Interpreting data

Question 1

What are the main issues with sampling?

Answer 1

• Target population can be difficult to determine and is subjective
• Sample must be selected from the population at random (each member of the population must have the same chance of being included in the sample
• A reasonably high response rate is needed (study sample must be high proportion of selected sample = representitive of population of interest)

Question 2

What is sample data used to calculate?

Answer 2

1. Estimate of population value e.g. mean
2. Precision of estimate
3. Range of values can be confident true population value lies within
4. P value

= statistica inference - applied to study sample to provide information about the population

Question 3

Distribution of sample means:

Answer 3

• Approximately normally distributed if sample size <100
• Mean of the distribution of sample means = population mean

Question 4

What is accurate?

Answer 4

How close sample is to the true population value we are trying to estimate (cannot be assess without gold standard/repeated measurement to compare)

= centred on target

n.b. cannot be accurate if measuring the wrong people

Question 5

What is precision?

Answer 5

Amount of variation in the estimate of the population (increased variation = decreased precision)

= all close together

Question 6

What is standard error of the mean?
And how is it calculated?

Answer 6

= measurement of precision of sample mean as estimate of population mean

SE = SD / √sample size

Larger sample size = smaller SE = more precise

Question 7

What is standard deviation?

Answer 7

Measurement of the amount of variability in the population (how far an individual observation is likely to be from the population mean

n.b. population SD is usually unknown so we have to use sample SD

Question 8

What is not affected by the size of the sample?

Answer 8

Standard deviation

Standard error DOES as sample size increases, standard error decreases = more precise estimate of the sample mean

Question 9

What are confidence intervals for means?

Answer 9

For large samples 95% of individual sample means are within 1.96 X SE of the population mean = 95% of the population mean will be within 1.96 X SE if an observed sample mean

Or… if several independent random samples are drawn from a population and sample measn are calculated for each, the confidence intervals will include the true population of the mean on 95% of occasions

Question 10

How is a 95% confidence of 150.5 to 150.9 interpreted?

Answer 10

With 95% confidence, the mean height of 11 year olds in the general population is between 150.5 and 150.9 cm

Question 11

What is the difference between reference ranges and confidence intervals?

Answer 11

RR = clinical practice -> using SD to inform if a patient is clinically normal or not

CI - statistical inference in research -> using SE and used in research when statistical inference is required (indication of how precise an estimate the sample mean is of the populations mean)

Question 12

Which of the following statements is true?

1. Data which are positively skewed can be used to calculate confidence intervals for mean values
2. Standard deviations are used to calculate confidence intervals
3. Confidence intervals provide a measure of precision e.g. of a smaple mean

Answer 12

3. confidence intervals provide a measurement of precision e.g. of a sample mean
   n. b.

not 1. as data should be normally distrivuted otherwise mean could be misleading

not 2. standard errors are used

Question 13

How are different confidence intervals calculated?

Answer 13

Using different multipliers

95% = 1.96 X SE

99% = 2.58 X SE

90% = 1.64 X SE

these are based on standard normal distribution and obtained from statistical tables

Question 14

What is a P value?

Answer 14

Probability of a difference at least as big as that observed if null hypothesis is true (no real difference between exposure groups of the population)

NOT the probability that the null hyporthesis is true

Question 15

What does a smaller p-value show?

Answer 15

Stronger evidence against null hypothesis (lower chance of getting a difference as big as the on observed if the null hypothesis was true)

Question 16

How are P values calculated?

Answer 16

Test statisitc = summary statistic/ SE e.g. difference in means between two groups

Compared with appripriate statistical distribution to derive p value (computer package tables -> compare with standard normal distribution/ t distribution)

Question 17

What type of test is used to get p value for standard normal distributions?

Answer 17

z test

for large samples

Question 18

What type of test is used to get p values from a t distribution?

Answer 18

t- test for large/small samples

= comparisons between means

Question 19

What can we infer from a p value of <0.001 when the difference in means is 110g?

Answer 19

Probability of getting a difference of at least 110g (in either direction) if the null hypothesis is true is less than 0.1%

i.e. very strong evidence against the null hypothesis

Question 20

When do we use two sided p-values?

Answer 20

Because we are interested to see if the absolute difference is >0

= assessment of probability that result due to chance is based on how extreme the size of the departure from the null hypothesis is and not its direction!

Question 21

Whether or not to reject a null hypothesis should be based on confidence intervals and…?

Answer 21

The strength of evidence against the null hypothesis as assessed by the p value = most relaible way of interpreting findings

Question 22

What are the 4 common errors made in interpreting data?

Answer 22

1. Accepting a hypothesis if p value is large (should interpret it in terms of strength of evidence against the hypothesis)
2. Interpreting p<0.05 as statistically significant
3. Basing conclusions on p value only
4. Ignoring the contect (if sample split into many subgroups and seperately tested we should take that in to consideration when comparing t values)

Question 23

Why can we not ‘accept’ the null hypothesis?

Answer 23

To prove hypothesis -> have to find every person >90 and check non-smoker

To disprove hypothesis -> find just 1 person >90 who smokes

= much easier to find evidence against hypothesis than prove it correct (absence of evidence is not evidence of absence)

= p value of 1 can be obtained even when the null hypothesis of false -> cannot reject the null hypothesis

Question 24

Why is p<0.05 not statistically significant?

Answer 24

preferable to consider exact p value /strength of evidence

Cutpoint of 0.05 is arbitury -> commly used but 1 in 20 get p < 0.05 purely by chance

p value depends on sample size (harder to get p value <0.05 in small samples)

Question 25

How do we interpret p values?

Answer 25

0. 1 = weak evidence against the null hypothesis
1. 01 = increasing evidence against the null hypothesis
2. 001 strong evidence against the null hypothesis

Question 26

Why is it important to use both confidence intervals & p values?

Answer 26

Confidence interval = range of values within which we are reasonably confident the population difference lies

P values = strength of evidence against null hypothesis

STATISTICAL SIGNIFICANCE DOES NOT EQUATE TO CLINICAL IMPORTANCE -> even when p value shows strong evidence against the null hypothesis

Question 27

Why must you look at the context when applying many statistical tests using different subgroups within a sampls?

Answer 27

P values should be interpreted with caution (small p value for one test simply due to chance)