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psyc 306 > Lecture 13: The Correlational Research Design > Flashcards

Lecture 13: The Correlational Research Design Flashcards

1
Q

correlational research

A
  • Intended to demonstrate the existence of a relationship between two variables
  • It does not determine cause-and-effect relationships
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2
Q

experimental research

A

demonstrates a cause-and-effect relationship between two variables

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3
Q

what do correlations describe?

A

the nature of the relationship

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4
Q

the nature of a relationship

A

includes its direction and degree

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5
Q

correlational data collection

A
  • No manipulations
  • Just measures variables
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6
Q

external validity of correlational research

A

high

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7
Q

examples of correlational research

A
  • The price of a box of chocolates and its quality (marketing)
  • Caffeine intake and alertness (basic research)
  • Movie topics and music preferences (art design)
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8
Q

unit of analysis of correlational research

A
  • The unit of analysis can be either a time point or a person
  • Usually, in psychological research, it is a person
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9
Q

assumptions of scatter plots

A
  • Each item/person is represented by only one data point
  • Each point in a dataset is independent of other points
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10
Q

visualizing correlational associations

A

The closer the points are to the line, the greater the association between variables

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11
Q

predicting correlations

A

Knowledge of the score on one dimension leads to the prediction of other dimension

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12
Q

quantitative representation of correlations

A

A quantitative representation: coefficient coefficient (r) ranges from -1.0 to +1.0

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13
Q

when do we use Spearman’s rho

A

if one of the variables being correlated is ordinal

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14
Q

when do we use Pearson’s r

A

When the two variables are on a ratio or interval scale

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15
Q

For both Spearman and Pearson correlations, we want to know:

A
  • Form (linear or nonlinear)
  • Sign (+ or -)
  • Strength (absolute value between 0 and 1)
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16
Q

linear correlation

A
  • Change in one variable is consistent with change in another variable
  • Makes a straight line
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17
Q

nonlinear correlation

A

change in one variable is not consistent with change in another variable

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18
Q

Spearman’s correlation

A
  • Measures monotonic relationships where there is a consistent directional relationship between x and y but no amount of constant change
  • Computed on rank values (smallest to largest)
  • Used most with ordinal scale data
  • Range= -1 to 1
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19
Q

monotonic relationship

A

a relationship where each of the two variables has values that continue in one direction or stay the same (neither variable can reverse direction)

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20
Q

You should use the Spearman correlation when:

A
  • The data is an ordinal scale
  • The data must be monotonic
  • There are at least 5 pairs of data; preferably > 8 pairs
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21
Q

when are ranks meaningful?

A

when there are not too many or too few pairs

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22
Q

what does Spearman’s correlation coefficient measure?

A

the strength and direction of the association between two ranked variables

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23
Q

interpreting Spearman’s Rho values

A

weak= 0.21-0.41
moderate= 0.41-0.60
strong= 0.61-0.80
very strong= 0.81-1.00

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24
Q

the Pearson correlation

A
  • Measures linear relationships, where stores cluster around a straight line
  • Y changes consistently and constantly with x
  • Used most with interval and ratio scale data
  • Range= -1 to 1
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25
Q

what does the term correlation usually refer to?

A

a Pearson correlation because most behavioural research uses interval or ratio scale data

26
Q

positive r value

A
  • when larger values of one variable are associated with larger values of another variable (or smaller with smaller)
  • r > 0 when x increases, y increases (or when x decreases, y decreases)
27
Q

negative r value

A
  • when larger values of one variable are associated with smaller values of another
  • r < 0 when x increases, y decreases (or when x decreases, y increases)
28
Q

what does the direction of the correlation indicate?

A

the nature of the change in the variables

29
Q

positive linear correlation

A
  • High scores on one variable are matched by high scores on another
  • The line slants up to the right
30
Q

negative linear correlation

A
  • High scores on one variable are matched by low scores on another
  • The line slants down to the right
31
Q

no linear correlation

A
  • No line, straight or otherwise, can be fit to the relationship between the two variables
  • Two variables are uncorrelated
32
Q

linear relationship

A

the data points in the scatter plot tend to cluster around a straight line

33
Q

positive linear relationship

A
  • each time the x variable increases by one point, the y variable increases in a consistently predictable amount
  • A Pearson correlation describes and measures linear relationships when both variables are numerical scores from interval or ratio scales
34
Q

nonlinear relationship

A
  • The data points do not cluster around a straight line
  • A Spearman correlation describes and measures monotonic nonlinear relationships when one or more variables are ordinal
35
Q

strength of the correlation

A
  • The degree of association or consistency tells us the strength of the relationship (correlation)
  • It is expressed mathematically as a correlation coefficient from -1 to +1
  • The stronger the association the closer to -1/+1
36
Q

interpreting Pearson correlations

A

no relationship= 0.10
weak relationship= 0.10-0.30
moderate relationship= 0.30-0.70
strong relationship= 0.70-1.00

37
Q

Spearman vs. Pearson correlation

A
  • Spearman correlation of 1 results when the two variables are monotonically related, even if their relationship is not linear
  • This means that all data points with greater x values than that of a given data point will have greater y values as well
  • When the data are roughly elliptically distributed (variance on both factors) and there are no prominent outliers, the Spearman correlation and Pearson correlation give similar values
38
Q

correlation coefficients for nonmonotonic relationships

A

Both Pearson and Spearman fail (yield values close to 0) for nonmonotonic relationships

39
Q

outlier

A
  • A data point that differs significantly from others in the set
  • Can be an outlier on the X variable or the Y variable
40
Q

outliers and the strength of the correlation

A

Outliers can greatly affect the strength of the correlation

41
Q

how are correlations usually defined?

A

by the variance in the variable

42
Q

outliers in Spearman vs. Pearson correlations

A
  • The Spearman correlation is less sensitive to outliers than the Pearson correlation
  • This is because Spearman’s p reassigns outliers with a rank and ranks cannot be outliers
43
Q

significance of correlations

A
  • Statistical significance suggests that a relationship is unlikely to be the result of chance (typical p < .05)
  • The probability (alpha) is < 5% that this correlation would have been this large (or larger) due to chance alone
  • Most likely represents a real relationship that exists in the population
44
Q

sample size and correlations

A
  • Small sample sizes are prone to producing large correlations, so the criteria for statistical significance becomes more stringent
  • As n increases, so does the likelihood that relationships found exist
45
Q

how is statistical significance determined?

A

by consulting a table that takes into account sample size and alpha (p) level

46
Q

statistical significance

A
  • Related to the p-value associated with n, df, the size of the correlation
  • Possible to have a small r but it can be statistically significant if the sample size is big enough
47
Q

practical significance

A

Related to any meaningful, real-world consequences of the observed correlation

48
Q

correlations with a small n

A
  • It is easy to obtain strong correlations with small samples when there is no relationship between the variables
  • When n = 2, we always get a correlation of 1.0 or -1.0
  • As the sample size increases, it becomes more likely that correlation from the sample reflects a real relationship in the population
49
Q

coefficient of determination

A

the shared variance; the percentage of changes in one variable (x) can be accounted for by changes in the other variable (y)

50
Q

what measurement scale are correlations on?

A

ordinal; they do not increase in equal increments

51
Q

correlations and variability

A
  • Correlations help explain some parts of the variability in x and y scores:
  • Other different variables can also explain variability in x, y
52
Q

how do we represent the portion in variability shared by two variables?

A
  • with Venn diagrams
  • The larger the degree of overlap, the greater the strength of the correlation
53
Q

r²

A

proportion of shared variance/variance accounted for/ coefficient of determination

54
Q

sign of r²

A

it is always positive

55
Q

statistical evaluation of correlations

A
  • You can use the coefficient of determination to measure the percentage of variability in one variable that is determined by its relationship with the other
  • Sometimes a variance of 3% is a lot but other times it’s meaningless
  • In the behavioural sciences, it is usual to predict only a small proportion of the variance (< 70% of the variance)
56
Q

interpreting the coefficient of determination

A

small= 0.01
medium= 0.09
large= 0.25

57
Q

advantages of correlational methods

A
  • Often quick and efficient
  • Often the only method available for practical or ethical reasons
  • High external validity
58
Q

limitations of correlational methods

A
  • Does not tell us why the two variables are related
  • Low internal validity
  • Very sensitive to outliers
  • Directionality problem
  • Third variable problem
59
Q

directionality problem

A

we don’t know what variable causes what

60
Q

third variable problem

A

there might be a third unidentified variable responsible for producing changes in x and y

61
Q

assuming directionality from correlations

A
  • The frequency of tub bathing was associated with a lower risk of cardiovascular disease among adults
  • But, you can’t assume directionality from correlations
  • People with lower-stress lifestyles may have time to take more baths
  • SES may influence bathing rates and eating patterns
  • High-temperature baths can exacerbate cardiovascular disease

psyc 306 (17 decks)

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