Comparing data

Question 1

Parametric test for comparing paired, continuous data?

Answer 1

Paired t-test

Question 2

What are the assumptions for the paired t-test

Answer 2

Differences are plausibly normally distributed

Differences are independent of each other

Question 3

Steps to calculate a p-value from a paired t-test

Answer 3

1. Calculate the differences between the values in each group (d)
2. Calculate the mean + standard deviation of the means
3. Calculate the standard error of the mean difference
4. Calculate the test statistic (t)
5. Under the null hypothesis, t is distributed as Student’s t, with n-1 degrees of freedom
6. Look up this value in tables to find p-value (gives two-tailed p value)

Question 4

How is the test statistic (t) calculated for paired t-test?

Answer 4

dbar(-0)/SE(dbar)

dbar = mean of the differences

Question 5

How is the 100% (1-α)% confidence interval for the mean difference in the population calculated?

Answer 5

d(bar)-[txSE(dbar)] to dbar+[txSE(dbar)]
dbar = mean difference
t taken from t distribution table with n-1 degrees of freedom

Question 6

What is the non-parametric equivalent of the paired t-test? (for assessing paired data)

Answer 6

Wilcoxon (matched pairs) signed rank test

Question 7

What does the Wilcoxon signed rank test test?

Answer 7

Test of null hypothesis that there is no tendency for the outcome under one set of conditions to be higher or lower than under the comparison set of outcomes

Question 8

What is the parametric test for independent, continuous data?

Answer 8

Independent samples t-test

Question 9

What are the assumptions for the independent two sample t-test

Answer 9

Two independent groups
Continuous outcome
Outcome data in both groups is normally distributed
Outcome data in both groups have similar standard deviations

Question 10

Steps to calculate a p value from the independent two sample t-test

Answer 10

1. Calculate the difference between means of groups
2. Calculate the pooled standard deviation of the means
3. Calculate the standard error of the difference between two means
4. Calculate the test statistic (t)
5. Compare the test statistic with the t distribution with n1+n2-2 degrees of freedom
6. Look up this value in tables to find p-value (gives two-tailed p value)

Question 11

How is pooled SD for two independent groups calculated?

Answer 11

√[(n1-1)SD1^2+(n2-1)SD2^2]/n1+n2-2

Question 12

How is standard error of difference between two means calculated for two independent groups?

Answer 12

pooled SDx√(1/n1)+(1/n2)

Question 13

How is the test statistic (t) calculated for independent samples t test?

Answer 13

d/SE
d = observed difference in means
SE = standard error of difference in means

Question 14

How is the 100% (1-α)% confidence interval for the difference between means in the population calculated?

Answer 14

(xbar1-xbar2) +/- [txSE(difference)]

Question 15

What is the non-parametric equivalent of the independent samples t-test?

Answer 15

Mann-Whitney U test

Question 16

What does the Mann-Whitney U test show?

Answer 16

Test of the null hypothesis that the distribution of the outcome variable in the two groups is the same

Question 17

Steps for Mann-Whitney U test

Answer 17

1. Arrange all data in increasing order
2. Choose one group: for each observation in that group, count how many observations in the other group lie below it
3. All numbers added up = U-statistic
4. Compare U test statistic with theoretical distribution under null hypothesis (that samples come from the same population)

Question 18

What two tests can be used when assessing more than two independent groups?

Answer 18

Analysis of variance technique (ANOVA) = parametric

Kruskal-Wallis test = non-parametric

Question 19

How can we compare binary outcome data?

Answer 19

Comparison of two proportions

Question 20

What are the requirements for a comparison of two proportions?

Answer 20

Only makes sense in 2x2 tables e.g. yes or no outcome
Two independent samples or groups
Large sample with all expected frequences >5
- np and n(1-p) should both exceed 5
- n = total number of individuals in both samples
- p = proportion of individuals with condition
Assumes a common proportion

Question 21

How is the common proportion calculated in a comparison of two proportions?

Answer 21

p=(n1p1 + n2p2)/(n1+n2)
n = sample size
p = proportion with condition

Question 22

How is the standard error for the difference in proportions calculated, where a common proportion is assumed?

Answer 22

SE(p1-p2) = √p(1-p)(1/n1+1/n2)

Where p is the common proportion calculated

Question 23

How is the test statistic (z) calculated in the comparison of two proportions

Answer 23

z=(p1-p2)(-0)/SE(p1-p2)

Question 24

How is the 95% confidence interval for the difference in proportions calculated?

Answer 24

(p1-p2)+/- [1.96xSE(p1-p2)]

Question 25

How is standard error of the difference in proportions calculated if no common proportion is assumed?

Answer 25

SE(p1-p2) = √(p1(1-p1))/n1 + (p2(1-p2))/n2

Question 26

What test is used when comparing unordered, categorical data?

Answer 26

Chi-squared test (χ^2)

Question 27

What are the requirements for chi-squared test?

Answer 27

Two independent groups
Unordered, categorical variables
At least 80% expected cell counts ≥5
All expected cell counts ≥1
Expected values calculated by total proportion healed used to predict proportion healed for each variable

Question 28

Steps for chi-squared test

Answer 28

1. Expected frequency = row totalxcolumn total/N where N is total sample size
2. Calculate difference between observed and expected value for each cell
3. Square each difference
4. Divide resultant quantity by expected value
5. Sum all of these to get a single number test statistic
6. Compare with table of chi-squared distribution

Question 29

How is the degrees of freedom calculated in the chi-squared test?

Answer 29

(no. rows -1)x(no. columns -1)

Question 30

What correction can be used on 2x2 tables to allow chi-squared calculations

Answer 30

Yates correction

Chi-squared = SUM ((|O-E|-0.5)^2)/E

Question 31

What test is done on 2x2 table when expected cell counts <5, or any cell count <1

Answer 31

Fisher’s exact test

Estimates probability of falsely rejecting the null hypothesis exactly

Question 32

When is the chi-squared test for trend used?

Answer 32

In a 2x3+ table

When the variable with 3+ categories is ordered

Question 33

How can risk be compared in a 2x2 table?

Answer 33

Relative risk
(a/a+c)/(b/b+d)
Under the null hypothesis, the expected value is 1

Odds ratio
ad/bc
Expected value is 1 under null hypothesis

Question 34

How is the standard error of the natural logarithm of RR calculated?

Answer 34

SE(logeRR) = √(1/a)-(1/a+c)+(1/b)-(1/b+d)

Question 35

How is the 95% CI for logeRR calculated?

Answer 35

logeRR +/- 1.96xSE(logeRR)

This can then be converted using the function of e

Question 36

How is the standard error of the natural logarithm of OR calculated?

Answer 36

√(1/a)+(1/b)+(1/c)+(1/d)

Question 37

How is the 95% CI for logeOR calculated?

Answer 37

logeOR +/- 1.96xSE(logeOR)

Converted using e function

Question 38

How is categorial data with paired outcomes compared?

Answer 38

McNemar’s test

e.g. patients treated with two different treatments + outcomes compared

Question 39

How is McNemar’s test calculated?

Answer 39

(|b-c|-1)^2/b+c