is twice as strong as r=.4

A

False

r =.8 is 4 times as strong as r=.4

64
Q

Expresses how much variance in our DV could be explained by our manipulation of the IV

This is known as…?

A

partial n^2

65
Q

Tells us how much of the variance in y can be ‘explained by’ x

This is known as…?

A

r

66
Q

Allows us to examine the relationship between two variables, while removing the influence of a third variable

This is known as…?

A

Partial correlation

67
Q

What is partial correlation?

A

Allows us to examine the relationship between two variables, while removing the influence of a third variable

68
Q

In our example, looking at the relationship between IQ and grade, we might want to remove the influence of test motivation

i.e. we want to ‘control for’ the effect of motivation

Would we use correlation or partial correlation for this?

A

Partial correlation

69
Q

Correlations between the three variables, Grade, IQ and Motivation, without partialling out motivation (zero-order correlations)

r = .522, p = .007

Correlations between Grade and IQ, with motivation partialled out

r = .353, p = .091

What does this result suggest?

A

The relationship measured between IQ and grade may be explained by the influence of motivation on both IQ and grade

70
Q

If the correlation between Grade and IQ, with motivation partialled out, had decreased but remained significant, what does this suggest?

A

The relationship was partially explained by motivation

71
Q

If the correlation between Grade and IQ, with motivation partialled out, had not decreased, what does this suggest?

A

The relationship was not influenced by motivation

72
Q

How many d.p. do we report r in?

A

3 d.p.

73
Q

Do we include a 0 in front of the decimal point when reporting r?

A

No

74
Q

How many d.p. do we report p in?

A

3 d.p.

75
Q

Do we include a 0 in front of the decimal point when reporting p?

A

No

YEAR 2 Stats (10 decks)

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