Data Analysis

Question 1

Why should you graph original data and not averages?

Answer 1

You can see for yourself where’s it the average is
You can see for yourself what the spread looks like
You can see if there is anything odd/interestiing about the data eg outliers, evidence of skewing etc

Question 2

How can you find true confiemdence intervals?

Answer 2

Using a T test

Question 3

Why do many sets of experimental observations for approximately to a normal distribution?

Answer 3

The mathematical explanation is the central limit therom
Why/what data may result in a normal distribution
If a variable is affected by a lot of different random factors
Each has a small effect
The effects are additive
The distribution will approximate to a normal distribution

Question 4

Sd

Answer 4

A statistical tool that tells you how tightly (close together) all the variations examples are clustered around the mean in a set of data
It is a more sophisticated indicator of the precision of a set of given measurements

Question 5

What does it mean if effect size is not large enough compared to variation?

Answer 5

It means that random variations in readings might account for the difference between treated and controlled

Question 6

What do statistical tests such as T tests do?

Answer 6

They ask how does variation compare with effect size

Question 7

Why should error bars be treated as a rough indication?

Answer 7

With low density samples, they underestimate the uncertainty

Error bars are not additive

All statistics only give a rough indication of confidence

Question 8

Why is it wrong to think that if error bars don’t overlap the result is significant and Vice Versa

Answer 8

Biological significance is best shown by effect size, not by statistical significance

The idea that error bars just touching is equivalent to p=0.05 does not apply to small sample numbers

Idea is just silly

Question 9

Confidence intervals

Answer 9

These get round the problem that SEM error bars are not additive.

By using a t test, we can get the best estimate, even when we have a small number of observations

The T test can calculate the 95% C.I for the difference between the means

Question 10

What is 95% C.I

Answer 10

C.I interval gives us an idea of how much larger or smaller and tells us that 95% of time the real answer should be within a his interval.

Question 11

What does a small p value <0.05 mean?

Answer 11

It indicates strong evidence against the null hypothesis, so you reject null hypothesis. This means that the probablity of the data due to only chance/random variation is less than 5%

Question 12

What does a large p value >0.05 indicate ?

Answer 12

It indicates weak evidence against the null hypothesis so you fail to reject the null hypothesis

Question 13

Advantages and disadvantages of confidence intervals

Answer 13

Adv;
-combine numerical information in effect size, statistical confidence and possible variation in the ‘real’ effect size
-ideal for simple comparisons such as treated vs control
-now the preferred approach in clinical research and epidemiology
Diaadv:
Harder to apply to more complex experiments, eg more than one control, more than one treatment

Question 14

How can the effect size be compared with the variation? For statistical reliability

Answer 14

a) by eye from the raw data
b) using sem error bars
c) more precisely using a 95% confidence interval

CI is more precise than error bars and more informative than a p value

Question 15

For sample sizes above 20 how do we treat the confidence intervals

Answer 15

We treat them as weak to moderate as long as the error bars don’t overlap

Question 16

Sem small compared to effect size

Answer 16

The real answer may be a little larger or smaller than our estimate, but not much

Strong statistical confidence

Question 17

Sems are moderate compared to effect size

Answer 17

The real answer may be quite a bit larger or smaller than our Estimate, but it is unlikely to be zero

Moderate statistical confidence

If sample size over 20, then double the larger error bar and it doesn’t overlap with the other one

Question 18

Sems are substantial compared to effect size

Answer 18

The real answer may be quite a lot larger or smaller than our own estimate. It could even be negative or zero

Weak statistical confidence

The error bars close but not overlapping

Question 19

Sems are large compared to effect size

Answer 19

The real answer may be a lot larger or smaller than our estimate. It could even be zero or negative

Weak to very weak statistical confidence

Error bars overlapping

Question 20

What do significance tests do?

Answer 20

They mathematically compare the variation with the effect size. They calculate a number called the p value. This is the probability of checking whether effect size is due to random variation or not

Question 21

P value strength 
P-0.001
P-0.01 
P-0.05
P>0.05

Answer 21

P-0.001 statistically very strong data
P-0.01 moderately strong data
P-0.05 statistically weak data
P>0.05 weak to very weak data

Question 22

Type 1 error vs type 2 error

Answer 22

Type 1 error is rejecting the null hypothesis, stating that the effect is significant when in fact there is no real effect

Type 2 error is accepting H0 and declaring that a result is not statistically significant, when in fact there is a real effect.

Question 23

Give 3 reasons why null hypothesis significance testing has proved extremely popular. For each reason, explain why this may cause problems with the correct interpretations of the data

Answer 23

People don’t like uncertainty and nhst appears to give a definite answer. This can lead to type 1 and type 2 errors because it is often the wrong answer

People don’t like making decisions so nhst let’s computer make decision. The problem is you should make the decision based on all the evidence

Ambitious-nhst allows you to publish more papers even if some conclusions are actually wrong

Often lazy- tells you a result is significant which implies that you don’t need to do more experiments, problem can arise when there is only weak evidence

Question 24

When do we use a students T test

Answer 24

When we are studying the difference between two groups of observations

• > measurements on treated and control samples
• > measurements on patients and normal controls

It is designed for cases where you have small numbers and observations
And you cannot tell the actual distribution of the data. It assumes a normal distribution

It compares effect size with variation and uses this to calculate a 95% confidence interval and a p value for null hypothesis

A one tailed T test gives a smaller value.

Question 25

When do you use a paired t test

Answer 25

By looking st before and after results in single individuals, we can ignore the variation between the individuals and study the effect and the variability of the effect itself s
Paired data can be analysed by a paired t test

Question 26

Why are non parametric tests not always useful

Answer 26

Non parametric tests don’t work well with small numbers of observations. They do not provide a 95% CI

Question 27

How to draw a confidence interval

Answer 27

Draw x axis with appropriate scale
Draw a line at effect size to represent the mean
The CI is saying that our mean could be as small or big as []
Draw lines at these points
Then join the lines together

Question 28

When is linear regression used

Answer 28

Linear regression is used when one variable is precisely fixed in advance eg time, dose etc

Correlation is used when both variables are measurements which may have random errors or random variation

Question 29

How many litres in one decilitre

Answer 29

0.1L in 1 dl

Question 30

What can you do to reduce probability of making type 1 error

Answer 30

Reduce significance level from 0.05 to 0.01