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# Sampling, measurement, and stats(2013)

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### Sampling, measurement, and stats(2013)

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 forinclusion or exclusion ofmembers in the targetpopulation 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 orMethods Sampling Error Random Variation Systematic Variation
5. 5. Sampling Error Random Variation The expected difference in values thatoccurs when different subjects fromthe same sample are examined. Difference is random because somevalues will be higher and others lowerthan the average population values.
6. 6. Sampling Error Systematic Variation (Bias) Consequence of selectingsubjects whose measurementvalues differ in some specificway from those of thepopulation. These values do not varyrandomly around thepopulation mean
7. 7. Sampling ErrorSampling ErrorPopulation SamplePopulationMeanSampleMean
8. 8. Sampling Theory Concepts Sample Mortality Subject Acceptance Rate: Percentage of individualsconsenting to be subjects Representativeness
9. 9. Representativeness Needs to evaluate: setting characteristics of the subjects:age, gender, ethnicity, income,education distribution of valuesmeasured 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 adultsscheduled for first time elective CABGsurgery without cardiaccatheterization, who had not hadother major surgery within theprevious year, and who were nothealth professionals met the studycriteria and were randomly assignedto one of two instruction conditions...
15. 15. Example Sample Based on a formulation of 80% power, amedium critical effect size of 0.40 for each ofthe dependent variables, and a significancelevel of .05 for one-tailed t-tests means, asample size of 40 was deemed sufficient totest the study hypotheses...
16. 16. Example Sample The study included a conveniencesample of 32 post-op Lung Cancerpatients. A power analysis wasconducted to determine size. Aminimum of 27 subjects was necessaryto achieve the statistical power of 0.8and a medium (0.5) effect size at the0.05 level of significance....Thesubjects were 25 men and 7 womenwith an age range from 18-58 years(mean = 32.74)....
17. 17. Critiquing the Sample Were the sample criteriaidentified? Was the sampling methodidentified? Were the characteristics ofthe sample described?
18. 18. Critiquing the Sample Was the sample size identified? Was the percent of subjectsconsenting to participateindicated? Was the sample mortalityidentified? Was the sample size adequate?
19. 19. Concepts ofMeasurement
20. 20. Measurement TheoryConcepts Directness of Measurement Direct measurement Oxygen saturation,Temperature, weight Indirect measurement Pain, depression, coping, self-care, self-esteem
21. 21. Measurement TheoryConcepts 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- gendernumbers) Ordinal categories with order, but intervals not necessarilyequal and no zero (ex – pain) Interval equal intervals, but no true zero (ex- temp scales) Ratio equal intervals with a true zero. These are realnumbers, 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 ofyour life? (1) Never (2) Seldom (3) Often (4) Almost always
25. 25. Age How old are you (years)? What LOM?
26. 26. Age How old are you? 25-34 35-44 45-54 55 or older What LOM?
27. 27. Income 1 = under \$35,000 2 = \$35-50,000 3 = \$50 - 100,000 LOM?
28. 28. What is reliability? Reliability - is concernedwith how consistently themeasurement techniquemeasures the concept ofinterest.
29. 29. Types of Reliability Stability -- isconcerned with theconsistency ofrepeated measures ortest-retest reliability
30. 30. Types of Reliability Equivalence -- is focusedon comparing two versionsof the same instrument(alternate forms reliability)or two observers (interraterreliability) measuring thesame event.
31. 31. Types of Reliability Homogeneity -- addresses thecorrelation of various itemswithin the instrument orinternal consistency;determined by split-halfreliability or Cronbach’s alphacoefficient.
32. 32. Inter-rater reliability Consistency in raters % = # behaviorsperformed/total # ofbehaviors Values below 0.8 are aproblem
33. 33. What is validity? The extent to which aninstrument reflects theconcept being examined.
34. 34. MeasurementStrategies
35. 35. Physiologic Measures Physical MeasurementMethods EKG, BP SVO2, Pulse Oximetry
36. 36. Physiologic Measures Chemical/biochemical Blood glucose SMA-24 PKU
37. 37. Physiologic Measures Microbiological Smears Cultures Sensitivities
38. 38. Observational Measurement Unstructured Observations Structured Observations Category Systems Checklists Rating Scales
39. 39. Interviews Unstructured Interviews Structured Interviews Describing interview questions Pretesting the interview protocol Training interviewers Preparing for an interview Probing Recording interview data
40. 40. Unstructured or Open ended: Tell me about….. What has been your experiencewith.... What was it like to hear youhave cancer?
41. 41. Closed ended: Structured Response alternatives fixed Which would you rather do,x or y?
42. 42. Measurement Strategies Questionnaires Scales Diaries
44. 44. Scales Rating Scales Likert Scales Semantic Differentials Visual Analog Scales
45. 45. Introductionto StatisticalAnalysis
46. 46. Normal Curve-3-3MeanMedianMode-2-2-1-10011223368.3%95.5%99.7%-2.58 -1.96 1.96 2.58
47. 47. TailednessOne-Tailed Test- .05 Level of SignificanceTwo-Tailed Test- .05 Level of SignificanceSignificantly differentfrom meanSignificantly differentfrom meanSignificantly differentfrom mean0.025 0.0250.05TailTail
48. 48. Process for Quantitative DataAnalysis• Preparation of the Data for Analysis• Description of the Sample• Testing the Reliability of the Instrumentsfor the Present Sample• Testing Comparability of Design Groups• Exploratory Analysis of Data• Confirmatory Analyses Guided byObjectives, Questions, or Hypotheses• Post Hoc Analyses
49. 49. Cleaning Data Examine data Cross-check every piece of data with theoriginal data If file too large, randomly check foraccuracy Correct all errors Search for values outside the appropriaterange of values for that variable.
50. 50. Missing Data Identify all missing data points Obtain missing data if at all possible Determine number of subjects with datamissing on a particular variable Make judgement - are there enoughsubjects with data on the variable towarrant using it in statistical analyses?
51. 51. Transforming Data Transforming skewed data so that it is linear(required by many statistics). Squaring each value calculating the square root of eachvalue
52. 52. Calculating Variables Involves using values from two ormore variables in your data set tocalculate values for a new variableto add to the data set. Summing scale values to obtaina total score Calculating weight by heightvalues to get a value for BodyMass Index
53. 53. Statistical Tools Used to allow easy calculation of statistics Computer-based tools allow rapid analysis butsometimes too easy Must still know what each type of test is for and how touse them Don’t fall into the trap of using a test just because it iseasy to do now Many papers appearing with questionable tests justbecause a computer program allows the calculation
54. 54. 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 advantagesof 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
55. 55. Descriptive Statistics Describes basic features of a data group. Basis of almost all quantitative data analysis Does not try to reach conclusions (inferences), onlydescribe. Provide us with an easier way to see and quickly interpretdata
56. 56. Descriptive Statistics Data Types Based on types of measurement Measurement scales can show magnitude, intervals, zero point, anddirection Equal intervals are necessary if one plans any statistical analysis ofdata 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 zeropoint Nominal data in non-numeric (not orderable) whereasordinal data is numeric and can be ordered but not basedon continuous scale of equal intervals
57. 57. Descriptive Statistics Goal of use is to be able to summarize the data in a waythat 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
58. 58. Descriptive Statistics Location Statistics How the data “falls” Examples would be statistics of central tendency Mean Average of numerical data Σ x / n Median Midpoint of data values Value of data where 50% of data values is above and 50% below (ifnumber 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
59. 59. Descriptive Statistics Location Statistics Data outliers may need to be accounted for and possiblyeliminated This can be done by trimming or weighting the mean toeffectively eliminate the effect from outliers
60. 60. Descriptive Statistics Count Statistics One of the simplest means of expressing an idea Works for ordinal and nominal data
61. 61. 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 deviationgreatly, so try to avoid their use if there are lots of outliersthat can not be weighted out
62. 62. Descriptive Statistics Distribution Shape Statistics Determines how far from “normal” the distribution of datais 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
63. 63. Inferential Statistics Attempts to come to conclusions about a data set that arenot exactly stated by the data (inferred) Many tests use probability to help determine if datapoints to a likely conclusion. Often used to compare two groups of data to see if theyare ‘statistically different’ Often used to decide whether or not a conclusion one istrying to reach from the data set is reliable (withinstatistical probability)
64. 64. Inferential Statistics Simplest form is the comparison of average data betweentwo data sets to see if they are different Students t-test is often used to compare differencesbetween 2 groups Usually one control group and one experimental Should be only one altered variable in experimentalgroup
65. 65. Inferential Statistics Most common inferential statistical tests belong to theGeneral Linear Model family Data is based on an equation in which a wide variety ofresearch outcomes can be described Problems with these types of analysis tools usually comesfrom the wrong choice of the equation used Errors in the wrong equation used can result in the dataconclusions being biased one way or the other, leading toaccepting or rejecting the null hypothesis wrongly
66. 66. Inferential Statistics Common Linear Model tests include: Students t-test Analysis of variance (ANOVA) Analysis of covariance (ANCOVA) Regression analysis Multivariate factor analysis
67. 67. Inferential Statistics Type of research design used also determines thetype of testing which can be done: Experimental analysis Usually involves comparison of one or more groups against acontrol, and thus t-test or ANOVA tests are the most commonlyused Quasi-experimental analysis Typically lack a control group, and thus the random analysis that isusually used to assign individuals to groups These types of analysis are much more complex to compensate forthe random assignments