Risk ratios and Odds ratios

Question 1

Any finding that we observe in our study can be wither of three things:

Answer 1

1. A true finding
2. A spurious (false) finding due to random error
3. A spurious /false) finding due to a “systematic”, non-random error: bias or conducting

Question 2

Random error:

Answer 2

Any difference between sample mean and population mean that is attributable to the sampling.

Question 3

Random error is a ….., Standard Error is its …..

Answer 3

Phenomenon and measure

Question 4

Standard error:

Answer 4

The standard error (SE) is the basic measure of random error for any quantity that we measure or calculate in a sample.

Question 5

What is the standard error inversely proportional to?

Answer 5

The square root of the sample

Question 6

Null hypothesis (H0):

Answer 6

Both population means are the same, μ1 = μ2, and any difference in sample means is due to random error.

Question 7

Alternative hypothesis (H1):

Answer 7

Population means are actually different μ1 ≠ μ2, and that is the cause of the difference in sample means.

Question 8

The two-sample t-test:

Answer 8

Are used to compare just two samples. They test the probability that the samples come from a population with the same mean value.

Question 9

If the probability is very low (by convention: p<0.05) then we have to

Answer 9

Reject the null hypothesis H0 and choose the alternative hypothesis (H1)

Question 10

Definition of p-value:

Answer 10

The p-value is the probability of getting this or a more extreme result if the null hypothesis is true.

Question 11

If the p-value is higher than 0.05 we have failed to reject the null hypothesis H0 and to show that there`s an underlying difference:

Answer 11

• There might be an underlying difference in population means that we have failed to demonstrate (e.g., because our sample size was too small) or there might not be.
• We describe the difference as “statistically non-significant”.
• We never ever accept the null hypothesis; we only fail to reject it.

Question 12

If p<0.05 then:

Answer 12

The 95% CI will not include zero (the “null” value).

Question 13

If p>0.05 then:

Answer 13

The 95% CI will include zero.

Question 14

If p=0.05:

Answer 14

One of the 95% CI limits will be equal to zero

Question 15

We can create a contingency table showing:

Answer 15

The frequency distribution of the two variables (cross-tabulation)

Question 16

The chi-square test:

Answer 16

It is a measure of the difference between actual and expected frequencies.

Question 17

What is the expected frequency:

Answer 17

Is the frequency we would see if the null hypothesis were true

Question 18

What happens if the observed and the expected frequencies are the same?

Answer 18

The x^2 value would be zero

Question 19

Fisher´s exact test (X^2 non-paramedic brother):

Answer 19

Is sometimes used to analyze contingency tables. It is the best choice as it always give the exact p-value, particularly where the number are small.

Question 20

What is risk?

Answer 20

Risk is he probability that an event will happen.

Question 21

How is risk calculated?

Answer 21

It is calculated by dividing the number of event by the number of people at risk.

Question 22

Odds ratio is used?

Answer 22

By epidemiologists in studies looking for factors which do harm, it is a way of comparing patient who already have a certain condition (cases) with patient who do not (controls) - a case-control study

Question 23

Relative risk (RR):

Answer 23

(Risk of the outcome among the exposed )/(Risk of the outcome among the unexposed) = (d/(c+d))/(b/(a+b))

Question 24

Odds ratio (OR):

Answer 24

(Odds of exposure among those with the outcome )/(Odds of exposure among those without the outcome ) = (d/b)/(c/a)

Question 25

Risk =

Answer 25

Probability

Question 26

The odds ratio is:

Answer 26

Symmetric

Question 27

The RR and OR have their own Standard Errors:

Answer 27

SE(logRR) = √(1/d=1/(c+d)=1/b=1/(a+b))
SE(logOR) = √(1/a=1/b=1/c=1/d)

Question 28

The RR and OR have their own Standard Errors, which means:

Answer 28

That means we can calculate a 95% Confidence Interval, by going ±1.96 Standard Errors from log RR and log OR (and then exponentiating, to return to the original scale)
(In practice, these calculations are done by computer with R * Extremely easy once you’ve got your data loaded)