Stats

Question 1

A characteristic of an individual measured or recorded in a study. What is this describing

Answer 1

A variable

Question 2

What is the difference between qualitative and quantitative variables

Answer 2

1. Categorical (or qualitative) variables which arise when an individual falls into a category. These can be subdivided into:
   (a) Nominal categorical variables - which have no ordering e.g. sex (male\ female), blood group (A\B\AB\O)
   (b) Ordinal categorical variables - which have an ordering e.g pain (mild \ moderate \ serve); breast cancer stage (1,2,3,4).
2. Quantitative (or interval scale) variables which arise when a response is measured on a scale e.g. height (in cm), temperature (in oC), blood pressure (in mmHg).

Question 3

Which one of the following variables is nominal categorical:
a) Number of episodes of disease
in a patient over a year.
b) Serum bilirubin level.
c) Blood group (O/A/B/AB).
d) Severity of haemophilia ( mild/moderate/severe).
e) Reduction in blood pressure following antihypertensive treatment.

Answer 3

C

Question 4

What does a frequency distribution show

Answer 4

A frequency distribution shows the frequency (or count) of the occurrence of different values of a variable, and may be presented either as a table or as a graph (called a bar chart).

Question 5

What is relative frequency

Answer 5

relative frequency is presented which is the frequency expressed as a proportion (or percentage) of the total frequency.

Question 6

What is the mean and how is it calculated

Answer 6

(Average)

(i) The mean is the most widely used measure of location.
i. e. the sum of all the observations divided by the total number of observations.

Question 7

What is the median

Answer 7

The median is the middle value if a sample is arranged in increasing order

Question 8

What is the range

Answer 8

The range is the difference between the largest and smallest observations in the sample

Question 9

What is the problem with using the range

Answer 9

severely affected by outlying observations

Question 10

What is the interquartile range

Answer 10

(ii) The interquartile range is the difference between the third and first quartiles.

Question 11

What is the variance

Answer 11

The variance (s2) is approximately the arithmetic mean of the squared deviations of the values from their mean

(Distance of each observation from the mean)

Question 12

The mean of a set of values:

a) Is a useful summary measure for a nominal categorical variable.
b) Coincides with the median if the distribution of the data is symmetrical.
c) Is always greater than the median.
d) Cannot be calculated if the data set contains both positive and negative values.
e) Is a useful summary measure of location if the data are skewed.

Answer 12

B

Question 13

What is standard deviation

Answer 13

(iv) The standard deviation is the square root of the variance. It has an advantage of being in the original scale of measurement, and is therefore used in preference to the variance.

Question 14

What is the coefficient of variation

Answer 14

This provides a measure of variation which is independent of the unit of measurement and hence can be used to compare the variation of variables measured on different scales.

Question 15

The median:

a) Is a useful measure of the spread of the data.
b) Is a useful summary measure when the data are skewed.
c) Is always less than the mean when the data are skewed.
d) Can be distorted by outliers.
e) Is equal to the 66th percentile

Answer 15

B

Question 16

What’s the significance of the mean and standard deviation in a normal distribution

Answer 16

The mean determines how far right or left the distribution sits on the x-axis. The standard deviation determines the width of the distribution; the larger the standard deviation the wider and shorter the distribution.

Question 17

What does the z value represent in normal distribution

Answer 17

Occasionally values of a variable are converted to Z-scores. This is equivalent to counting the number of standard deviations above or below the mean a value is

Question 18

What is the definition if probability

Answer 18

Using the relative frequency definition, the probability of an event of interest occurring in an experiment is the proportion of times the event of interest occurs (its relative frequency) when the experiment is repeated a large number of times.

Question 19

Which one of the following variables is nominal categorical:

a) Number of episodes of disease in a patient over a year.
b) Serum bilirubin level.
c) Blood group (O/A/B/AB).
d) Severity of haemophilia (mild/moderate/severe).
e) Reduction in blood pressure following antihypertensive treatment.

Answer 19

C

Question 20

Which one of the following variables is ordinal categorical:

a) Number of episodes of disease in a patient over a year
b) Serum bilirubin level
c) Blood group (O/A/B/AB)
d) Severity of haemophilia (mild/moderate/severe)
e) Reduction in blood pressure following antihypertensive treatment

Answer 20

d

Question 21

Which one of the following variables is interval scale:

a) Height in cm.
b) Ethnic group.
c) Social class (I/II/III-N/III-M/IV/V).
d) Age categorised as young, middle-aged or old.
e) Blood group.

Answer 21

a

Question 22

Which one of the following statements is true:

a) A nominal variable has categories that can be ordered in some way.
b) Quantitative data arises when an individual falls into categories.
c) Categorical and quantitative data are presented in exactly the same way.
d) A categorical variable can be either nominal or ordinal.
e) Nominal data are usually measurements made on a scale.

Answer 22

d

Question 23

A histogram:

a) Can be used to display any type of variable.
b) Is the same as a bar chart but there are larger gaps between the bars.
c) Contains bars, with the height of each bar being proportional to the frequency of the observations in the range specified by the bar.
d) Can be used instead of a pie chart to display categorical data.
e) Is used to show the relationship between two variables.

Answer 23

c

Question 24

A bar chart:

a) Is used to display categorical data.
b) Should be drawn without gaps between the bars.
c) Can only be used to display data which have a symmetrical distribution.
d) Can be used to display any type of variable.
e) Is used to show the relationship between two variables.

Answer 24

a

Question 25

The mean of a set of values:

a) Is a useful summary measure for a nominal categorical variable.
b) Coincides with the median if the distribution of the data is symmetrical.
c) Is always greater than the median.
d) Cannot be calculated if the data set contains both positive and negative values.
e) Is a useful summary measure of location if the data are skewed.

Answer 25

b

Question 26

The median:

a) Is a useful measure of the spread of the data.
b) Is a useful summary measure when the data are skewed.
c) Is always less than the mean when the data are skewed.
d) Can be distorted by outliers.
e) Is equal to the 66th percentile

Answer 26

b

Question 27

Which one of the following statements is true. The standard deviation:

a) Is a measure of location.
b) Has the same units of measurement as the raw data.
c) Is a measure of spread which is equal to the range.
d) Is unaffected by outliers.
e) Is an appropriate measure of spread for skewed data.

Answer 27

b

Question 28

What is a ‘population’

Answer 28

A population is any collection of individuals (or measurements made on those individuals) in which we are interested.

Question 29

What is the population distribution

Answer 29

The frequency distribution of a variable in the population is referred to as the population distribution

Question 30

What are population parameters

Answer 30

Summary values (e.g. means, proportions) calculated in populations are referred to as population parameters

Question 31

What is a sample

Answer 31

A sample is any subset of a population and is ideally selected to be representative of the population

Question 32

What makes a sample random

Answer 32

A random sample is one chosen in such a way that each member of the population has the same chance of selection.

Question 33

What are sample statistics and what are they used for

Answer 33

Summary values calculated in samples (e.g. means and proportions)

These sample statistics are used to estimate population parameters.

Question 34

Describe accuracy

Answer 34

Absence of bias

Question 35

Describe precision

Answer 35

Repeatability from one sample to the next

Question 36

What is the sampling distribution of a statistic

Answer 36

The sampling distribution of a statistic is the frequency distribution of that statistic over all possible samples of a given size selected from the population

Question 37

What is the standard error and what is it used for

Answer 37

The standard deviation of the sampling distribution of a statistic is referred to as its standard error and is used to calculate confidence intervals.

Question 38

What is the definition of 95% confidence intervals

Answer 38

In 95% of repeated samples from the population confidence intervals calculated in this way will capture the population parameter

Question 39

The 95% confidence interval for a
proportion:
a) Cannot be calculated if the sample size is large.
b) Is the interval within which all sample proportions would lie if we were to take repeated samples of a given size from the population.
c) Is the interval within which we expect the population proportion to lie with 95% certainty .
d) Is wider than the 99% confidence interval for the proportion.
e) Is calculated as the sample proportion ± standard error of the proportion.

Answer 39

C

Question 40

Describe a null hypothesis and an alternative hypothesis

Answer 40

In a trial, the null hypothesis (H0) often that the true difference in mean/proportion on treatment or on placebo is 0.

An alternative hypothesis (H1) is also stated which usually just contradicts the null hypothesis

Question 41

What is the p-value

Answer 41

The P-value is: the probability of observing a test statistic (i.e. results) as, or more, extreme than that observed in your sample, in hypothetical repetitions of the study assuming that the null hypothesis is true

Question 42

How do we use the p value to accept/reject a null hypothesis

Answer 42

If P < 0.05, the test is “statistically significant” at the 5% level and the null hypothesis is rejected. Alternatively if P > 0.05, the test is not “statistically significant” at the 5% level there is insufficient evidence to reject the null hypothesis.

Question 43

Describe a type I error

Answer 43

A Type I error occurs if the null hypothesis is rejected when it is true. The probability of a Type I error, the rejection of a true null hypothesis, equals the significance level (and is therefore usually 5%).

If you reject the null hypothesis there is. Chance of type I error

Question 44

Describe a type II error

Answer 44

A Type II error occurs if the null hypothesis is not rejected when it is false

If you don’t reject the null hypothesis then chance of type II error

Question 45

When is a chi-squared test used

Answer 45

used to compare proportions between two independent groups

Question 46

What is the absolute risk reduction

Answer 46

The absolute risk reduction is the difference in risk between the two treatment groups

Question 47

What is the relative risk

Answer 47

The relative risk (RR) or risk ratio is the risk in the treatment divided by the placebo group

Question 48

The best approximation of a truly random sample of the general population would be obtained by:

a) Selecting an individual from every fourth house on a street.
b) Selecting every individual with a surname beginning with the letter ‘S’.
c) Allocating each individual from the electoral roll a unique number, putting these numbers in order and selecting every 20th individual from this list.
d) Allocating each individual from the electoral roll a unique number and using a computer to randomly generate numbers for selection.
e) Closing your eyes and sticking a pin into a telephone directory.

Answer 48

d

Question 49

The 95% confidence interval for a proportion:

a) Cannot be calculated if the sample size is large.
b) Is the interval within which all sample proportions would lie if we were to take repeated samples of a given size from the population.
c) Is the interval within which we expect the population proportion to lie with 95% certainty.
d) Is wider than the 99% confidence interval for the proportion.
e) Is calculated as the sample proportion ± standard error of the proportion.

Answer 49

c

Question 50

The mean BMI of a random sample of 5926 US men was found to be 28.7, with 95% confidence interval (28.3, 29.1). The confidence interval is interpreted to mean that:

a) 95% of US men have a BMI between 28.3 and 29.1.
b) We are 95% certain that a US man has BMI between 28.3 and 29.1.
c) If we were to take a different sample of 5926 US men, the mean BMI of this new sample would lie within 28.3 and 29.1 with 95% certainty.
d) There is a 95% chance that the mean BMI score in the population of US men is greater than 29.1.
e) There is a 95% chance that the mean BMI in the population of US men lies within the calculated confidence interval.

Answer 50

e

Question 51

In a prospective study of post-traumatic stress disorder in children involved in road traffic accidents, post-traumatic stress was found in 41/119 children (35%, 95% CI 26% to 44%). Select all of the following statements which you believe to be true:

a) In the population of children involved in road traffic accidents, the true rate of post-traumatic stress is greater than 35%.
b) In this sample, the rate of post-traumatic stress could take any value between 26% and 44%.
c) In 95% of random samples, confidence intervals calculated in this way would capture the proportion with post-traumatic stress of the population of children involved in road traffic accidents.
d) The authors would have obtained a more precise estimate of the proportion of children with post-traumatic stress if they had included fewer children.
e) If an earlier study into the same issue had reported that the rate of post-traumatic stress in children after road traffic accidents was only 27%, we could conclude that the rate of post-traumatic stress was increasing.

Answer 51

c

Question 52

In the same prospective study of post-traumatic stress disorder in children the authors decided to calculate a 99% confidence interval. Bearing in mind the original estimate was 35% (95% CI 26% to 44%), without doing calculations, which of the following is the 99% confidence interval:

a) 0% to 44%.
b) 26% to 44%.
c) 28% to 42%.
d) 0% to 99%.
e) 24% to 46%.

Answer 52

e

Question 53

In a study to evaluate the importance of different factors on the development of cirrhosis among hepatitis C virus positive individuals (Verbaan H et al. J Vir Hep 1998; 5: 43-51), 35/79 of those without cirrhosis reported alcohol abuse compared to 10/20 of the individuals with cirrhosis (P=0.84).

We could use the unpaired t-test to analyse these data.

b) The appropriate null hypothesis is that the same number of individuals in the populations with and without cirrhosis report alcohol abuse.
c) The appropriate null hypothesis is that the same proportion of individuals in the populations with and without cirrhosis report alcohol abuse.
d) An appropriate null hypothesis is that the same mean alcohol abuse is the same in individuals number of individuals in the populations with and without cirrhosis report alcohol abuse.
e) The appropriate null hypothesis is that the same proportion of individuals in the samples with and without cirrhosis report alcohol abuse.

Answer 53

C

Question 54

(Q 2 study: In a study to evaluate the importance of different factors on the development of cirrhosis among hepatitis C virus positive individuals (Verbaan H et al. J Vir Hep 1998; 5: 43-51), 35/79 of those without cirrhosis reported alcohol abuse compared to 10/20 of the individuals with cirrhosis (P=0.84)) In the study in question 2 the P-value of 0.84 indicates that:

a) There is evidence of a difference in the true rates of alcohol abuse in the two groups.
d) The rates of alcohol abuse in the cirrhosis group is 0.84 times that of the non-cirrhosis group.
c) There is an 84% probability the rates are different.
d) The rates of alcohol abuse in the non-cirrhosis group is 0.84 times that of the cirrhosis group.
e) There is no evidence of a difference in the true rates of alcohol abuse in the two groups.

Answer 54

E

Question 55

When is McNemar’s test used

Answer 55

McNemar’s test is used to compare an outcome with two categories between two paired groups

Question 56

When is an independent samples t-test used

Answer 56

An independent samples t-test is used to test whether the mean of an interval scale variable in one group is equal to the mean in another group when the two groups are independent.

Question 57

What would the null hypothesis and alternative hypothesis be in an independent samples t-test

Answer 57

The Null hypothesis (H0) is that the population or true mean in group 1 equals the
population or true mean in group 2 (μ1 = μ2).
The Alternative hypothesis (H1) is that the population or true mean in group 1 does not equal the population or true mean in group 2 (μ1 ≠ μ2).

Question 58

What are the two assumptions made if a sample size is small (<30) in an independent samples t-test

Answer 58

1) Normally distributed outcome in both groups,

2) standard deviation of outcome similar in groups.

Question 59

A Chi-squared for a 2x2 table is used:

a) To compare an interval scale variable between two groups.
b) To compare two proportions between two independent groups.
c) To compare an interval scale variable between two groups provided that the variable is normally distributed.
d) To compare two proportions between two paired groups.
e) To compare any outcome between two independent groups.

Answer 59

b

Question 60

In an observational study of defibrillation in theatre, 23 surgeons and 25 anaesthetists were asked to manage simulated ventricular fibrillation. The percentage successful managing to defibrillate according to advanced life support protocols was 28% (7/25) of the surgeons and 4% (1/23) of the anaesthetists (P=0.06).

a) This lack of significance could be due to a Type 1 error.
b) The chance of a Type 2 error increases as the sample size increases.
c) A larger sample size would have reduced the risk of Type 1 error.
d) If this study was repeated and a difference of 24% (28%-4%) was observed again, this difference would not be significant, regardless of the size of the study.
e) This lack of significance could be due to a Type 2 error.

Answer 60

e

Question 61

Q3.5) In a study of critical ill patients with severe acute kidney injury, patients were randomly allocated to early initiation of renal replacement therapy (RRT) or delayed initiation of RRT. The proportion dead at 90 days was 39% (44/112) in the early group and 55% (65/119) in the delayed group (P=0.02).

a) There is a 2% chance of no difference between the two groups.
b) In hypothetical repetitions of the study assuming the null hypothesis is true, there is a 2% chance of observing a difference in proportions as extreme or more extreme than that observed in our samples.
c) We accept the null hypothesis.
d) There is a 2% chance the difference is real.
e) There is no evidence of a difference in the true rates of death in the two groups.

Answer 61

b

Question 62

In the study in Q5.
(Q5: In a study of critical ill patients with severe acute kidney injury, patients were randomly allocated to early initiation of renal replacement therapy (RRT) or delayed initiation of RRT. The proportion dead at 90 days was 39% (44/112) in the early group and 55% (65/119) in the delayed group (P=0.02).)
a) There is the possibility of a type 2 error.
b) The relative risk in the early group compared with the delayed group = 0.39 - 0.55 = 0.16.
c) The relative risk is 0.02
d) The relative risk in the early group compared with the delayed group = 0.39/0.55 = 0.72.
e) A type 1 error has occurred.

Answer 62

d

Question 63

The P-value is:

a) The probability that the null hypothesis is true.
b) The probability that the alternative hypothesis is true.

c) The probability of obtaining the observed or more extreme
results if the alternative hypothesis is true.

d) The probability of obtaining the observed results or results which are more extreme if the null hypothesis is true.
e) Always less than 0.05.

Answer 63

D

Question 64

A study is conducted to investigate a new ingestible and inflatable balloon system as a noninvasive way to fill up the stomach and curb appetite. Sixty clinically obese men (selected from the population of obese men) are randomly allocated to the intervention (i.e. the balloon) or a placebo. After 6 months, BMI is measured in the two groups. Which of the following is an appropriate null hypothesis for the study:

a) At the end of the 6 month period, the difference in BMI in the placebo and obese group is not statistically significant.
b) At the end of the 6 month period, the mean BMI on placebo is equal to that on the intervention in the population of obese men.
c) At the end of the 6 month period, the mean BMI on placebo is less than that on the intervention in the population of obese men.
d) At the end of the 6 month period, BMI in the placebo group and obese group is identical.
e) At the end of the 6 month period, the difference in BMI in the placebo and obese group is statistically significant.

Answer 64

B

Question 65

In a study, CD4 counts were measured in 48 HIV positive mothers who gave birth to children without HIV (mean=728, SD=274) and 11 HIV positive mothers whose children were HIV infected (mean=465, SD=271, P=0.006).

a) A paired t-test was performed on these data as the two groups were dependent.
b) The results are significant at the 5% level suggesting that the null hypothesis cannot be rejected.
c) There is the possibility of Type 2 error.
d) The null hypothesis can be rejected, there is evidence of lower CD4 counts in mothers who transmitted HIV to their children.
e) CD4 counts in these women are Normally distributed.

Answer 65

D

Question 66

When is a paired samples t-test used

Answer 66

To compare interval scale variable between two paired groups

Question 67

When is the analysis of variance used

Answer 67

To compare interval scale variable between three or more independent groups

Question 68

When is the Mann-Whitney U test used

Answer 68

To compare interval scale variable between two independent groups

Question 69

The Mann-Whitney U test:

a) Assumes that the outcome variable in each of the two groups are Normally distributed.
b) Can only be used when numbers are small.
c) Is appropriate when we wish to compare the distributions of an ordinal variable in two paired groups of individuals.
d) Is equivalent to the Chi-squared test.
e) Makes no assumption about the shape of the distribution of the outcome variable.

Answer 69

e

Question 70

In a study to evaluate the efficacy of the Attempted Suicide Short Intervention Program (ASSIP) 60 patients who had recently attempted suicide were randomly allocated to ASSIP or usual care. Over the two year follow-up period, the numbers of days in hospital, which was heavily skewed, was recorded in the ASSIP (n=29, median 29 days) and usual care group (n=31, median 102, Mann-Whitney U test P = 0.04)

a) An appropriate null hypothesis is that there is no difference in the median number of days in hospital on ASSIP or usual care in the population who had recently attempted suicide.
b) The Mann-Whitney U test is an alternative test to the paired samples t-test.
c) A Mann-Whitney U test was appropriate because the number of patients in each group was not the same.
d) An independent samples t-test could have been used to test these data.
e) An appropriate null hypothesis is that there is no difference in the mean number of days in hospital on ASSIP or usual care in the in the population who had recently attempted suicide.

Answer 70

a

Question 71

what is survival analysis

Answer 71

Survival analysis is the name given to a collection of statistical procedures for analysing data for which the outcome of interest is the time taken for some event to occur.

Question 72

what is a Kaplan-Meier or survival curve

Answer 72

A Kaplan-Meier or survival curve (shown on the right for a small sample of prostate cancer patients) is a diagram which plots the proportion of the population that have survived up until a certain time against time

Question 73

when is the log-rank test used

Answer 73

To compare time to event variable between two independent groups

Question 74

what are hazard ratios

Answer 74

the hazard can be considered as the rate of an event and the hazard ratio is the rate of the event in one group divided by the other and is calculated with 95% confidence intervals

Question 75

In a randomized controlled trial patients were randomly allocated to once only colorectal cancer screening with flexible sigmoidoscopy or a usual care group who received no screening. After a median of six years of follow-up, the hazard ratio for mortality from colorectal cancer, comparing intervention with control, was 0.73 (95% confidence interval 0.47 to 1.13).

a) The result is not statistically significant at the 5% level because a HR of 1 (indicative of no association) is captured by the 95% confidence interval.
b) A hazard ratio was calculated because the outcome was mortality.
c) The result is statistically significant at the 5% level because a HR of 0 (indicative of no association) is not captured by the 95% confidence interval.
d) The rate of death from colorectal cancer in the screened is 73% greater than in the usual care group.
e) A Type 1 error may have occurred.

Answer 75

a

Question 76

Survival analysis techniques are used:

a) Only when the outcome is mortality.
b) When the outcome is not Normally distributed but displays heavy negative skew.
c) When the outcome is a time taken for an event to occur.
d) When the sample sizes are small.
e) When the outcome is Normally distributed.

Answer 76

c

Question 77

A randomized controlled trial was conducted of tamoxifen versus usual care in healthy women at increased risk of breast cancer to investigate the effect on long term breast cancer risk. After 16 years of follow-up, 601 breast cancers were reported (251 [7%] in 3579 patients in the tamoxifen group versus 350 [10%] in 3575 women in the placebo group; hazard ratio 0.70 [95% CI 0.60–0.81], P<0.0001).

a) The result is not statistically significant at the 5% level.
b) The rate of breast cancer in the tamoxifen group is reduced by 70% compared with the control group (i.e. HR=0.7).
c) Survival analysis techniques should not have been used because breast cancer was the outcome.
d) The rate of breast cancer in the tamoxifen group is 0.70 times that of the control group (i.e. reduced by 30%).
e) A Type 2 error may have occurred.

Answer 77

d

Question 78

what is meant by the ‘number needed to treat’ and how is it calculated

Answer 78

The number need to treat is based upon the absolute risk reduction and gives the number of patients that would need to be treated to prevent one adverse outcome.
Number needed to treat = 1 / absolute risk reduction

Question 79

Which of the following statements is correct:

a) Randomisation is when patients are randomly selected from a patient population to participate in a trial.
b) The main advantage of randomisation is that it reduces the sample sizes required.
c) Randomisation is when patients are randomly allocated to an intervention or a control group.
d) Randomisation is always unethical.
e) In a randomised controlled trial patients are asked what treatment they would like to receive.

Answer 79

c

Question 80

The main advantage of randomisation is that:

a) The intervention and control group are exactly the same size.
b) There will be no loss to follow-up in the intervention and control group.
c) The intervention and control group will not know what treatment they are receiving and therefore this will not bias their responses.
d) The intervention and control group is likely to be similar with respect to known and unknown characteristics.
e) It saves time.

Answer 80

d