Statistics V - Correlation, Causation, Regression

Question 1

Regression is a model of what?

Answer 1

A model of the influence of x on y.

Question 2

What’s a multivariate regression?

Answer 2

Regression with
1 independent and
several dependent variables
(-> several univeriate regressions)

Question 3

What’s a multiple regression?

Answer 3

Regression with
several independent and
1 dependent variable.

Question 4

What’s a multivariate multiple regression?

Answer 4

Regression with
several independent and
several dependent variables

Question 5

What’s a regression with
1 independent and
several dependent variables
(-> several univeriate regressions)?

Answer 5

A multivariate regression.

Question 6

What’s a regression with
several independent and
1 dependent variable?

Answer 6

A multiple regression.

Question 7

What’s a regression with
several independent and
several dependent variables?

Answer 7

A multivariate multiple regression.

Question 8

What is the multivariate regression used for?

Answer 8

It is used for investigating the effects of one independent variable on several dependent variables.

Question 9

In a multiple regression: What does ßi stand for?

Answer 9

the partial coefficient of regression

Question 10

Is the partial coefficient of regression equal to the bivariate coefficient of regression?

Answer 10

No!

Question 11

What can we learn from the following example?
Epidemiological studies showed that women who were taking combined hormone replacement therapy (HRT) also had a lower- than-average incidence of coronary heart disease (CHD), leading doctors to propose that HRT was protective against CHD. But controlled trials showed that HRT caused a small and significant increase in risk of CHD. Re-analysis of the data showed that women undertaking HRT were more likely to be from higher socio-economic groups (ABC1), with better than average diet and exercise regimes.

Answer 11

Correlation DOES NOT imply causation!

Question 12

What is a confounding variable?

Answer 12

A confounding variable is an extraneous variable in a statistical model that correlates (positively of negatively) with both the dependent and the independent variable.

Question 13

Other terms for confounding variable include…

Answer 13

… confounding factor, hidden variable, lurking variable, confound or confounder.

Question 14

What is the Simpson paradox / Simpson reversal (aka. Yule-Simpson effect)?

Answer 14

In probability and statistics, Simpson’s paradox, or the Yule–Simpson effect, is a paradox in which a trend that appears in different groups of data disappears when these groups are combined, and the reverse trend appears for the aggregate data.

Question 15

Two examples of Simpson’s paradox?

Answer 15

Kidney Stone Treatment

Berkeley gender bias case

Question 16

What does selection bias mean?

Answer 16

Selection bias is a statistical bias in which there is an error in choosing the individuals or groups to take part in a scientific study.

Question 17

What is the Berkson’s paradox?

Answer 17

Specifically, it arises when there is an ascertainment bias inherent in a study design.
The result is that two independent events become conditionally dependent (negatively dependent) given that at least one of them occurs.

Question 18

If you give a class of students a test on two successive days, the worst performers on the first day will tend to improve their scores on the second day, and the best performers on the first day will tend to do worse on the second day. The phenomenon occurs because …

Answer 18

… each sample is affected by random variance.

→ negative correlation between the two successive scores

Question 19

What is meant by regression to the mean?

Answer 19

If a pair of independent measurements are made from the same distribution, samples far from the mean on the first measurement will tend to be closer to the mean on the second one. Moreover, the farther from the mean on the first measurement, the stronger the effect is.

Question 20

What is meant by Reichenbach’s “no correlation without causation”?

Answer 20

If any two variables are dependent, then one is the cause of the other or (!) there is a third variable causing both.

Question 21

Hume (18. century) on causality:

Answer 21

We can only perceive post hoc (nacheinander), never propter hoc (wegeneinander).

Question 22

Describe the pattern of the post hoc fallacy!

Answer 22

The form of the post hoc fallacy can be expressed as follows:

    A occurred, then B occurred.
    Therefore, A caused B.

When B is undesirable, this pattern is often extended in reverse: Avoiding A will prevent B.

Question 23

Kant (18. century) on causality:

Answer 23

Agrees with Hume: Causality derives from reasoning not from perception.

Question 24

Explain spurious correlation!

Answer 24

Spurious correlation does not imply causality.

Question 25

Rules for causality according to Davis (1985):

Answer 25

A causes B if:

• A starts before B
• A comes in a known order before B
• A is more stable, more difficult to influence or more influential.

Question 26

To control variables Sir Ronald Fischer suggests …

Answer 26

… randomization included in the experimental design.

Question 27

Statistical means to control for variables:

Answer 27

• residuals of regression
• repetition among control categories
• weighting of data

Question 28

Controlling of prior and intervening variables can lead to the …

Answer 28

… direct effect.