Interpreting Evidence

Question 1

Identify different kinds of variability. Give examples for each category.

Answer 1

Between people

e. g differential effectiveness of treatment
e. g. Do or do not develop particular side-effect
e. g. differential response to environment

Within people

e. g. measures of blood pressure over a day
e. g. strength of left and right hands

Question 2

What is the null hypothesis and the alternative/research hypothesis in the following scenario:

• In a small study we enrol 200 Patients with anaemia and persistent gastrointestinal bleeding.
• Half are given oral iron supplementation and half given intravenous iron supplementation
• End of the study we measure the haemoglobin concentrations of the 200 patients.
• We want to compare the mean haemoglobin levels in patients given each of the alternative treatments

Answer 2

Null hypothesis (Ho )
• there is no difference in haemoglobin levels between patients receiving oral compared with intravenous iron supplementation

Alternative hypothesis H1 (Research Hypothesis)
• there IS a difference in haemoglobin levels between patients in the two treatment groups

Question 3

What is a confidence interval ?

Answer 3

Confidence interval is a range of values we are 95% confident includes the ‘true’ mean of our population of interest.
In other words, if we repeat the study 100 times and calculate a 95% CI each time, we would expect 95 of these intervals to contain the ‘true’ population mean.

Question 4

Interpret the following data:

Oral iron supplementation mean = 11.6 g/dl CI (10.7 to 12.4 g/dl)

Intravenous iron supplementation mean = 14.1 g/dl CI (12.8 to 15.5 g/dl)

Answer 4

95% confidence intervals around the two means do not overlap

The mean haemoglobin level under intravenous supplementation is significantly higher than with intravenous supplementation.

Question 5

Interpret the following data:

Randomised trial of aspirin versus control in secondary prevention after TIA or ischaemic stroke. Odds of a fatal stroke in aspirin group compared with those in the control group

Refer so graph on slide 16.

Answer 5

Aspirin within the first six weeks significantly reduces the odds of a secondary fatal stroke.

Aspirin 6-12 weeks after TIA: No evidence that this treatment significantly lowers the odds of a subsequent fatal stroke

Question 6

Identify different comparisons which may be made as part of a statistical test ?

Answer 6

• Comparing our results with a gold standard

* Comparing one sample with another after an intervention

Question 7

What question is answered in statistical tests for comparing groups ?

Answer 7

When is a difference STATISTICALLY SIGNIFICANT?
• i.e When do we reject the Null hypothesis?

(ideally want a simple yes or no answer)

Question 8

Identify factors which will affect the type of statistical test used to determine whether a difference is statistically different.

Answer 8

Type of data (categorical or continuous, ordinal etc.)

Distribution of outcome (normal vs non normal)

Question 9

Identify examples of statistical tests.

Answer 9

T-Test-

Analysis of variance (extension of T-test)

Chi-square test-

Question 10

Identify the types of variables used in a T-test.

Answer 10

• 1 dependent continuous variable (e.g height)

* 1 independent binary categorical variable (e.g. sex)

Question 11

Identify the types of variables used in a Chi-square-test.

Answer 11

• 1 dependent categorical variable (e.g. alternative drug types)
• 1 independent categorical variable (e.g. Deprivation category)

Question 12

What is the aim of a T-Test ?

Answer 12

T-Test- used to determine whether two means are significantly different from each other (gives probability (p-value) that such a difference in means (or a greater difference) would be found by chance, IF THE NULL HYPOTHESIS IS TRUE)

Question 13

What is the aim of a Chi-Square-Test ?

Answer 13

Chi-square-test allows us to statistically determine if the difference between the observed and expected numbers in each cell is significant (GIVEN THE SAMPLE SIZE).

• A difference implies a ‘relationship’ or ‘association’
i.e values of one variable may influence values of the other

Question 14

Identify the main kinds of T-tests. How are these different kinds of test interpreted ?

Answer 14

• One sample t-test: Comparison of mean with a single value (e.g. mean BP in sample vs
literature standard value)
• Independant samples t-test: Comparison of means of independent samples (mean effect of statin 1 vs statin 2)
• Paired t-test: Comparison of means of paired data ( BP before and after treatment measured in the same people)

• All interpreted in the same way. Report the t-statistic, degrees of freedom (df) and the associated probability (p-value).

Question 15

Define one sample t-test.

Give an example of sample t-test.

Answer 15

Comparison of a single mean with hypothesized value

• From previous large studies of women drawn at random from the healthy general public, a resting systolic blood pressure of 120 mm Hg was predicted as the population mean for the relevant age group
• In a sample of 20 women from your clinic, mean systolic BP was measured as 130.05 sd= 16.4
• Null Hypothesis: the systolic BP of women in my clinic is not significantly different from that found in the literature (120 mm Hg)

Question 16

What is the formula for the t value of a one sample t-test ?

Answer 16

t= (sample mean - hypothesized mean) / (Sample error of sample mean)

Question 17

Define p-value.

Answer 17

Probability that the observed difference (between systolic BP in my clinic compared with the previous literature) occurred by chance alone….if the Null Hypothesis is true.

• When p-value for a test statistic is below 0.05, we ‘reject’ the Null Hypothesis (i.e reject the hypothesis that there is no difference between my sample and findings in the literature), accept alternative hypothesis that there IS a difference.

Question 18

Define independent samples t-test.

Give an example of sample t-test.

Answer 18

“(AKA two sample t-test) determines whether there is a statistically significant difference between the means in two unrelated groups”

Do two alternative statins have different effects on serum cholesterol levels?

1. NULL HYPOTHESIS
   • Ho : There is no difference in mean serum cholesterol levels between the groups treated with statin1 and statin2
   • Essentially saying the two samples have been drawn from the same underlying population, and just differ by chance alone

Question 19

What is the formula for the t value of independent samples t-test ?

Answer 19

t = difference in sample means (i.e. mean 1 - mean 2) / SE of difference in sample means

Question 20

State the interpretation for the following:

Research Question
Do two alternative statins have different effects on serum cholesterol levels?

Reporting : t209= 3.24 p=0.0013

Answer 20

One statin lowers serum cholesterol levels significantly more than the other (since p value lower than 0.05)

Question 21

What is the aim of ANOVA ?

Answer 21

T-test can only deal with 2 means, whereas ANOVA (extension of t-test) can deal with more than 2 means

Question 22

Identify the main kinds of ANOVA tests, giving an example for each.

Answer 22

• One-way ANOVA: “A one-way ANOVA compares three or more than three categorical groups to establish whether there is a difference between them (e.g. The null hypothesis (H0) is that there is no difference between the groups and equality between means. (Walruses weigh the same in different months)”
- Results: F-test and p-value

• Two-way ANOVA: Two independent variables and one outcome. Therefore have three sets of null hypotheses.
(e.g. H0: The means of all month groups are equal, H0: The means of the gender groups are equal, H0: There is no interaction between the month and gender)

Question 23

What is one limiting factor of T-test and ANOVA test ?

Answer 23

Both have an underlying assumption that in the population the outcome has a normal distribution

Question 24

Which tests should you used when:

1. May not know the distribution
2. May know the distribution is not Normal
3. May have a small sample, which is unlikely to have a normal distribution
4. Using ordinal scales not continuous data
5. Have outliers and therefore not Normal

Answer 24

Use non-parametric statistical alternatives (rank the data, and see whether ranks of one group tend to be on average higher than those of the other groups)

Question 25

State the null, and alternative hypotheses for the following:
• Is there a significant difference (higher or lower) in cholesterol status between men and women in our study?

Which statistical test should be used ?

Answer 25

Null hypothesis (Ho )
• there is no difference in proportion of men and women with high cholesterol
Alternative hypothesis H1
• there IS a difference between males and females with respect to cholesterol status

Chi-square test (because two categorical variables)

Question 26

Describe the formula for Chi Square Test.

Answer 26

square of the difference between the observed (o) and expected (e) values and divide it by the expected value.

Question 27

Identify the main possible aims of Chi-square tests.

Answer 27

Chi-Square-Test for independence:
• association between two categorical variables (e.g: Is cholesterol status associated with gender?) *

Chi-square test for goodness of fit:
• Tests the difference between frequencies of a single categorical variable and some hypothesised frequency (e.g. is the frequency of depression sufferers in our sample the same as the proportion quoted in the literature?)

Question 28

Explain the problem with conducting different tests (e.g. in a sample of 100 men, including 50 smokers and 50 non-smokers, test difference in height, lung capacity, reaction time, marital status… using the 5% significance level each time). What is the solution ?

Answer 28

• Each time we test a difference we use the 5% level of significance
i.e 5% of the time would you expect to see that big a difference by chance alone if the Null Hypothesis is in fact TRUE

• If we do many tests, we increase our chance of a false positive (i.e. rejecting the true Null hypothesis)
• At 5% level of significance could expect ~ one in every 20 tests to be a false positive

• SOLUTION –don’t use 5% significance for each test – be more strict (i.e use a more extreme p-value). Bonferroni correction:
-If do 5 tests then for each test only accept as significant tests with p-value< 0.05/5
-If do n tests then for each test only accept as significant tests with p-value< 0.05/n
This means that across all n test you have only 5% chance of false positive

Question 29

Define correlation. How is it measured ?

Answer 29

Measures the strength of relationship between two numerical variables.

• Measured by the correlation coefficient (r) (a significant correlation coefficient is indicative by a p-value in statistical packages)

Question 30

What are possible values for the correlation coefficient ?

Answer 30

• The correlation coefficient varies between -1 and +1
r=-1 a perfect negative correlation (as one variable increases the other decreases)
r=+1, a perfect positive correlation (as one variable increases so does the other)

Question 31

What type of data must be used for basic correlation ?

Answer 31

Continuous data

Question 32

How is p-value relevant to correlation ?

Answer 32

“The P-value is the probability that you would have found the current result if the correlation coefficient were in fact zero (null hypothesis). If this probability is lower than the conventional 5% (P<0.05) the correlation coefficient is called statistically significant”

Question 33

What is the aim of a linear regression ? What is the requirement to be able to use this ?

Answer 33

Used to predict relationship between independent variables and an outcome (dependent) variable. Want to predict the change in outcome associated with a particular change in the independent variable.

• Must be a linear relationship between independent and outcome

Question 34

How does linear regression predict change in outcome associated with change in independant variable ?

Answer 34

Estimate the regression coefficient (beta) which can be thought of as the slope of the best –fitting straight line through a scatter plot of the data

y= (beta)x + b

beta = slope of best fitting straight line (e.g. if 0.2 then for every unit increase in X, Y increases by 0.2)
e.g. For a 1 unit increase in sleep quality there is an increase in average blood glucose level of 0.32.
b = intercept

Question 35

How is p-value relevant to linear regression ?

Answer 35

P-value for regression coefficient indicates probability that the ‘true’ slope of the line is = 0 (i.e Null hypothesis is NO SLOPE).

Significant p-value (p<0.05) indicates that there is a significant slope (i.e b not equal to 0)