Sampling Theory Concepts Population Target Population Accessible Population Elements of a Population Sampling Criteria
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
Sampling Theory Concepts Sampling Plans orMethods Sampling Error Random Variation Systematic Variation
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.
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
Sample Size Factors influencing sample size Effect size Type of study conducted Number of variables studied Measurement sensitivity Data analysis techniques
Power Analysis Standard Power of 0.8 Level of Significance alpha = .05, .01, .001 Effect Size .2 Small; .5 Medium; .8 Large Sample Size
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...
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...
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)....
Critiquing the Sample Were the sample criteriaidentified? Was the sampling methodidentified? Were the characteristics ofthe sample described?
Critiquing the Sample Was the sample size identified? Was the percent of subjectsconsenting to participateindicated? Was the sample mortalityidentified? Was the sample size adequate?
Measurement TheoryConcepts Directness of Measurement Direct measurement Oxygen saturation,Temperature, weight Indirect measurement Pain, depression, coping, self-care, self-esteem
Measurement TheoryConcepts Measurement Error Scoreobs = Scoretrue +Scoreerr Systematic error Random error Levels of Measurement
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.
Interviews Unstructured Interviews Structured Interviews Describing interview questions Pretesting the interview protocol Training interviewers Preparing for an interview Probing Recording interview data
Unstructured or Open ended: Tell me about….. What has been your experiencewith.... What was it like to hear youhave cancer?
Closed ended: Structured Response alternatives fixed Which would you rather do,x or y?
Normal Curve-3-3MeanMedianMode-2-2-1-10011223368.3%95.5%99.7%-2.58 -1.96 1.96 2.58
TailednessOne-Tailed Test- .05 Level of SignificanceTwo-Tailed Test- .05 Level of SignificanceSignificantly differentfrom meanSignificantly differentfrom meanSignificantly differentfrom mean0.025 0.0250.05TailTail
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
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.
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?
Transforming Data Transforming skewed data so that it is linear(required by many statistics). Squaring each value calculating the square root of eachvalue
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
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
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
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
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
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
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
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
Descriptive Statistics Count Statistics One of the simplest means of expressing an idea Works for ordinal and nominal data
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
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
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)
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
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
Inferential Statistics Common Linear Model tests include: Students t-test Analysis of variance (ANOVA) Analysis of covariance (ANCOVA) Regression analysis Multivariate factor analysis
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