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Research Skills B > Correlation > Flashcards

Correlation Flashcards

1
Q

How can we assess the relationship/correlation between two variables?

A

Pictorially - Scatterplot. Useful when have wide range of scores or large sample size. Allows to see levels of association between variables

Numerically - Correlation coefficient

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2
Q

What happens when there is a negative association between two variables

A

Higher values on variable A corresponding to lower levels on variable B

As one variable deviates from the mean, the other deviates from the mean in the opposite direction.

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3
Q

What happens when there is a perfect positive association between two variables?

A

Higher values on variable A perfectly corresponding to higher values on variable B.

As one variable deviates from the mean, the other variable deviates in the same direction.

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4
Q

What happens when there is a perfect negative association between two variables?

A

Higher values on variable A perfectly correspond to lower values on variable B

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5
Q

What happens when there is no association between two variables?

A

Higher values on variable A corresponding to either high or low values on variable B

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6
Q

What happens when there is a non-linear association between two-variables?

A
  • There is an association, but it is not linear

- E.g. if practice too much then performance decreases

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7
Q

What does the strength of a relationship refer to?

A

How closely bunched around the imaginary line the dots are in the scattergraph

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8
Q

What are the two axes on a scattergram called?

A
  • Ordinate and abscissa
  • Vertical and horizontal axis
  • Y-axis and x-axis
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9
Q

What does the direction of a relationship refer to?

A
  • If points upward from bottom left to right = positive relationship
  • If points down from top left to bottom right = negative relationship
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10
Q

What does the form of a relationship refer to?

A
  • Linear = Straight line cutting across dots fits data nicely
  • Non-linear = If a curve fits better
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11
Q

Correlation coefficient

A

Numerical way of expressing a linear relationship

Tells you how strong the relationship is between variables

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12
Q

What are the steps for calculating Pearson’s r?

A
  1. Transform raw scores into z-scores
  2. Multiply the two z-scores for each participant
  3. Sum all of the products of the paired z-scores then divided the result by the number of cases - 1
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13
Q

Provide an example of a negative relationship from Pearson’s r

A

-0.61

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14
Q

Provide an example of no relationship from Pearson’s r

A

0.00

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15
Q

Provide an example of a small positive relationship from Pearson’s r

A

0.06

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16
Q

Pearson’s r forumla

A

The mean of the products of paired z-scores

Numerator = Sum of all the products of the paired z-scores
Denominator = Number of cases - 1

Values range from -1 (perfect negative correlation) to +1 (perfect positive correlation). Value of 0 implies no linear correlation. The stronger from 0, the stronger the relationship.

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17
Q

Which values can the Pearson’s r take?

A

From -1 to 1

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18
Q

Undefined Correlation

A
  • When you assess the correlation between two variables and one of them is constant.
  • Scatterplot will be perfectly horizontal
19
Q

One-tailed

A

Hypotheses specify direction

20
Q

Two-tailed

A

Hypotheses don’t specify direction

21
Q

How do you report the results of correlation?

A
  • Describe magnitude of relationship, direction, whether statistically significant
  • E.g. “There was a strong, positive, statistically significant relationship between class test scores and number of revision scores; r(10) = 0.82, p = 0.001.
22
Q

What happens when the relationship between two variables departs from linearity?

A

When it is u-shaped - Pearson’s r will underestimate the correlation between X and Y

When serious departure - Pearson’s r is not appropriate

23
Q

What happens when you calculate the correlation for two variables using a restricted range of scores?

A

Correlation is…

  • Reduced
  • Inflated
24
Q

What happens to the value of Pearson’s r when there are outliers?

A

Value of r will be inflated or reduced

25
Q

When does a perfect positive correlation occur?

A

r = 1

X and Y distributions have exactly the same shape.

26
Q

Skewed Distribution

A

A distribution where the most frequently occuring scores are clustered at one end of the scale

Not a symmetrical distribution

27
Q

Kurtosis

A

Peakedness of a distribution

Distributions can vary in terms of how peaked it is.

28
Q

What should you do if the assumptions for the test of inference regarding Pearson’s r are not satisfied?

A
  • Ignore if violations are not severe
  • Lower alpha level if not severe
  • Use tests designed for data that are not interval if severe violations.
29
Q

What happens to the correlation in a population in different hypotheses?

A

Alternative hypothesis = Correlation is different to 0

Null Hypothesis = 0

30
Q

When Pearson’s r is being used to measure the degree of correlation between 2 variables in a sample. What assumptions need to be satisfied?

A

Data measured on interval scale

31
Q

When Pearson’s r is being used to measure the degree of correlation between 2 variables in a population. What assumptions need to be satisfied?

A
  • Each variable is normally distributed

- Each variable is normally distributed at all levels of the other variable.

32
Q

Is there a difference between a population and a sample? Explain why.

A

Sample = Actual participants in study. Doesn’t represent the population at large.

Population = Broader group of people who you intend to generalise the results of the study.

33
Q

What does a statistically significant correlation between two variables suggest?

A

Two variables are unlikely to be uncorrelated in the population.

Does not concern the strength of the correlation.

Question if you believe the correlation is real.

34
Q

When do you look at r?

A
  • To see the strength of the correlation

- Larger the sample size, the smaller the value of r you need in order to obtain statistical significance.

35
Q

Cohen (1988)

A

Suggested the following values for the strength of a correlation coefficient.

.10 = Small correlation
.30 = Moderate correlation
.50 = Large correlation
36
Q

R-squared

A

Another way to judge the size of a correlation.

Multiply r-squared by 100, obtain the proportion of variance that X and Y share in common.

Correlation of .40 means 16% of variance shared in common by X and Y.

37
Q

Does a statistically significant result tell us that X has a strong effect on Y?

A

No

Does not say about what the effect is likely to be in the population.

Tells us that the effect is unlikely to be a null effect.

38
Q

Does p=.03 mean that the null hypothesis has a 3% chance of being true and research hypothesis has a 97% of being correct?

A

No

P-value gives no information about the probabilities of the observed effects being correct.

39
Q

What does a non-significant difference mean?

A

A null effect in the population is statistically consistent with the observed results

40
Q

What is the best way to assess normality?

A

Histogram

Allows to see if deviates from normality

41
Q

Name the factors which can affect the size of the correlation coefficient

A
  • They hide the true nature of the relationship between the two variables being correlated, misleading the researcher
  • Inverted U-shaped relationship
  • Restricted range
  • Outliers
  • Shape of the X and Y distributions
42
Q

When does a perfect negative correlation occur?

A

R = -1

Can only occur when X and Y distributions have exactly the same shape or when X and Y distributions are oppositely skewed.

43
Q

Variance

A

The average amount that the data vary from the mean

Research Skills B (6 decks)

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