Statistics

School of Veterinary Medicine and Science


Statistics

• Statistics are like bikinis. What they reveal is suggestive, but what they conceal is vital. ~Aaron Levenstein


Nice statistics


CONFIDENCE INTERVALS


What is a confidence interval?

Confidence is generally described as a state of being certain either that a hypothesis or prediction is correct or that a chosen course of action is the best or most effective

And a confidence interval?How confident can you be that your answer

from your study is true of the whole population?


You only have a sample

• You can never measure the whole population

• Even if you sample the whole population you wont get information about all of it


From your sample…

• Something is being quantified:– A mean– An odds ratio– A disease frequency

And we get a single value = point estimate

• How close is the point estimate of your sample to the true value in the population?


Point estimate

• E.g. A mean

• You can then work out a standard error, which tells you about the precision of the estimate of the mean of the real population

• But an interval is easier than a standard error….


What is a confidence interval?

Confidence interval: Confident that the true population value of whatever we are measuring is within this range of values

……………………………….not entirely true!


The truth

If we are talking 95% confidence intervals• If we performed the study 100 times and

calculate a 95% confidence interval each time

• Then about 95 of the 100 confidence intervals calculated will include the true value of whatever we are interested in


How do you calculate a CI?

• Use nasty sums ……..Or a table ……..Or a computer


Calculate a confidence interval (mean)

1. Work out the mean2. Work out the standard error of the mean

(how precise a measurement is the sample mean of the population mean?)

3. The CI is some kind of multiple of the standard errors

E.g. 95% CI = ± 1.96 (SE) 99% CI = ± 2.58 (SE)


Why 95%?

• Convention• You can calculate anything you like but it

is normally 90%, 95% or 99% • NEVER 100% confident

100% confidence = arroganceArrogance: an attitude of superiority

manifested in an overbearing manner or in presumptuous claims or assumptions


So……

• To see how believable something is – you want a confidence interval

• Don’t just believe the point estimate of a sample is the true value in your population


Look for…

• The point estimate, the P value and the confidence interval – you want the actual numbers not ‘95% confidence’

E.g. Cases were 3 times more likely to be over the age of

15 rather than 5-10 years old, when compared to controls (OR = 2.87, 95% CI 1.38 – 5.99, p = 0.005).

Cases were significantly more likely to have ever have received a vaccine of any type in their lifetime compared to controls cats (OR = 6.8, 95% CI = 1.9 - 50.4, p = 0.03).


Now what?

1. How wide is it?

2. What does the interpretation of the CI mean? Clinically? Biologically?

3. Does it include the null value?


1. Width?

• CI are calculated from standard errors

• Standard errors depend on sample size and variation within the sample


Sooooo…..

• Small sample = bigger standard error = bigger CI

• More variation in sample bigger CI

• Wide CI = imprecise estimate• Narrow CI = more precise estimate


Examples

Cases were 3 times more likely to be over the age of 15 rather than 5-10 years old, when compared to controls (OR = 2.87, 95% CI 1.38 – 5.99, p = 0.005).



Now what?

1. How wide is it?




2. Interpretation

• The upper and lower limits can be used to see whether the results are useful

• A value can be significant with a low p value but the CI interval can help tell you whether you should get excited about it or not!


Examples




Now what?

1. How wide is it?




The null value?

• In Odds Ratios and Risk Ratios where you compare two groups and a value of 1 means there is no difference then 1 is the null value

• If 1 is included in the CI e.g. 0.56-1.2, then there is no statistically significant effect

………………………………..dont worry I will remind of this later in the year


Examples




Another example

The odds ratio for practice type B reporting multiple cases compared to practice type A was not significant

(OR = 1.02, 95% CI 0.25 – 4.10, p = 0.98)


AT A GLANCE!


Look at the CI

• Is it massive? If so, bin it! The power is rubbish and no matter how small p is, you have no confidence in it!

• Does it include values that are relevant? Do we care about the numbers? If not bin it!

• Does it include the null value? If it does, bin it!


Forest plots


Cool words…

• Bootstrapping: refers to a group of metaphors that share a common meaning: a self-sustaining process that proceeds without external help.


Cool words…

• Jack(k)nifing: means the folding of an articulated vehicle articulated vehicle (such as one towing a trailer) such that it resembles the acute angle of a folding pocket knife.


Similar techniques

• Repeated sampling (iterative processes)

• Use distribution of many estimates & CIs to get an overall estimate and CI

• Help!


BEING CONFIDENT…..

Is not that difficult….



In the packages….

Date post:	06-Jan-2016
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