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Research & Stats > Week 4 - Measures of association > Flashcards

Week 4 - Measures of association Flashcards

1
Q

What is in between exposure and outcome?

A

association

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2
Q

Measures of association

A
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3
Q

Measures of association with numeric outcome

A
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4
Q

What is mean difference?

A
  • 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
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5
Q

In what situations are mean difference applicable?

A
  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
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6
Q

Mean difference formula?

A
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7
Q

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

A

(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

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8
Q

Within-subjects mean difference formula?

A
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9
Q

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

A

(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

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10
Q

What is important regarding within-subjects mean difference?

A

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

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11
Q

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

A

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

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12
Q

What is the within-subjects factor?

A

Time-point

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13
Q

What is the between-subjects factor?

A

More than one group

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14
Q

How do we asses association between two numerical values?

A

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)

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15
Q

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

A
  1. Derive a scatter plot
  2. Perform a correlation analysis
  3. Perform a linear regression analysis
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16
Q

What is a scatterplot?

A
  • 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
17
Q

What can scatterplots show us?

A
  • 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
18
Q

What is direct and inverse association?

A

– 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

19
Q

What is correlation?

A

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

20
Q

What is the difference between positive and negative correlation?

A
  • 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
21
Q

What is the correlation coefficient?

A

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)

22
Q

What are the three types of correlation coefficients?

A

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

23
Q

Strength of correlation?

A
24
Q

r=0 graph

A
25
Q

r=1 and r=-1 graph

A
26
Q

0<r<1

A
27
Q

-1<r<0

A
28
Q

What is the strength of correlation examples?

A

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

29
Q

What are the 2 main types of correlation?

A
  • 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
30
Q

What is linear regression?

A
  • 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
31
Q

What is the regression coefficient?

A

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

32
Q

What is the formula for line of best fit?

A

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

33
Q

What does the sign of the regression coefficient mean?

A

Shows increase or decrease of Y when X is changed.

34
Q

What is correlation coeffient?

A

how strong is the association?

35
Q

What is the regression coefficient?

A

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

Research & Stats (13 decks)

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