chapter 7/week 6

Question 1

correlational research

Answer 1

used to describe the relation between two or more naturally occurring variables

ex: Is income related to age? Is self confidence related to GPA? Is depression related to anxiety?

Question 2

covary

Answer 2

vary or change together

Question 3

correlation coefficient

Answer 3

a statistic that indicates the degree to which two variables are related to one another in a linear fashion

Question 4

pearson correlation coefficient (r)

Answer 4

the most commonly used measure of correlation

Ranges from -1.00 to +1.00

Most commonly used; always this just the name is not said

The magnitude or numerical value of a correlation expresses the strength of the relation between the two variables
When r = .00 the variables are not related
A correlation of 0.78 indicates that the variables are more strongly related than does a correlation of 0.30
Magnitude is unrelated to the sign of the correlation; two variables with a correlation of 0.78 are just strongly related as two variables with a correlation of -0.78.

Question 5

sign of the correlation coefficient

Answer 5

indicates the direction of the relation between the two variables

Variables can either positively or negatively related

positive correlation
negative correlation

Question 6

positive correlation

Answer 6

a direct, positive relation between two variables; as one increases the other increases

Question 7

negative correlation

Answer 7

an inverse, negative relation between two variables; as one variable increases the other decreases

Question 8

perfect correlation vs no correlation

Answer 8

When there is a perfect correlation all of the data will fall into a straight line
- Should never happen; something is wrong

no correlation – scattered points

Question 9

when r = .00

Answer 9

A correlation of .00 indicates that there is no linear relation between the two variables. However, there could be a curvilinear relation between them.

Ex: anxiety and performance – not linear

Question 10

What are the components of the equation to calculate r?

Answer 10

X and y: participants score

Σxy: multiply each participant’s x- and y-scores together, then sum these products across all participants

(Σx)(Σy): sum all participants’ x-scores, sum all participants’ y-scores, then multiply these two sums

Question 11

Coefficient of determination

Answer 11

r^2 or the square of the correlation coefficient

proportion of variance in one variable that is accounted for by the other variable
- It ranges from 0 to 1
- closer to 1, better you can calculate the variance in your target variable
- indicator of systemic variance

Question 12

If the correlation between children’s and parent’s scores is .40

Answer 12

Coefficient of determination is (0.16). That is 16% of the variance in children’s IQ scores can be accounted for by their parent’s scores

In other words, 16% of the total variation in children’s IQ scores is systematic variance that is variance related to the parent’s IQ scores

Question 13

Statistical significance

Answer 13

a finding that is very unlikely to be due to error variance; exists when a correlation coefficient calculated on a sample has a very low probability of being zero in the population

A correlation coefficient is statistically significant when the correlation calculated on a sample has a very low probability of being zero in the population from which the sample came

Question 14

What probability level (we call this alpha) is very low?

Answer 14

It depends on your field of study, prior research and how much risk you want to take of being wrong

In psychology we generally pick an Alpha level of 0.05. We think 5% is very low.

Question 15

what must you do before you run any statistical test

Answer 15

you must first determine your alpha level, which is also called the “significance level.” this is the test probability of making a wrong decision (Type I error)

Question 16

Directional hypothesis

Answer 16

predicts the direction of correlation (pos/neg)

Question 17

Nondirectional hypothesis

Answer 17

predicts that two will be correlated, doesn’t specify the direction

Question 18

Statistical Significance of r is affected by several factors!!!!!!!!!!

Answer 18

sample size
effect size
significance level

Question 19

sample size (affects SS)

Answer 19

i.e., power
An increase in your sample will increase your power, that is your ability to find a significant result

Question 20

effect size (affects SS)

Answer 20

i.e., coefficient of determination

If the effect size ss larger, you are more likely to find a significant result

Question 21

significance level (affects SS)

Answer 21

i.e., alpha level

If the alpha level (i.e., .05 or .01 or .001) is set at a higher level, you are more likely to find a significant result

Question 22

3 factors that distort correlation coefficient

Answer 22

Restricted range
Outliers
Reliability of measures

Question 23

Restricted Range

Answer 23

data in which participants’ scores are confined to a narrow range of the possible scores on a measure

Having a restricted range artificially lowers correlations below what they would be if the full range of scores were present
Ex – sampling one school to see if ses correlates to grades
- Restricted range; will not see a correlation because everyone in that school lives in the same zip code and has the same ses status
- Need to sample more schools from other areas

Question 24

Outliers

Answer 24

A score is considered an outlier if it is more that 3 standard deviations away from the mean

On line outliers
off line outliers

Question 25

on line outliers

Answer 25

fall in the same pattern as the rest of the data and tend to artificially inflate r

Question 26

off line outliers

Answer 26

fall outside of the pattern of the rest of the data and tend to artificially deflate r

Question 27

Reliability of Measures

Answer 27

The more unreliable a measure is, the lower its correlations with other measures will be If the true correlation between college aspirations and SAT score is 0.45, but you use an aspiration scale that is unreliable, the obtained correlation will not be 0.45 but rather near .00.

Question 28

Correlation and Causality

Answer 28

Correlation does not mean causation Even when two variables have a perfect correlation of 1.00, we cannot conclude that one variable causes the other variable

Question 29

criteria for inferring causality

Answer 29

covariation directionality extraneous variables Correlational research satisfies the first (and sometimes the second) criterion, but never the third

Question 30

Covariation

Answer 30

changes in one variable are associated with changes in the other variable; same as correlation (i.e., high school GPA → SAT score)

Question 31

Directionality

Answer 31

the presumed causal variable preceded the presumed effect in time (i.e., smoking → lung cancer)

Question 32

Extraneous variables

Answer 32

all other variables that may affect the relation between the two target variables are controlled or eliminated (think discrimination and depression?)

Question 33

Spurious correlation

Answer 33

a correlation between two variables that is not due to any direct relationship between them but rather to their relation to other variables Some other variance (z) may cause both x and y Ex: students who are highly depressed do not do well in class, and they may try to relieve depression by drinking

Question 34

Partial correlation

Answer 34

the correlation between two variables with the influence of one or more other variables statistically removed If a partial correlation between two variables (with the influence of a third variable removed) is significantly lower than the Pearson correlation between the two variables, then the correlation between them is at least partly due to the third variable For example, the correlation between motivation and test performance may be lower because of a third variable, such as study time. In other words, partial correlation between motivation and test performance is a function of study time

Question 35

Other indices of correlation

Answer 35

Remember Pearson correlation coefficient (r) si only appropriate when you have a continuous variable (i.e., interval or ratio scale) spearman rank-order correlation phi coefficient point-biserial correlation

Question 36

Spearman rank-order correlation

Answer 36

correlation used when variables are measured on an ordinal scale, that is when the numbers reflect the rank ordering of participants on some attribute Ex: correlation between starred reviews and box office reviews

Question 37

Phi coefficient

Answer 37

correlation used when both variables are dichotomous (i.e., nominal with categories) Ex: correlation between gender and HS dropout

Question 38

Point-biserial correlation

Answer 38

correlation used when only one of the variables is dichotomous Ex: gender and IQ