ADVANCED STATISTICS FOR MEDICAL STUDIES

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ADVANCED STATISTICS FOR MEDICAL STUDIES

• Mwarumba Mwavita, Ph.D.
• School of Educational Studies
• Research Evaluation Measurement and Statistics
  (REMS)
• Oklahoma State University

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Statistics

• Set of methods and rules for organizing,
  summarizing, and interpreting information.
• Two categories of statistical procedures to
  organize and interpreting data.

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Descriptive and Inferential Statistics

• Descriptive statistics are statistical procedures
  that are used to summarize, organize, and
  simplify data.
• Inferential statistics techniques used to study
  samples and make generalizations about the
  populations from which they were selected.

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Descriptive Statistics

• Descriptive measure computed from the data of a
  sample is called a statistic
• Descriptive measure computed form the data of a
  population is called a parameter

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Central Tendency

• A statistical measure that identifies a single
  score as representative for an entire
  distribution
• The goal of central tendency is to find the
  single score that is most typical or most
  representative of the entire group
• Mean commonly referred as the average
• Mode most frequent score in a distribution
• Median the middle value in a distribution

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Variability

• Range - highest score lowest score
• Semi-interquartile range - (Q3 Q1)/2
• Standard Deviation the standard distance from
  mean
• Variance - the mean of the squared deviations
• Coefficient of Variation (CV) - useful for
  comparing two or more data with different units
  of measurement because it is expressed in
  percentage (CV SD/mean x 100)
• Confidence Interval (CI) - is a measure of the
  precision of the point estimate

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Normal distribution

• A bell shape distribution
• It is symmetrical

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Terms

• IV Independent variable (treatment)
• DV Dependent variable (outcome)

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Z- Test

• Used in hypothesis testing when a sample mean is
  used to test a hypothesis about an unknown
  population, generally a population that has
  received treatment
• Note the parameters of the population that did
  not receive treatment are known

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T- test

• T statistic is used to test hypotheses about µ
  when the value for population standard deviation
  is not known
• Uses a t-distribution- thus degree of freedom
  (number of scores in a sample that are free to
  vary)
• Sample size determines use of t-distribution

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Independent and Dependent t-test

• Independent t-test uses two samples of the
  treatment conditions. (rule of thumb at least 10
  subjects per each group)
• Dependent also is referred as repeated-measure. A
  single sample of individuals is measured more
  than once on the same dependent variable

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ANOVA (Analysis of Variance)

• ANOVA - hypothesis-testing procedure used to
• 1. test hypotheses about population variances
• 2. evaluate mean differences between two or more
  treatments (or populations)
• Uses variances to determine if the means are
  significantly different.

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ANOVA (Analysis of Variance)

1. Single factor (one way) - one treatment under
   different levels
2. Factorial designs involves more than one factor
   (treatment)
3. Repeated measures assess a measurement on the
   same participants under different condition/time

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Correlation and Regression Analysis

• Correlation analyses mathematically identify and
  describe relationships between variables
• Regression analysis attempts to predict or
  estimate the value of a response variable form
  the known values of one or more explanatory
  variables

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Factor Analysis

• Exploratory factor analysis used when the
  researcher does not know how many factors are
  necessary to explain the inter-relationships
  among a set of characteristics, indicators, or
  items (Reduction)
• Confirmatory factor analysis- assess the extent
  to which the hypothesized organization of a set
  of identified factor fits the data

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Survival Analysis

• Survival/failure analysis is a family of
  techniques dealing with the time it takes for
  something to happen cure, a failure, a relapse,
  a death and so on
• Two major varieties of the technique are life
  tables, which describe the course of survival of
  one or more groups of cases
• The second one encompasses a set of regression
  techniques in which the DV is survival time

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Nonparametric techniques

• Usually do not state hypotheses in terms of a
  specific parameter
• They make vary few assumptions about the
  population distribution- distribution-free tests.
• Suited for data measured in ordinal and nominal
  scales
• Not as sensitive as parametric tests more likely
  to fail in detecting a real difference between
  two treatments

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Types of nonparametric tests

• Chi-square statistic tests for Goodness of Fit
  (how well the obtained sample proportions fit the
  population proportions specified by the null
  hypothesis
• Test for independence tests whether or not
  there is a relationship between two variables

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More Terms

• Type I error rejecting a true null hypothesis.
  (treatment has an effect when in fact the
  treatment has no effect)
• Alpha level for a hypothesis test is the
  probability that the test will lead to a Type I
  error

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Scenario 1

• Alcohol appears to be involved in a variety of
  birth defects, including low birth weight and
  retarded growth. A researcher would like to
  investigate the effect of prenatal alcohol on
  birth weight.
• How will the researcher do this?
• D.V.
• I.V.
• Participants

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Scenario 2

• A researcher would like to know whether room
  temperature affects eating behavior.
• Design
• I.V.
• D.V.
• Others
• Participants

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Scenario 3

• A patient recently visited her physician
  complaining of backache. The physician is aware
  of a new technique of disc replacement. The
  physician would like to test the technique but
  does not want to use it on the patient.
• What would you advise the physician to do in
  this case?

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Scenario 4

• You notice that students from a nearby elementary
  school that you have attended suffer from the
  common cold, a disease that has been at the
  school for a while. How does this school compare
  to an elementary school across town?
• How would you go about investigating this problem?

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Scenario 5

• Suppose you are interested in finding out how a
  new treatment on osteoporosis among women will
  work.
• Design
• IV
• DV
• Others

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Scenario 6

• Using scenario 5, how can we make it a two-way
  ANOVA?
• How could we make it a Repeated-measures ANOVA?

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Scenario 7

• Diabetes has been on the increase among American
  adolescents. A researcher is interested in
  determining factors that contribute to rise of
  diabetes among adolescents

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Scenario 8

• A physician is interested in finding out the
  factors that contribute to lung cancer. How would
  you design this study?

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Scenario 9

• How would you investigate factors that contribute
  to high blood pressure among people?

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Summary

• Problem
• Design issues
• Variables
• Participants
• Sample size