Sampling Theory Concepts Population Target Population
Accessible Population Elements of a Population Sampling
Criteria
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Characteristics essential for inclusion or exclusion of members
in the target population Between the Ages of 18 & 45 Ability to
speak English Dx of diabetes within last month, or No Hx of chronic
illness
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Sampling Theory Concepts Sampling Plans or Methods Sampling
Error Random Variation Systematic Variation
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Sampling Error Random Variation The expected difference in
values that occurs when different subjects from the same sample are
examined. Difference is random because some values will be higher
and others lower than the average population values.
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Sampling Error Systematic Variation (Bias) Consequence of
selecting subjects whose measurement values differ in some specific
way from those of the population. These values do not vary randomly
around the population mean
Sample Size Factors influencing sample size Effect size Type of
study conducted Number of variables studied Measurement sensitivity
Data analysis techniques
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Power Analysis Standard Power of 0.8 Level of Significance
alpha =.05,.01,.001 Effect Size.2 Small;.5 Medium;.8 Large Sample
Size
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Example Sample A convenient sample of 55 adults scheduled for
first time elective CABG surgery without cardiac catheterization,
who had not had other major surgery within the previous year, and
who were not health professionals met the study criteria and were
randomly assigned to one of two instruction conditions...
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Example Sample Based on a formulation of 80% power, a medium
critical effect size of 0.40 for each of the dependent variables,
and a significance level of.05 for one-tailed t-tests means, a
sample size of 40 was deemed sufficient to test the study
hypotheses...
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Example Sample The study included a convenience sample of 32
post-op Lung Cancer patients. A power analysis was conducted to
determine size. A minimum of 27 subjects was necessary to achieve
the statistical power of 0.8 and a medium (0.5) effect size at the
0.05 level of significance....The subjects were 25 men and 7 women
with an age range from 18-58 years (mean = 32.74)....
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Critiquing the Sample Were the sample criteria identified? Was
the sampling method identified? Were the characteristics of the
sample described?
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Critiquing the Sample Was the sample size identified? Was the
percent of subjects consenting to participate indicated? Was the
sample mortality identified? Was the sample size adequate?
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Concepts of Measurement
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Measurement Theory Concepts Directness of Measurement Direct
measurement Oxygen saturation, Temperature, weight Indirect
measurement Pain, depression, coping, self- care, self-esteem
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Measurement Theory Concepts Measurement Error Score obs = Score
true + Score err Systematic error Random error Levels of
Measurement
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Nominal data categorized, but no order or zero (ex- gender
numbers) Ordinal categories with order, but intervals not
necessarily equal and no zero (ex pain) Interval equal intervals,
but no true zero (ex- temp scales) Ratio equal intervals with a
true zero. These are real numbers, for things such as weight,
volume, length.
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Gender 1 = Male 2 = Female (Nominal Data)
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Likert Scale How often do you feel in control of your life? (1)
Never (2) Seldom (3) Often (4) Almost always
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Age How old are you (years)? What LOM?
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Age How old are you? 25-34 35-44 45-54 55 or older What
LOM?
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Income 1 = under $35,000 2 = $35-50,000 3 = $50 - 100,000
LOM?
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What is reliability? Reliability - is concerned with how
consistently the measurement technique measures the concept of
interest.
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Types of Reliability Stability -- is concerned with the
consistency of repeated measures or test-retest reliability
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Types of Reliability Equivalence -- is focused on comparing two
versions of the same instrument (alternate forms reliability) or
two observers (interrater reliability) measuring the same
event.
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Types of Reliability Homogeneity -- addresses the correlation
of various items within the instrument or internal consistency;
determined by split-half reliability or Cronbachs alpha
coefficient.
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Inter-rater reliability Consistency in raters % = # behaviors
performed/total # of behaviors Values below 0.8 are a problem
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What is validity? The extent to which an instrument reflects
the concept being examined.
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Measurement Strategies
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Physiologic Measures Physical Measurement Methods EKG, BP SVO
2, Pulse Oximetry
Interviews Unstructured Interviews Structured Interviews
Describing interview questions Pretesting the interview protocol
Training interviewers Preparing for an interview Probing Recording
interview data
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Unstructured or Open ended: Tell me about.. What has been your
experience with.... What was it like to hear you have cancer?
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Closed ended: Structured Response alternatives fixed Which
would you rather do, x or y?
Questionnaires Administration In person/on phone Self
administered Mail
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Scales Rating Scales Likert Scales Semantic Differentials
Visual Analog Scales
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Introduction to Statistical Analysis
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Normal Curve -3 Mean Median Mode -2-200112233 68.3% 95.5% 99.7%
-2.58 -1.96 1.96 2.58
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Tailedness One-Tailed Test-.05 Level of Significance Two-Tailed
Test-.05 Level of Significance Significantly different from mean
0.025 0.05 Tail
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Process for Quantitative Data Analysis Preparation of the Data
for Analysis Description of the Sample Testing the Reliability of
the Instruments for the Present Sample Testing Comparability of
Design Groups Exploratory Analysis of Data Confirmatory Analyses
Guided by Objectives, Questions, or Hypotheses Post Hoc
Analyses
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Cleaning Data Examine data Cross-check every piece of data with
the original data If file too large, randomly check for accuracy
Correct all errors Search for values outside the appropriate range
of values for that variable.
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Missing Data Identify all missing data points Obtain missing
data if at all possible Determine number of subjects with data
missing on a particular variable Make judgement - are there enough
subjects with data on the variable to warrant using it in
statistical analyses?
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Transforming Data Transforming skewed data so that it is linear
(required by many statistics). Squaring each value calculating the
square root of each value
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Calculating Variables Involves using values from two or more
variables in your data set to calculate values for a new variable
to add to the data set. Summing scale values to obtain a total
score Calculating weight by height values to get a value for Body
Mass Index
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Statistical Tools Used to allow easy calculation of statistics
Computer-based tools allow rapid analysis but sometimes too easy
Must still know what each type of test is for and how to use them
Dont fall into the trap of using a test just because it is easy to
do now Many papers appearing with questionable tests just because a
computer program allows the calculation
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Statistics Exercises Stat Trek http://stattrek.com/ Tutorial
for exercises Understand rationale for the selection of each test
type. Be prepared to utilize test if asked, and know major
advantages of each main test. Miller Text (Chapter 21, Fifth
Edition, pgs 753-792) Material very thorough. Many little-used
tests described. Read for idea of why other tests are available
Dont get bogged down in the details
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Descriptive Statistics Describes basic features of a data
group. Basis of almost all quantitative data analysis Does not try
to reach conclusions (inferences), only describe. Provide us with
an easier way to see and quickly interpret data
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Descriptive Statistics Data Types Based on types of measurement
Measurement scales can show magnitude, intervals, zero point, and
direction Equal intervals are necessary if one plans any
statistical analysis of data Interval scales possess equal
intervals and a magnitude Ratio scales show equal intervals,
magnitude and a zero point Ordinal scales show only magnitude, not
equal intervals or a zero point Nominal data in non-numeric (not
orderable) whereas ordinal data is numeric and can be ordered but
not based on continuous scale of equal intervals
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Descriptive Statistics Goal of use is to be able to summarize
the data in a way that is easy to understand May be described
numerically or graphically Describe features of the distribution
Examples include distribution shape (skewed, normal (bell-shaped),
modal, etc), scale, order, location
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Descriptive Statistics Location Statistics How the data falls
Examples would be statistics of central tendency Mean Average of
numerical data x / n Median Midpoint of data values Value of data
where 50% of data values is above and 50% below (if number of data
points is even, then the middle two values are averaged) Mode Most
frequent data value May be multi-modal if there is an identical
number of max data values
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Descriptive Statistics Location Statistics Data outliers may
need to be accounted for and possibly eliminated This can be done
by trimming or weighting the mean to effectively eliminate the
effect from outliers
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Descriptive Statistics Count Statistics One of the simplest
means of expressing an idea Works for ordinal and nominal data
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Descriptive Statistics Statistics of Scale Measures how much
dispersal there is in a data set (variability) Example statistics
include sample range, variance, standard deviation (the square root
of the variance), SEM (SD/sq root of N) Outliers can influence
variance and standard deviation greatly, so try to avoid their use
if there are lots of outliers that can not be weighted out
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Descriptive Statistics Distribution Shape Statistics Determines
how far from normal the distribution of data is based on normal
distribution shapes (Gaussian) Skewness measures how tailed the
data distribution is (positive to right, negative to left) Kurtosis
measures whether the tail is heavy or light
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Inferential Statistics Attempts to come to conclusions about a
data set that are not exactly stated by the data (inferred) Many
tests use probability to help determine if data points to a likely
conclusion. Often used to compare two groups of data to see if they
are statistically different Often used to decide whether or not a
conclusion one is trying to reach from the data set is reliable
(within statistical probability)
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Inferential Statistics Simplest form is the comparison of
average data between two data sets to see if they are different
Students t-test is often used to compare differences between 2
groups Usually one control group and one experimental Should be
only one altered variable in experimental group
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Inferential Statistics Most common inferential statistical
tests belong to the General Linear Model family Data is based on an
equation in which a wide variety of research outcomes can be
described Problems with these types of analysis tools usually comes
from the wrong choice of the equation used Errors in the wrong
equation used can result in the data conclusions being biased one
way or the other, leading to accepting or rejecting the null
hypothesis wrongly
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Inferential Statistics Common Linear Model tests include:
Students t-test Analysis of variance (ANOVA) Analysis of covariance
(ANCOVA) Regression analysis Multivariate factor analysis
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Inferential Statistics Type of research design used also
determines the type of testing which can be done: Experimental
analysis Usually involves comparison of one or more groups against
a control, and thus t-test or ANOVA tests are the most commonly
used Quasi-experimental analysis Typically lack a control group,
and thus the random analysis that is usually used to assign
individuals to groups These types of analysis are much more complex
to compensate for the random assignments