An easy to understand about statistics and its application in life science research and medicine.

1. Applied Statistics
Part 5
By:
MM. H. Farjoo MD, PhD, Bioanimator
Shahid Beheshti University of Medical Sciences
Instagram: @bio_animation

2. Applied Statistics
part 5
 Outliers
 Transforming Data
 Normalizing Data
 Weighting Data
 Torturing Data
 Robustness
 Homoscedasticity and Heteroscedasticity

3. Outliers
 When analyzing data, sometimes one value is far
from the others; Such a value is called an outlier.
 With an outlier, consider these:
 Was the value entered into the computer correctly?
 Is the outlier value scientifically impossible? (negative
height or weight, etc)
 Were there any experimental problems caused by a flaw in
the Lab. devices?
 Could the outlier be caused by biological diversity? (this
may be the most exciting finding in your data!)

5. Outliers Cont,d
 Don't throw out the data as an outlier until first thinking
about whether the finding is scientifically interesting.
 You may have discovered a polymorphism in a gene, or a
new clinical syndrome.
 It is especially important to beware of lognormal
distributions.
 In lognormal distribution, you find very high values
which can easily be mistaken for outliers.
 Removing these values would be a mistake.

6. Outliers
Hands-on practice
 To find outliers in SPSS:
 Analyze => Descriptive Statistics => Explore... => Statistics...
=> Outliers check box
 To find outliers in Prism:
 Column statistics (from welcome screen) => frequency
distribution data and histogram => Analyze => Column
analysis => Identify outliers

7. Transforming Data
 Data transformations are an important tool for the proper
statistical analysis of biological data.
 It is tried if a quantitative variable:
 Does not fit a normal distribution
 Has greatly different SD in different groups (SD)
 It is NOT a form of playing around with your data in order to
get the answer you want!
 So it is essential to be able to defend data transformation.

8. Transforming Data Cont,d
 For transforming, a mathematical operation is performed
on each observation, and statistics is done on the
transformed numbers.
 It is better to use a transformation that other researchers
commonly use in your field.
 It is rather better to use a more common, but less effective
transformation, so people are not skeptical.
 Data don't have to be perfectly normal; parametric tests
aren't sensitive to this assumption.

10. Transforming Data Cont,d
 It is NOT a good idea to report your results (means,
SD, CI etc.) in transformed units.
 You should back-transform the results, and do the
opposite math function used for transformation.
 It is also important that you decide which
transformation to use before you do the statistical test.
 Trying different transformations until you find one
that gives you a significant result is cheating.

11. Transforming Data Cont,d
 Log transformation:
 Consists of taking the log of each observation.
 You can use either base-10 logs or base-e logs, It
makes no difference for a statistical test
 You should specify which log you're using, as it
affects the slope and intercept in a regression
 Many variables in biology have log-normal
distributions
 It means after log-transformation, the values are
normally distributed.

12. Transforming Data Cont,d
 Square-root transformation:
 Consists of taking the square root of each observation
 Arcsine transformation.
 Consists of taking the arcsine of the square root of a
number.
 The numbers must be in the range 0 to 1
 This is used for proportions, which range from 0 to 1

13. Transforming Data
Hands-on practice
 To transform data in SPSS:
 Transform => compute variables
 To transform data in Prism:
 Column statistics (from welcome screen) => frequency
distribution data and histogram => Analyze => Transform,
Normalize… => Transform => “Transform Y values using”
check box

14. Normalizing Data
 We often want to compare data on different scales or
even different units.
 To do so, we “eliminate” the scale of measurements,
and “constrain” them to predetermined restrictions.
 This is called normalization, and puts different
variables into comparable units.
 Investigators commonly normalize dose-response
curves so all curves begin, and end at constant values
(usually 0% & 100%).

16. Normalizing Data Cont,d
 To fit a curve to the normalized data, we “constrain”
the bottom and top plateaus to predetermined values
(usually 0% and 100%).
 In this way all parameters of the curves are
comparable (eg: EC50, slope, intercept, etc)
 If you normalize, don't also weight the data.

18. Normalizing Data
Hands-on practice
 To normalize data in SPSS:
 Transform => Analyze => Regression => Probit...
 To normalize data in Prism:
 Column statistics (from welcome screen) => frequency
distribution data and histogram => Analyze => Transform,
Normalize… => Normalize

19. Weighting Data
 The USA election candidates in 1936, were Alfred Landon,
and Franklin Roosevelt.
 The magazine “Literary Digest” had always correctly
predicted the results in 1920, 1924, 1928 and 1932.
 It surveyed 10 million people in 1936, and 2.4 million of them
responded (wow!).
 Literary Digest predicted, Landon is the winner, but Landon
failed and Roosevelt won (a louder wow!!).
 The sampling error was 19%, the largest ever in the USA.
 The magazine was so discredited that it folded 2 years later in
1938; after 48 years of brilliant circulation.

20. Alfred Landon
Franklin Roosevelt

21. Weighting Data (Cont’d)
 A sample may NOT be representative of its population.
 This happens because of:
 Non-response
 Self-selection (in an online survey)
 Sampling error (eg. selection bias) or just bad luck!
 A commonly applied correction technique is weighting.
 Under-represented variables, get a weight larger than 1, and
over-represented groups get a weight smaller than 1.
 In the calculations, not the variables proper, but the
weighted values are used.

22. Weighting Data (Cont’d)
 A weighting adjustment can only be carried if appropriate and
valid auxiliary variables are available.
 Gallup's Institute of Public Opinion correctly predicted the
result of the 1936 election using a sample size of only 50,000.
 The morals of the Literary Digest story is:
 Making a bad sample bigger, does NOT correct the sampling error
 A badly chosen big sample is much worse than a well-chosen small
sample
 Watch out for selection bias and nonresponse bias and correct them
by weighting
 Gallup institute was better than Literary Digest!!

23. Male Female
Population 50% 50%
Sample 20% 80%
What film? Action (Western) Drama (Indian)
Weight 2.5 (50 / 20) 0.625 (50 / 80)
Result in sample 50% (2.5 * 20%) 50% (0.625 * 80%)
Weighting Data
Gender is an auxiliary variable

25. Weighting Data
Hands-on practice
 To weight data in SPSS:
 Data => weight cases...
 To weight data in Prism (note: prism uses weighting
for nonlinear regression):
 XY (from welcome screen) => Nonlinear regression =>
Analyze => XY analysis => Nonlinear regression (curve fit)
=> choose an equation from “Fit” tab => Weight tab =>
Weighting method

27. Torturing Data
 When scientists don't get the results they want, they often
resort to tactics such as:
 Change the definition of the outcome.
 Use a different time scale.
 Try different criteria for including or excluding a subject.
 Arbitrarily decide which points to remove as outliers.
 Try different ways to clump or separate subgroups.
 Try different ways to normalize the data.
 Try different algorithms for computing statistical tests.
 Try different statistical tests.
 If the results are still 'negative', then don't publish them!!

28. Robustness
 Robustness in statistical tests means the test can
“resist” violation(s) of the test assumption(s).
 If a tests is robust, the result is not affected
considerably by the absence or alterations of the
condition (eg: normal distribution).
 It is similar to buffer solutions in chemistry which
resist against changes in pH.

29. Homoscedasticity & Heteroscedasticity
 Homoscedasticity & Heteroscedasticity are a notion
usually considered in ANOVA, and t Test
 Parametric tests assume that data are homoscedastic (have
the same SD in different groups).
 If the SDs are heteroscedastic, the probability of
obtaining a false positive is greater than alpha level.
 Heteroscedasticity is not a problem with balanced designs
(equal sample sizes in each group).
 You should always compare the SDs of the groups for
heteroscedasticity (especially with unbalanced designs).

30. Homoscedasticity & Heteroscedasticity Cont,d
 There is no agreement about when heteroscedasticity
is big enough for not using a test that relies on it.
 To test homoscedasticity, Bartlett's test is used (H0 is
desirable)
 Bartlett is not a very good test, so do not panic if it
returns a significant P value.
 When SDs are different The first action is data
transformation.

31. Homoscedasticity & Heteroscedasticity Cont,d
 Bartlett test is often used to compare the effect of
various transformations to obtain the biggest P value.
 If data transformation is not successful, Welch test
(correction) is used as an alternative.
 Welch test does not assume equal SDs.
 Non-parametric tests do not assume normal
distribution but they do assume homoscedasticity.
 So Non-parametric tests are NOT a good solution for
heteroscedasticity.

33. Thank you
Any question?