Chapter 8- Bivariate correlational research

Question 1

Bivariate correlation

Answer 1

An association that involves exactly 2 variables

Question 2

Graphing associations when one variable is categorical

Answer 2

You can use a scatter plot to evaluate categorical data as well. The lines will be vertical, and you check to see if they slope up from right to left, slope down, or slope flat. The researchers can also plot categorical data using a bar graph- the mean marital satisfaction rating is graphed for each category

Question 3

How can you tell a study is correlational?

Answer 3

No matter what kind of graph you see, when both variables are measured, the study is correlational and can support an association claim- an association claim is supported by study design. If a variable is manipulated, that would be an experiment

Question 4

Construct validity

Answer 4

How well was each variable measured?

Question 5

How to interrogate the construct validity of an association claim

Answer 5

In a study investigating the associations between deep conversations and well being, you would ask how each variable was operationalized. Once you know that, you could ask questions to assess the construct validity of each. Does the measure have good reliability? Is it measuring what it’s intended to measure? What is the evidence for its face validity, its concurrent validity, and its discriminant and convergent validity?

Question 6

Effect size

Answer 6

Describes the strength of a relationship between 2 or more variables. Judgements of effect size depend on context, but r values of .1, .3, and .5 are considered weak, moderate, and strong, respectively

Question 7

Are small effect sizes important?

Answer 7

Larger effect size is often considered more important than a small one if all else is equal. However, small effect sizes can compound over many observations and have an important impact. Ex- star batters in baseball are more likely to get on base during any one at bat, r= .05. This seems small, but over hundreds of at bats during the season, the star batters score many more runs. Small effect sizes can become more important when they are aggregated over many people as well. In one study about the effect of growth mindset, teens assigned to the growth mindset group had better grades, with an effect size of r= .05. This effect size was large enough to prevent 79,000 US teens from scoring in the D or F grade range.

Question 8

What is the average effect size in psychology?

Answer 8

The average effect size in psychology studies is r= .2, and it will rarely be as high as r= .4

Question 9

Confidence interval

Answer 9

To communicate the precision of their estimate of r, researchers report a 95% confidence interval. The CI calculations ensure that 95% of CIs will contain the true population correlation. Analogy- a contractor might estimate that repair costs are between $1000-$1500.

Question 10

How does sample size affect confidence interval?

Answer 10

When an estimate is based on a small sample, it’s less stable. Therefore, they have wider confidence intervals. Have to be wider to capture the degree of uncertainty we have when the sample is small

Question 11

Statistically significant

Answer 11

A statistically significant correlation is unlikely to have come from a population in which the association is zero. An association is said to be statistically significant when the confidence interval doesn’t contain zero

Question 12

Replication

Answer 12

Another way to estimate the population association is to conduct the study again and find multiple estimates- this is called replication.

Question 13

Outlier

Answer 13

An extreme score, a single case or a few cases that stand out from the pack- it exerts disproportionate influence. Adding one outlier data point can change the correlation coefficient drastically, making the relationship appear stronger or weaker than it actually is

Question 14

When are outliers considered problematic with bivariate correlation?

Answer 14

In a bivariate correlation, outliers are mainly problematic when they involve extreme scores on both variables. When interrogating an association claim, you should ask if there were any outliers. The best way to determine this is to look at the scatter plot and see if any data points stand out

Question 15

Restriction of range

Answer 15

If there is not a full range of scores on one of the variables in an association, it can make the correlation appear smaller than it really is. Ex- a college only admits students who get a 1200 or higher on their SAT. When looking at the correlation between SAT scores and first year college grades, the correlation between the two for students at that college doesn’t seem very strong. However, looking at the full range of data points for all SAT scores makes the correlation much stronger. The college restricted the range of SAT scores (1200-1600) for students at their college, underestimating the true correlation between SAT scores and grades

Question 16

If researchers suspect restriction of range, they could (2)

Answer 16

1. Admit all students to the college regardless of their SAT scores to see what grades they obtain, and then compute the correlation.
2. Use a statistical technique- correction for restriction of range.

Question 17

When does restriction of range apply?

Answer 17

Restriction of range can apply when, for any reason, one of the variables has very little variance. When testing the correlation between parental income and child school achievement, researchers would have to include parents of all incomes.

Question 18

Curvilinear association

Answer 18

The relationship between two variables is not a straight line, it’s positive up to a point and then becomes negative. One example is use of healthcare services- as people get older, their use of healthcare services decreases to a point, and as they get to age 60 and beyond, healthcare use increases again. R is designed to describe the slope of a straight line, so it doesn’t work very well in these situations, and doesn’t accurately describe the relationship.

Question 19

3 criteria to establish causation

Answer 19

1. Covariance of cause and effect
2. Temporal precedence
3. Internal validity

Question 20

Covariance of cause and effect

Answer 20

The results must show a correlation, or association, between the cause variable and the effect variable.

Question 21

Temporal precedence

Answer 21

The method must ensure that the cause variable preceded the effect variable, it must come first in time

Question 22

Internal validity

Answer 22

There must be no plausible alternative explanations for the relationship between the two variables. An alternative would be a hidden third variable- the third variable must correlate logically with both of the measured variables in the original association to be plausible.

Question 23

Spurious association

Answer 23

The bivariate correlation is there, but only because of some third variable (gender). A study examining the association between height and hair length found that tall people tend to have shorter hair. However, men tend to be taller than women and also tend to have shorter hair. Therefore, gender caused the association.

Question 24

How can we tell that a third variable isn’t causing a correlation?

Answer 24

A study finds that height and weight are positively correlated. Gender could also be a third variable here, because men tend to be taller than and weigh more than women. However, on a scatter plot, we can see that height and weight are still correlated within the two gender groups. This means that gender is not a third variable in this correlation.

Question 25

How is external validity interrogated for an association claim?

Answer 25

To interrogate the external validity, you ask whether the association can generalize to other people, places, and times. The size of the sample does not matter as much as the way the sample was selected. If it was selected randomly, you can generalize to that population. If a correlational study didn’t use a random sample, you can accept the study’s results and leave the question of generalization to the next study, which might test the association between the variables in another population.

Question 26

Moderator

Answer 26

When the relationship between two variables changes depending on the level of another variable, that other variable is called a moderator. When an association is moderated by a variable, we know that it doesn’t generalize to another situation.