3. ODDS RATIO - Measures Of Association

Question 1

What is in between exposure and outcome?

Answer 1

association

Question 2

Measures of association

Answer 2

Question 3

Measures of association with numeric outcome

Answer 3

Question 4

What is mean difference?

Answer 4

• Mean difference refers to the comparison between two means (averages)
• Mean difference is a measure of association which assesses the presence of an association between a categorical exposure and a numeric outcome

Question 5

In what situations are mean difference applicable?

Answer 5

1. Comparing means between categories (groups) of a categorical variable (i.e. between independent groups of individuals): BETWEEN-SUBJECTS designs
2. Comparing means in a single group of individuals in two or more different time points (e.g. before and after an intervention) or under different conditions: WITHIN-SUBJECTS or REPEATED MEASURES designs

Question 6

Mean difference formula?

Answer 6

Question 7

What statistical test provide a mean difference for between-subjects?

Answer 7

(i) Independent samples t-test in case our exposure variable (IV) has 2 categories and (
(ii) one-way Analysis of Variance (ANOVA) in case our exposure variable (IV) has >2 categories
ASSUME NORMALLY-DISTRIBUTED VARIABLES

Question 8

Within-subjects mean difference formula?

Answer 8

Question 9

What statistical tests are used for in-between mean difference?

Answer 9

(i) paired samples t-test in case our exposure variable (IV) has 2 categories and
(ii) repeated measures Analysis of Variance (repeated measures ANOVA) in case our exposure variable (IV) has >2 categories

Question 10

What is important regarding within-subjects mean difference?

Answer 10

Within-subjects/repeated measures designs compare measurements in the same participants /same sources of variability (hence the term repeated measures)
* Repeated measurements can be collected at different time points, where change over time is assessed: this has been the emphasis so far.
* However, other within-subjects studies may compare the same participants under two or more different conditions
* For instance: comparing pain intensity for the same participants receiving different (over time) pharmacotherapies for pain relief (e.g. cross-over trials, see later in the course)
* Thus if same participants compared➔use paired t test or repeated measures ANOVA as per previous slides

Question 11

What statistical test is used for independant groups (between-subjects IV) and repeated measures (within-subjects IV)?

Answer 11

mixed-design Analysis of Variance (mixed-design ANOVA)

Question 12

What is the within-subjects factor?

Answer 12

Time-point

Question 13

What is the between-subjects factor?

Answer 13

More than one group

Question 14

How do we asses association between two numerical values?

Answer 14

WE DON’T USE MEAN
* Instead, we use a mathematical model (an equation) to predict a change in the outcome (Y) for a standard change in the exposure (X) (regression coefficient)
* We also quantify the strength of the association (as captured by this model) (correlation coefficient)

Question 15

What are the 3 steps that are followed to fully investigate the association between 2 numeric variables?

Answer 15

1. Derive a scatter plot
2. Perform a correlation analysis
3. Perform a linear regression analysis

Question 16

What is a scatterplot?

Answer 16

• The relationship between any two numeric variables can be portrayed graphically
• Each individual (i) has a value for the exposure/independent variable (X) and a value for the outcome/dependent variable (Y)
• Thus, for each participant, we have (Xi, Yi)
• When the entire sample of participants is plotted in a 2-dimensional plot, the result is called scatter plot

Question 17

What can scatterplots show us?

Answer 17

• Scatterplots can provide an overall (graphical) impression for the association between the 2 numeric variables of interest
• Scatterplots can reveal a trend for a direct (positive) association or an inverse (negative) association

Question 18

What is direct and inverse association?

Answer 18

– direct (positive) association: as the exposure (X) increases, the outcome (Y) also increases
– inverse (negative) association: as the exposure (X) increases, the outcome (Y) decreases

Question 19

What is correlation?

Answer 19

Correlation is a term usually used interchangeably with ‘association’; however ‘correlation’ more accurately refers to the association between numeric variables

Question 20

What is the difference between positive and negative correlation?

Answer 20

• in situations where an increase in the exposure (X) leads to an increase in outcome (Y), we have a positive correlation
  – in situations where an increase in the exposure (X) leads to a decrease in outcome (Y), we have a negative correlation

Question 21

What is the correlation coefficient?

Answer 21

A measure of association that describes the strength of the correlation between 2 numeric variables is called the correlation coefficient (r)The correlation coefficient ranges between -1 to +1 and CANNOT take any value outside of this range
* The sign ( + or - ) indicates the direction of the association (i.e. positive or negative)

Question 22

What are the three types of correlation coefficients?

Answer 22

correlation coefficient (r) = 1
=> perfect positive correlation
correlation coefficient (r) = -1
=> perfect negative correlation
correlation coefficient (r) = 0
=> no correlation

Question 23

Strength of correlation?

Answer 23

Question 24

r=0 graph

Answer 24

Question 25

r=1 and r=-1 graph

Answer 25

Question 26

0<r<1

Answer 26

Question 27

-1<r<0

Answer 27

Question 28

What is the strength of correlation examples?

Answer 28

r ≥ +/- 0.7 => strong correlation
r = +/- 0.5 to 0.7 => moderate correlation
r = +/- 0.3 to 0.5 => weak correlation
r < +/- 0.3 => very weak or no correlation
* Note: there is no hard rule about these cut-offs and the exact numbers to indicate the strength of the correlation can vary depending on the specific variables analyzed

Question 29

What are the 2 main types of correlation?

Answer 29

• Pearson’s correlation is the most commonly used of the two and it denotes the correlation between 2 variables using the original values of these variables
• Spearman’s correlation (also called Spearman’s Rank correlation), denotes the correlation between 2 variables by first ranking the values (i.e. from lower to higher) and then assessing the correlation between the ranks
• Use Pearson’s correlation when 1) Continuous data 2) normally distributed 3) linear relationship
• Use Spearman’s when the above do not apply e.g. when data ordinal, not normally distributed, relationship not linear

Question 30

What is linear regression?

Answer 30

• Linear regression is another statistical technique for assessing the association between 2 numeric variables
• Linear regression assesses the extent to which
  an increase in one variable is associated with an increase in another variable
• Linear regression goes ‘hand-in-hand’ with correlation and in fact the 2 techniques complement each other in giving a complete picture about the association between 2 numeric variables
• Linear regression operates by fitting a line-of-best-fit in a scatterplot using the least-squares method

Question 31

What is the regression coefficient?

Answer 31

*The regression coefficient represents the estimated change (increase or decrease) in the Y variable for each 1 unit increase in the X variable

Question 32

What is the formula for line of best fit?

Answer 32

Y=a+bX*Yꞌ is the predicted value of Y (predicted by X )
*The slope (beta or b) of the line is the regression coefficient

Question 33

What does the sign of the regression coefficient mean?

Answer 33

Shows increase or decrease of Y when X is changed.

Question 34

What is correlation coeffient?

Answer 34

how strong is the association?

Question 35

What is the regression coefficient?

Answer 35

how much does a change in X predict a change in Y