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Statistics

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?.

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Statistics

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

  2. Nice statistics

  3. Confidence intervals

  4. 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?

  5. 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

  6. 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?

  7. 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….

  8. 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!

  9. 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

  10. How do you calculate a CI? • Use nasty sums ……..Or a table ……..Or a computer

  11. Calculate a confidence interval (mean) • Work out the mean • Work out the standard error of the mean (how precise a measurement is the sample mean of the population mean?) • The CI is some kind of multiple of the standard errors E.g. 95% CI = ± 1.96 (SE) 99% CI = ± 2.58 (SE)

  12. Why 95%? • Convention • You can calculate anything you like but it is normally 90%, 95% or 99% • NEVER 100% confident 100% confidence = arrogance Arrogance: an attitude of superiority manifested in an overbearing manner or in presumptuous claims or assumptions

  13. 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

  14. 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).

  15. Now what? • How wide is it? • What does the interpretation of the CI mean? Clinically? Biologically? • Does it include the null value?

  16. 1. Width? • CI are calculated from standard errors • Standard errors depend on sample size and variation within the sample

  17. Sooooo….. • Small sample = bigger standard error = bigger CI • More variation in sample bigger CI • Wide CI = imprecise estimate • Narrow CI = more precise estimate

  18. 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). 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).

  19. Now what? • How wide is it? • What does the interpretation of the CI mean? Clinically? Biologically? • Does it include the null value?

  20. 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!

  21. 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). 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).

  22. Now what? • How wide is it? • What does the interpretation of the CI mean? Clinically? Biologically? • Does it include the null value?

  23. 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

  24. 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). 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).

  25. 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)

  26. At a glance!

  27. 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!

  28. Forest plots

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

  30. 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.

  31. Similar techniques • Repeated sampling (iterative processes) • Use distribution of many estimates & CIs to get an overall estimate and CI • Help!

  32. Is not that difficult…. Being confident…..

  33. In the packages….

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