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Sampling

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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

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Sampling Error PopulationSample PopulationMean SampleMean

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Sampling Theory Concepts Sample Mortality Subject Acceptance Rate: Percentage of individuals consenting to be subjects Representativeness

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Needs to evaluate: setting characteristics of the subjects: age, gender, ethnicity, income, education distribution of values measured in the study

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Probability (Random) Sampling Methods Simple Random Sampling Stratified Random Sampling Cluster Sampling Systematic Sampling

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Nonprobability (Nonrandom) Sampling Convenience (Accidental) Sampling Quota Sampling Purposive Sampling Network Sampling

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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

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Physiologic Measures Chemical/biochemical Blood glucose SMA-24 PKU

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Physiologic Measures Microbiological Smears Cultures Sensitivities

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Observational Measurement Unstructured Observations Structured Observations Category Systems Checklists Rating Scales

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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?

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Measurement Strategies Questionnaires Scales Diaries

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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