Transcript factors influencing calculus course success among freshmen

ADVANCED STATISTICS
FOR MEDICAL STUDIES
Mwarumba Mwavita, Ph.D.
School of Educational Studies
Research Evaluation Measurement and Statistics (REMS)
Oklahoma State University
Statistics
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Set of methods and rules for organizing,
summarizing, and interpreting information.
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Two categories of statistical procedures to
organize and interpreting data.
Descriptive and Inferential
Statistics
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Descriptive statistics are statistical
procedures that are used to summarize,
organize, and simplify data.
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Inferential statistics – techniques used to
study samples and make generalizations about
the populations from which they were selected.
Descriptive Statistics
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Descriptive measure computed from the
data of a sample is called a statistic
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Descriptive measure computed form the
data of a population is called a parameter
Central Tendency
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A statistical measure that identifies a single score
as representative for an entire distribution
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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
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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
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A bell shape distribution
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It is symmetrical
Terms
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IV – Independent variable (treatment)
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DV – Dependent variable (outcome)
Z- Test
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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
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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
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Independent and Dependent t-test
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Independent t-test uses two samples of
the treatment conditions. (rule of thumb at
least 10 subjects per each group)
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Dependent also is referred as repeatedmeasure. A single sample of individuals is
measured more than once on the same
dependent variable
ANOVA (Analysis of Variance)
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ANOVA - hypothesis-testing procedure used to
1. test hypotheses about population variances
2. evaluate mean differences between two or more
treatments (or populations)
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Uses variances to determine if the means are
significantly different.
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
Correlation and Regression
Analysis
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Correlation analyses mathematically identify and
describe relationships between variables
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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
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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)
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Confirmatory factor analysis- assess the extent
to which the hypothesized organization of a set of
identified factor fits the data
Survival Analysis
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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
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Two major varieties of the technique are life tables,
which describe the course of survival of one or more
groups of cases
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The second one encompasses a set of regression
techniques in which the DV is survival time
Nonparametric techniques
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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
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Chi-square statistic tests for Goodness of Fit
(how well the obtained sample proportions fit the
population proportions specified by the null
hypothesis
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Test for independence – tests whether or not
there is a relationship between two variables
More Terms
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Type I error – rejecting a true null hypothesis.
(treatment has an effect when in fact the
treatment has no effect)
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Alpha level for a hypothesis test is the probability
that the test will lead to a Type I error
Scenario 1
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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
Scenario 2
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A researcher would like to know whether
room temperature affects eating behavior.
 Design
 I.V.
 D.V.
 Others
 Participants
Scenario 3
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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
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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
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Suppose you are interested in finding out
how a new treatment on osteoporosis
among women will work.
 Design
 IV
 DV
 Others
Scenario 6
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Using scenario 5, how can we make it a twoway ANOVA?
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How could we make it a Repeated-measures
ANOVA?
Scenario 7
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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
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A physician is interested in finding out the
factors that contribute to lung cancer. How
would you design this study?
Scenario 9
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How would you investigate factors that
contribute to high blood pressure among
people?
Summary
 Problem
 Design
issues
 Variables
 Participants
 Sample size