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biosampl. Statistics. Discriptive Statistics.

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Types of Data, Descriptive Statistics, andStatistical Tests for Nominal Data
Patrick F. Smith, Pharm.D.
University at BuffaloBuffalo, New York
NONPARAMETRIC STATISTICS
I.
DEFINITIONSA. Parametric statistics1. Variable of interest is a measured quantity.2. Assumes that the data follow some distribution which can be described by specific parametersa. Typically a normal distribution3. Example: There are an infinite number of normal distributions, all which can be uniquelydefined by a mean and standard deviation (SD).B. Nonparametric statistics1. Variable of interest is not measured quantity. Mean and SDhave little meaning.2. Does not make any assumptions about the distribution of the data3. Distribution-free statisticsC. Dependent variable1. The variable of interest, the outcome of which is
dependent
on something elseD. Independent variable1. The variable that is being tested for an effect on the dependent variableE. Example1. Does high-dose ciprofloxacin lead to seizures?a. Seizures = dependent variableb. Dose
=
independent variableII. PARAMETRIC STATISTICSA. Developed primarily to deal with categorical data (non-continuous data)1. Example: disease vs no disease; dead vs aliveB. Nonparametric statistical tests maybe used on continuous data sets.1. Removes the requirement to assume a normal distribution2. However, it also throws out some information, as continuous data contains information in theway that variables are related.
Some Commonly Used Statistical Tests
CorrespondingNormal theory-based tests nonparametric tests Purpose of test.t test for independent samples Mann-Whitney
U
test; Compares two independentWilcoxon rank sum test samplesPaired t test Wilcoxon matched pairs signed., Examines a setof differencesrank testPearson correlation coefficient Spearman rank correlation Assesses the linear associationcoefficient between two variablesOne-way analysis of Kruskal-Wallis analysis of Compares three or morevariance (F test) variance by ranks groupsTwo-way analysis of vanance Friedman two-way analysis Compares groups classifiedbyof variance two different factors
III.
NONP ARAMETRIC PROS AND CONS
A. Nonparametric pros1. Nonparametric tests make less stringent demands ofthe data.a. For a parametric test to be valid, certain underlying assumptions must be met.i. example: For a paired t test, assume that: data are drawn ITomnormal distribution;every observation is independent of each other, and the SDs of the two populations areequal. Data are continuous.b. Nonparametric tests do not require these assumptions.i. can be used to evaluate data that are not continuousii. no assumptions about distributions, independence, etc.B. Nonparametric cons1. If using for a continuous data set, nonparametric tests throw information inherent incontinuous data.2. Reduces power to detect a statistical differencea. A more conservative approach3. Example: For data IToma normally distributed population, if the Wilcoxon signed-ranktestrequires 1000observations to demonstrate statistical significance, a t test will onlyrequire 955.
IV.
CONTINGENCY TABLES
A. Contingency tables are used to examine the relationship between subjects' scores on two qualitativeor categorical variables.B. One variable determinesthe row categories; the other variable defines the column categories.C. Example: In studying the association between smoking and disease, the row categories in thefigure below denote the categories of smoking status while the columns denote the presence orabsence of disease.SmokeADiseaseYes No13 376 144BDiseaseYes No26% 74%4% 96%100%100%YesNo
v. cm-SQUARED TEST
A. Commonly used procedure, uses contingency tablesB. Used to evaluate
unpairedsamples
(unrelated groups)C. Often used to evaluate proportionsD. Is there a difference in the proportion of viral infections in patients administered avaccine? (12/100 vs. 2/100)E. Assumes nominal data (no ordering between variable groups)
F. Limited when the numbers of subjects in any cell is low (rule of thumb, <5)G. Generallogic1. Given two groups (vaccine vs control), the EXPECTED infection rate if the vaccine has noeffect would be equal among the two groups. This is thenull hypothesis. The chi-squared testcompares the EXPECTED frequency of a particular event to the OBSERVED frequency in thepopulation of interest.H. Formulas
x2
=
L
(0-E)2
E
withdf= (r-l)(c -1)ExpectedFrequencies(E)foreachcell:
I. Distribution
E
.. Ti X
T
.
1J
=
J
N
16 20 244 8 12
Chi-Square distribution
Chi-squared, by strict definition, is not a true nonparametric test. It assumes adistribution that can be described by a single parameter, degrees of freedom.J. Chi-squared example problems (refer to Example Problem handout)
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