2. Sampling Theory Concepts
Population
Target Population
Accessible Population
Elements of a Population
Sampling Criteria
3. Sampling Criteria
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
4. Sampling Theory Concepts
Sampling Plans or
Methods
Sampling Error
Random Variation
Systematic Variation
5. 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.
6. 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
8. Sampling Theory Concepts
Sample Mortality
Subject Acceptance Rate:
Percentage of individuals
consenting to be subjects
Representativeness
9. Representativeness
Needs to evaluate:
setting
characteristics of the subjects:
age, gender, ethnicity, income,
education
distribution of values
measured in the study
12. Sample Size
Factors influencing sample size
Effect size
Type of study conducted
Number of variables studied
Measurement sensitivity
Data analysis techniques
13. Power Analysis
Standard Power of 0.8
Level of Significance
alpha = .05, .01, .001
Effect Size
.2 Small; .5 Medium; .8 Large
Sample Size
14. 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...
15. 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...
16. 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)....
17. Critiquing the Sample
Were the sample criteria
identified?
Was the sampling method
identified?
Were the characteristics of
the sample described?
18. 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?
22. Levels of Measurement
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.
24. Likert Scale
How often do you feel in control of
your life?
(1) Never
(2) Seldom
(3) Often
(4) Almost always
25. Age
How old are you?
25-34
35-44
45-54
55 or older
26. Income
1 = under Rs-35,000/ 2 = Rs-35-50,000/ 3 = Rs-50 - 100,000/-
27. What is reliability?
Reliability - is concerned
with how consistently the
measurement technique
measures the concept of
interest.
28. Types of Reliability
Stability -- is
concerned with the
consistency of
repeated measures or
test-retest reliability
29. 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.
30. Types of Reliability
Homogeneity -- addresses the
correlation of various items
within the instrument or
internal consistency;
determined by split-half
reliability or Cronbach’s alpha
coefficient.
47. 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
48. 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.
49. 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?
50. Transforming Data
Transforming skewed data so that it is linear
(required by many statistics).
Squaring each value
calculating the square root of each
value
51. 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
52. 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
Don’t 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
53. 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
Don’t get bogged down in the details
54. 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
55. 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
56. 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
57. Descriptive Statistics
Location Statistics
How the data “falls”
Examples would be statistics of central tendency
Mean
Median
Average of numerical data
Σx/n
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
58. 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
59. Descriptive Statistics
Count Statistics
One of the simplest means of expressing an idea
Works for ordinal and nominal data
60. 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
61. 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
62. 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)
63. 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
64. 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
65. Inferential Statistics
Common Linear Model tests include:
Students t-test
Analysis of variance (ANOVA)
Analysis of covariance (ANCOVA)
Regression analysis
Multivariate factor analysis
66. 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