Sampling
Sampling Theory Concepts
 Population
 Target Population
 Accessible Population
 Elements of a Population

 Sampling C...
Sampling Criteria
 Characteristics essential for

inclusion or exclusion of
members in the target
population

 Between t...
Sampling Theory Concepts
 Sampling Plans or
Methods
 Sampling Error
 Random Variation
 Systematic Variation
Sampling Error
 Random Variation
 The expected difference in values that

occurs when different subjects from
the same s...
Sampling Error
 Systematic Variation (Bias)
 Consequence of selecting

subjects whose measurement
values differ in some ...
Sampling Error
Sampling Error

Population

Sample

Population
Mean

Sample
Mean
Sampling Theory Concepts
 Sample Mortality
 Subject Acceptance Rate:
 Percentage of individuals

consenting to be subje...
Representativeness
 Needs to evaluate:
 setting
 characteristics of the subjects:

age, gender, ethnicity, income,
educ...
Probability (Random)
Sampling Methods
 Simple Random Sampling
 Stratified Random Sampling

 Cluster Sampling
 Systemat...
Nonprobability (Nonrandom)
Sampling
 Convenience (Accidental)

Sampling
 Quota Sampling
 Purposive Sampling

 Network ...
Sample Size
 Factors influencing sample size
 Effect size
 Type of study conducted
 Number of variables studied
 Meas...
Power Analysis
 Standard Power of 0.8
 Level of Significance
 alpha = .05, .01, .001

 Effect Size
 .2 Small; .5 Medi...
Example Sample
 A convenient sample of 55 adults
scheduled for first time elective CABG
surgery without cardiac
catheteri...
Example Sample
 Based on a formulation of 80% power, a
medium critical effect size of 0.40 for each of
the dependent vari...
Example Sample
 The study included a convenience
sample of 32 post-op Lung Cancer
patients. A power analysis was
conducte...
Critiquing the Sample
 Were the sample criteria

identified?
 Was the sampling method

identified?
 Were the characteri...
Critiquing the Sample
 Was the sample size identified?
 Was the percent of subjects

consenting to participate
indicated...
Concepts of
Measurement
Measurement Theory
Concepts
 Directness of Measurement
 Direct measurement
 Oxygen saturation,
Temperature, weight
 In...
Measurement Theory
Concepts
 Measurement Error


Scoreobs = Scoretrue +
Scoreerr

 Systematic error

 Random error

 ...
Levels of Measurement
 Nominal
 data categorized, but no order or zero (ex- gender

numbers)

 Ordinal
 categories wit...
Gender
 1 = Male
 2 = Female
 (Nominal Data)
Likert Scale
 How often do you feel in control of

your life?
 (1) Never
 (2) Seldom
 (3) Often
 (4) Almost always
Age
 How old are you?
 25-34
 35-44

 45-54
 55 or older
Income
 1 = under Rs-35,000/ 2 = Rs-35-50,000/ 3 = Rs-50 - 100,000/-
What is reliability?
 Reliability - is concerned

with how consistently the
measurement technique
measures the concept of...
Types of Reliability
 Stability -- is
concerned with the
consistency of
repeated measures or
test-retest reliability
Types of Reliability
 Equivalence -- is focused
on comparing two versions
of the same instrument
(alternate forms reliabi...
Types of Reliability
 Homogeneity -- addresses the
correlation of various items
within the instrument or
internal consist...
Inter-rater reliability
 Consistency in raters
 % = # behaviors

performed/total # of
behaviors
 Values below 0.8 are a...
What is validity?
 The extent to which an

instrument reflects the
concept being examined.
Measurement
Strategies
Physiologic Measures
 Physical Measurement

Methods
 EKG, BP
 SVO2, Pulse Oximetry
Physiologic Measures
 Chemical/biochemical
 Blood glucose
 SMA-24
 PKU
Physiologic Measures
 Microbiological
 Smears

 Cultures
 Sensitivities
Observational Measurement
 Unstructured Observations
 Structured Observations
 Category Systems
 Checklists
 Rating S...
Interviews
 Unstructured Interviews
 Structured Interviews
 Describing interview questions
 Pretesting the interview p...
Unstructured or Open ended:
 Tell me about…..
 What has been your experience

with....
 What was it like to hear you

h...
Closed ended:
 Structured
 Response alternatives fixed

 Which would you rather

do, x or y?
Measurement Strategies
 Questionnaires
 Scales
 Diaries
Questionnaires
 Administration
 In person/on phone
 Self administered
 Mail
Scales
 Rating Scales
 Likert Scales

 Semantic Differentials
 Visual Analog Scales
Introduction
to Statistical
Analysis
Normal Curve
Mean
Median
Mode
68.3%

95.5%

-3
-3

-2
-1
-2
-1
-2.58 -1.96

99.7%

0
0

1
1

2
2
1.96

3
3
2.58
Tailedness
Significantly different
from mean

Significantly different
from mean

0.025

0.025

Tail

Tail

Two-Tailed Test...
Process for Quantitative Data
Analysis
• Preparation of the Data for Analysis
• Description of the Sample
• Testing the Re...
Cleaning Data
 Examine data
Cross-check every piece of data with the
original data
 If file too large, randomly check fo...
Missing Data
 Identify all missing data points
 Obtain missing data if at all possible
 Determine number of subjects wi...
Transforming Data
 Transforming skewed data so that it is linear

(required by many statistics).

 Squaring each value

...
Calculating Variables
 Involves using values from two or
more variables in your data set to
calculate values for a new va...
Statistical Tools
 Used to allow easy calculation of statistics
 Computer-based tools allow rapid analysis but

sometime...
Statistics Exercises
 Stat Trek
 http://stattrek.com/
 Tutorial for exercises
 Understand rationale for the selection ...
Descriptive Statistics
 Describes basic features of a data group.

 Basis of almost all quantitative data analysis
 Doe...
Descriptive Statistics
 Data Types
 Based on types of measurement
 Measurement scales can show magnitude, intervals, ze...
Descriptive Statistics
 Goal of use is to be able to summarize the data in a way

that is easy to understand
 May be des...
Descriptive Statistics
 Location Statistics
 How the data “falls”
 Examples would be statistics of central tendency
 M...
Descriptive Statistics
 Location Statistics
 Data outliers may need to be accounted for and possibly
eliminated


This ...
Descriptive Statistics
 Count Statistics
 One of the simplest means of expressing an idea
 Works for ordinal and nomina...
Descriptive Statistics
 Statistics of Scale
 Measures how much dispersal there is in a data set
(variability)
 Example ...
Descriptive Statistics
 Distribution Shape Statistics
 Determines how far from “normal” the distribution of data
is base...
Inferential Statistics
 Attempts to come to conclusions about a data set that are

not exactly stated by the data (inferr...
Inferential Statistics
 Simplest form is the comparison of average data between

two data sets to see if they are differe...
Inferential Statistics
 Most common inferential statistical tests belong to the

General Linear Model family
 Data is ba...
Inferential Statistics
 Common Linear Model tests include:
 Students t-test
 Analysis of variance (ANOVA)
 Analysis of...
Inferential Statistics
 Type of research design used also determines the
type of testing which can be done:
 Experimenta...
Sampling of Blood
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Sampling of Blood

  1. 1. Sampling
  2. 2. Sampling Theory Concepts  Population  Target Population  Accessible Population  Elements of a Population  Sampling Criteria
  3. 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. 4. Sampling Theory Concepts  Sampling Plans or Methods  Sampling Error  Random Variation  Systematic Variation
  5. 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. 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
  7. 7. Sampling Error Sampling Error Population Sample Population Mean Sample Mean
  8. 8. Sampling Theory Concepts  Sample Mortality  Subject Acceptance Rate:  Percentage of individuals consenting to be subjects  Representativeness
  9. 9. Representativeness  Needs to evaluate:  setting  characteristics of the subjects: age, gender, ethnicity, income, education  distribution of values measured in the study
  10. 10. Probability (Random) Sampling Methods  Simple Random Sampling  Stratified Random Sampling  Cluster Sampling  Systematic Sampling
  11. 11. Nonprobability (Nonrandom) Sampling  Convenience (Accidental) Sampling  Quota Sampling  Purposive Sampling  Network Sampling
  12. 12. Sample Size  Factors influencing sample size  Effect size  Type of study conducted  Number of variables studied  Measurement sensitivity  Data analysis techniques
  13. 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. 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. 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. 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. 17. Critiquing the Sample  Were the sample criteria identified?  Was the sampling method identified?  Were the characteristics of the sample described?
  18. 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?
  19. 19. Concepts of Measurement
  20. 20. Measurement Theory Concepts  Directness of Measurement  Direct measurement  Oxygen saturation, Temperature, weight  Indirect measurement  Pain, depression, coping, selfcare, self-esteem
  21. 21. Measurement Theory Concepts  Measurement Error  Scoreobs = Scoretrue + Scoreerr  Systematic error  Random error  Levels of Measurement
  22. 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.
  23. 23. Gender  1 = Male  2 = Female  (Nominal Data)
  24. 24. Likert Scale  How often do you feel in control of your life?  (1) Never  (2) Seldom  (3) Often  (4) Almost always
  25. 25. Age  How old are you?  25-34  35-44  45-54  55 or older
  26. 26. Income  1 = under Rs-35,000/ 2 = Rs-35-50,000/ 3 = Rs-50 - 100,000/-
  27. 27. What is reliability?  Reliability - is concerned with how consistently the measurement technique measures the concept of interest.
  28. 28. Types of Reliability  Stability -- is concerned with the consistency of repeated measures or test-retest reliability
  29. 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. 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.
  31. 31. Inter-rater reliability  Consistency in raters  % = # behaviors performed/total # of behaviors  Values below 0.8 are a problem
  32. 32. What is validity?  The extent to which an instrument reflects the concept being examined.
  33. 33. Measurement Strategies
  34. 34. Physiologic Measures  Physical Measurement Methods  EKG, BP  SVO2, Pulse Oximetry
  35. 35. Physiologic Measures  Chemical/biochemical  Blood glucose  SMA-24  PKU
  36. 36. Physiologic Measures  Microbiological  Smears  Cultures  Sensitivities
  37. 37. Observational Measurement  Unstructured Observations  Structured Observations  Category Systems  Checklists  Rating Scales
  38. 38. Interviews  Unstructured Interviews  Structured Interviews  Describing interview questions  Pretesting the interview protocol  Training interviewers  Preparing for an interview  Probing  Recording interview data
  39. 39. Unstructured or Open ended:  Tell me about…..  What has been your experience with....  What was it like to hear you have cancer?
  40. 40. Closed ended:  Structured  Response alternatives fixed  Which would you rather do, x or y?
  41. 41. Measurement Strategies  Questionnaires  Scales  Diaries
  42. 42. Questionnaires  Administration  In person/on phone  Self administered  Mail
  43. 43. Scales  Rating Scales  Likert Scales  Semantic Differentials  Visual Analog Scales
  44. 44. Introduction to Statistical Analysis
  45. 45. Normal Curve Mean Median Mode 68.3% 95.5% -3 -3 -2 -1 -2 -1 -2.58 -1.96 99.7% 0 0 1 1 2 2 1.96 3 3 2.58
  46. 46. Tailedness Significantly different from mean Significantly different from mean 0.025 0.025 Tail Tail Two-Tailed Test- .05 Level of Significance 0.05 Significantly different from mean One-Tailed Test- .05 Level of Significance
  47. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 59. Descriptive Statistics  Count Statistics  One of the simplest means of expressing an idea  Works for ordinal and nominal data
  60. 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. 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. 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. 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. 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. 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. 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
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