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PSY247 Research Design and Analysis > Chapter 16 > Flashcards

Chapter 16 Flashcards

1
Q

Correlation coefficient measures

A

Descriptive statistic that measures the degree of the relationship between two variables. Look at two variables at the same time.

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2
Q

Pearson product-moment correlation coefficient (Pearson r)

A

The correlation coefficient appropriate for interval/ratio data

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3
Q

What are names of the two correlation coefficient measures?

A

Pearson product-moment correlation coefficient (Pearson r) and the Spearman rank-order correlation coefficient (Spearman rs)

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4
Q

What does Pearson r stand for?

A

Pearson product-moment correlation coefficient

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5
Q

What does Spearman rs stand for? (little s)

A

Spearman rank-order correlation coefficient

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6
Q

Spearman rank-order correlation coefficient (Spearman rs)

A

The correlation coefficient appropriate for ordinal data where two variables are ordinal, or between a pair of variables where one is ordinal and the other interval/ratio.

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7
Q

What does a correlation coefficient of .0 indicate?

A

No statistical relationship.

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8
Q

What does a correlation coefficient of 1.0 indicate?

A

The strongest possible degree of relationship.

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9
Q

Scatter diagram

A

A graphical method of representing the relationship between two variables where one variable is plotted on the x-axis and the other is plotted on the y-axis.

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10
Q

What are some alternative names for a scatter diagram?

A

Scattergram, scatter chart, scatter graph, scatterplot

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11
Q

What is the symbol for the correlation coefficient in a population?

A

p

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12
Q

What is the symbol for the correlation coefficient in a sample?

A

r

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13
Q

What is the number of correlation coefficient?

A

lies between -1 and +1

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14
Q

What two characteristics of scatter diagrams should be noted?

A

The slope and width of the imaginary ellipse that can be drawn around most of the points in the scatter diagram.

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15
Q

What does the slope determine in a scatter diagram?

A

The slope determines the sign of r (correlation coefficient in a sample) . If the slope is from the lower left to the upper right then the correlation coefficient is positive. If the slope is from upper left to lower right the correlation coefficient is negative. If you can’t tell which way they slope, r is about zero.

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16
Q

What is a positive correlation?

A

High values of one variable tend to occur with high values of the other variable, and low values of one variable tend to occur with low values of the other variable.

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17
Q

What is a negative correlation?

A

High values of one variable tend to occur with low values of the other variable, and low values of one variable tend to occur with high values of the other variable.

18
Q

How do you get a z score?

A

Subtract the mean from each raw score and divide the result by the standard deviation.

19
Q

What does .5 correlation co-efficient indicate?

A

Likely (but not necessarily the case) that the two variables are positively correlated.

20
Q

What does 1.0 correlation co-efficient indicate?

A

Know for a fact that the variables are positively correlated.

21
Q

What does .0 correlation co-efficient indicate?

A

No statistical relationship.

22
Q

What kind of data does a correlation co-efficient always deal with?

A

Always based on pairs of data. e.g. pairs of identical twins. Sometimes these pairs are the same measurements on different (but paired) subjects. Sometimes these pairs are different measurements on the same subjects.

23
Q

What does a scatter diagram do?

A

Illustrates data to explore the concept of correlation.

24
Q

What does the width of the imaginary ellipse that can be drawn around most points of the scatter diagram correspond with?

A

The magnitude of the correlation coefficient.

25
Q

If the imaginary ellipse is extremely narrow…

A

the magnitude is 1 (the strongest possible degree of relationship).

26
Q

If the imaginary ellipse is wide as it can be thus making it a circle…

A

the magnitude is 0 (indicates that there is no relationship between the two variables).

27
Q

How do you get a z score?

A

Subtract the mean from each raw score and divide the result by the standard deviation.

28
Q

What does a z score do?

A

Counts the number of standard deviations a point is from the mean.

29
Q

What is the numerator in the pearson r correlation coefficient formula?

A

The sum of all the values.

30
Q

How do you eye ball estimate Pearson’s r on a scatter diagram?

A
  • Superimpose a tic-tac-toe grid over the scatter diagram.
  • Pearson’s r is highly positive if many points are in the + cells (top right, bottom left) and very few points in the - cells (top left, bottom right).
  • Pearson’s r is highly negative if many points are in the - cells and few are in the + cells.
  • Pearson’s r is 0 if points are equally distributed in + and - cells.
31
Q

A low correlation coefficient means that there is little or no relationship between two variables being measured. However, what are the two exceptions?

A
  • Non-linear relationships - Pearson’s r measures only the degree of the linear relationship between two variables. It can happen (though not often in practice) that variables have a strong nonlinear relationship and yet Pearson’s r is quite small or 0.
  • Restrictions of the range - If the total range of one (or both) of the variables we are measuring is truncated (shortened) or diminished in any way, the correlation of the two variables is likely to be reduced. In plain English, restricting the range of one or both variables generally reduces the correlation coefficient.
32
Q

What does correlation does not imply causation mean?

A

If x and y are related, x might cause (at least in part) y, or y might cause (at least in part) x, or some third variable might cause (at least in part) both x and y. Inferences about cause and effect must be made on the basis of evidence gathered from experiments or knowledge about the situation other than correlations.

33
Q

Pearson’s r can be considered as a descriptive statistic and also an inferential statistic. How?

A
  • r describes the relationship between a sample of two variables.
  • r can be used to test inferences about the population correlation coefficient p.
34
Q

Null hypothesis

A

(in a statistical test) the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.

35
Q

Alternative Hypothesis

A

The alternative hypothesis is the hypothesis used in hypothesis testing that is contrary to the null hypothesis. It is usually taken to be that the observations are the result of a real effect (with some amount of chance variation superposed).

36
Q

Degrees of freedom

A

Degrees of freedom are often broadly defined as the number of “observations” (pieces of information) in the data that are free to vary when estimating statistical parameters.

37
Q

What is the formula for testing a hypothesis about r? p441

A

test statistic = (sample statistic - population parameter) / (standard error of the sample statistic).

38
Q

What is statistical power?

A

The probability of correctly rejecting the null hypothesis, and that one of the most important uses of power analysis is in determining the sample size necessary for an experiment to have the desired power.

39
Q

What do you need to do to have statistical power? p.442-3

A

Specify the effect size index of the population from which we expect the sample subjects to be drawn. In the case of a correlation experiment, the appropriate effect size is p, the correlation coefficient of the population. p=.1 (small effect size), p=.3 (medium), p=.5 (large). For a medium correlation an experiment must have 66 participants to have an 80% chance of rejecting the null hypothesis.

40
Q

How do you eye ball estimate Spearmans rs (little s)?

A

Same approach as Pearson’s r. Tic-tac-toe grid.

41
Q

Does ordinal data and Spearmans rs (little s) have degrees of freedom?

A

No.

PSY247 Research Design and Analysis (15 decks)

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