ADVANCED STATISTICS FOR MEDICAL STUDIES

Mwarumba Mwavita, Ph.D.School of Educational Studies

Research Evaluation Measurement and Statistics (REMS)Oklahoma State University

StatisticsSet of methods and rules for organizing,

summarizing, and interpreting information.

Two categories of statistical procedures to organize and interpreting data.

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.

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

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

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

Normal distribution

A bell shape distribution

It is symmetrical

Terms

IV – Independent variable (treatment)

DV – Dependent variable (outcome)

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

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

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

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.

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

ANOVA (Analysis of Variance)

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

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

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

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

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

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

Scenario 1Alcohol 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

Scenario 2

A researcher would like to know whether room temperature affects eating behavior.

DesignI.V.D.V.OthersParticipants

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?

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?

Scenario 5

Suppose you are interested in finding out how a new treatment on osteoporosis among women will work.

DesignIVDVOthers

Scenario 6

Using scenario 5, how can we make it a two-

way ANOVA?

How could we make it a Repeated-measures

ANOVA?

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

Scenario 8

A physician is interested in finding out the

factors that contribute to lung cancer. How

would you design this study?

Scenario 9

How would you investigate factors that

contribute to high blood pressure among

people?

Summary

ProblemDesign issuesVariables ParticipantsSample size