1、A Statistical Sampler,Dr. Ed Greenberg ASU College of Nursing Center for Research & ScholarshipAugust 2005,To understand Gods thoughts we must study statistics, for these are the measure of His purpose. Florence Nightingale,Statistical Terms Crossword,To behold is to look beyond the fact; to observe
2、, to go beyond the observation. Look at the world of people, and you will be overwhelmed by what you see. But select from that mass of humanity a well-chosen few, and observe them with insight, and they will tell you more than all the multitudes together., Paul D. Leedy From his book, “Practical Res
3、earch,” 1993,Some factors to consider: Research design Number of groups Number of variables Level of measurement (nominal, ordinal, interval/ratio),Choosing the Appropriate Statistic,Statistical Methods,Descriptive Statistics,Inferential Statistics,While the individual man is an insoluble puzzle, in
4、 the aggregate he becomes a mathematical certainty. You can, for example, never foretell what any one man will be up to, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. So says the statistician. Arthur Conan Doyle,Some Statistic
5、s-Related Web Sites,Types of Statistics,Descriptive statistics characterize the attributes of a set of measurements. Used to summarize data, to explore patterns of variation, and describe changes over time.Inferential statistics are designed to allow inference from a statistic measured on sample of
6、cases to a population parameter. Used to test hypotheses about the population as a whole.,Requisite Conditions for Causation,In order for X to cause Y: X & Y must be associated X must precede Y in timeX contains unique information about Y that is not articulated elsewhere,The invalid assumption that
7、 correlation implies cause is probably among the two or three most serious and common errors of human reasoning. Stephen Jay Gould, The Mismeasure of Man,Smoking is one of the leading causes of statistics. Fletcher Knebel,Randomization,Random selection is how you draw the sample for your study from
8、a population. This is related to the external validity, or generalizability, of your results.,Randomization,Random assignment is how you assign your sample to groups or treatments in your study. This is related to internal validity. Random assignment is a required feature of a true experimental desi
9、gn.,Randomization,Variables,Variables are qualities, properties, or characteristics of persons, things, or situations that change or vary and are manipulated, measured, or controlled in research.More simply stated: Variables are things that we measure, control, or manipulate in research.,Types of Va
10、riables,Independent variables are manipulated or varied by the researcher, for example, intervention or treatment. Dependent variables are the responses, outcomes, etc. that are measured by the researcher. Extraneous variables are not part of the research design, but may have an impact on the depend
11、ent variable(s).,Levels of Measurement,NominalOrdinalIntervalRatio,Nominal-Level Variables,Data are organized into categories Categories have no inherent order Categories are exclusive Categories are exhaustive Examples are sex, ethnicity, marital status,Examples of Nominal-Level Questions,Do you ha
12、ve a loss of appetite?Do you smoke a lot? What is your ethnicity?,Ordinal-Level Variables,Categories can be ranked in order Intervals between categories may not be equal Examples are socioeconomic status, level of education attained (elementary school, high school, college degree, graduate degree),E
13、xamples of Ordinal-Level Questions,Would Intervention X be your 1st, 2nd, or 3rd choice of treatment for Condition Y? 1 First choice 2 Second choice 3 Third choiceBeck Depression Scale Sadness Item 0 I do not feel sad 1 I feel sad 2 I am sad all the time and I cant snap out of it 3 I am so sad or un
14、happy that I cant stand it,Interval-Level Variables,Distances between levels of the scale are equalAssumed to be a continuum of valuesAn example is temperature (measured in Fahrenheit or Centigrade),Examples of Interval-Level Variables,IQ scoresGRE scoresComposite scores of multi-item scales,Ratio-L
15、evel Variables,Equal spacing between intervals Have an identifiable absolute zero point Examples are weight, length, volume, and temperature (measured in Kelvin) In statistical analysis, typically there is no distinction made between interval level and ratio level,Same Variable, Different Levels of
16、Measurement,Interval level: What is your age in years? _Ordinal level: What is your age group? 18 years or younger 19-44 years 45 years or older,Importance of Levels of Measurement,Level of measurement is associated with the type of statistical method used. Higher levels of measurement provide more
17、information than do lower levels. In general, you should use the highest level of measurement possible. For example, measure actual age in years, not in age groups.,Some Major Types of Analyses,DescriptionRelationships among variablesDifferences between groups or treatments,There are three kinds of
18、lies lies, damned lies and statistics. Benjamin Disraeli,Measures of Central Tendency,Example of Central Tendency,15,20,21,20,36,15,25,1515,15,15,20,20,21,25,36,Example of Mode,Example of Median,Example of Mean,MEAN,I abhor averages. I like the individual case. A man may have six meals one day and n
19、one the next, making an average of three meals per day, but that is not a good way to live. Louis D. Brandeis,Measures of Variation,Curves of Distribution,Normal Distribution,Normal Curve,Example: Number of categories,Example of Range,Example of Standard Deviation,Measures of Relationships,Statistic
20、s have shown that mortality increases perceptibly in the military during wartime. Robert Boynton,Example of Spearman Correlation,Scatterplot of Self Esteem By Height,Relationship Between Two Variables,Positive Correlation,Negative Correlation,Curvilinear Relationship,Example of Pearson Correlation,V
21、ariable HEIGHT is measured in inches Variable ESTEEM is the average of 5 items measured on a four-point scale (1-4),Example of Chi-Square Test,A Statistical Sampler,Take a 15 minute break!,Statistical thinking will one day be as necessary a qualification for efficient citizenship as the ability to r
22、ead and write. H.G. Wells,Some Terminology,Descriptive statistics Statistics that allow the researcher to organize or summarize data to give meaning or facilitate insight. Inferential statistics Methods that allow inferences to be made from a sample to a population Hypothesis testing A statistical t
23、est of an expected relationship between two or more variables,Statistical inference is the process of estimating population parameters from sample statistics.,Statistical inference,Are males taller than females?,Statistical inference may be used to ascertain whether differences exist between groups.
24、,Is there a relationship between age and self-esteem? Does this relationship differ for males and females?,. or whether there is a relationship among variables.,Examples of Some Commonly Used Statistical Tests,Some Commonly-Used Multivariate Methods,Analysis of Variance and Covariance Tests for diff
25、erences in group means Multiple Regression Analysis Estimates the value of a dependent variable based on the value of several independent variables,Some Commonly-Used Multivariate Methods,Reliability analysis Assesses the consistency of multi-item scales Factor Analysis Examines the relationships am
26、ong variables and reveals related sets of variables (constructs) Structural Equation Modeling Methods for testing theories about the relationships among variables,Hypothesis Testing Decision Chart,Decision,Reality,Males and females are asked a question that is measured on a five-point Likert scale:,
27、Do males and females differ in their response to this question?,Difference between two group means: The independent samples t-test,25 males and 25 females answered our question. Here is how they responded:,First we enter the data into SPSS.,Then we invoke the Independent Samples T-Test procedure.,We
28、 can use the SPSS statistical package to run an independent samples t-test:,We tell SPSS which is the dependent variable and which is the independent variable to use in performing the t-test:,The t-test reveals a significant difference between males & females:,SPSS gives us summary statistics for ea
29、ch group:,Reporting Results,See the guidelines in the APA Publication Manual, Fifth Edition The manual provides very specific instructions for presenting statistical results. Example: The mean exercise score for females, 3.24, was significantly higher than for males, 2.56, t(48) = 2.12, p = .032.,Do
30、 the educational levels of males and females differ?,For each group, the Sum and mean of ranks Is computed.,The test statistics suggest that males and females education levels do not differ in this population.,Because the dependent variable (education level) is ordinal-level, we use the Mann-Whitney
31、 U Test.,Difference between two groups over time: Repeated measures analysis of variance,Asthmatic elementary school children are given training intended to reduce the number of asthmatic episodes. A control group is not given the training. Childrens school attendance is monitored during the month b
32、efore training is given to the intervention group, and during each of the two months following the intervention.Does the asthma training intervention improve the school attendance relative to the control group?,The experimental design:,First we enter the data into SPSS.,We can use the SPSS statistic
33、al package to perform a repeated measures ANOVA on the sample data:,Then we request the General Linear Models procedure for Repeated Measures.,And here are the results involving group:,Here are the results involving time:,This is a plot of the group means over time,The General Social Survey (GSS) is
34、 an “almost annual” personal interview survey of U.S. households conducted by the National Opinion Research Center. In the 1993 GSS, approximately 1500 adult respondents (18 years or older) were asked about their music preferences.Just for the fun of it, I performed a factor analysis on the music qu
35、estions to see if we could identify a pattern of underlying dimensions, or factors, in the data.,Factor Analysis Example,Im going to read you a list of some types of music.Can you tell me which of the statements on this card comes closest to your feeling about each type of music. (HAND CARD “B” TO R
36、ESPONDENT.) Lets start with big band music. Do you like it very much, like it, have mixed feelings, dislike it, dislike it very much, or is this a type of music that you dont know much about?,1 Like Very Much 2 Like It 3 Mixed Feelings 4 Dislike It 5 Dislike Very Much 8 DK Much About It 9 NA,RESPONS
37、E CARD “B”,Folk Jazz Opera Rap Heavy Metal,Big Band Bluegrass Country/Western Blues or R & B Broadway Musicals Classical,MUSIC GENRES,Factor Analysis Results,The factor analysis revealed four factors in the music preference items. The varieties of music were associated with the factors as shown belo
38、w:,FACTORS,MEASURED VARIABLES,Factor Analysis Results,Do not put faith in what statistics say until you have carefully considered what they do not say. William W. Watt,More Cool Statistics Web Sites,Rice Virtual Lab in Statistics http:/www.ruf.rice.edu/lane/rvls.html,Multimedia Resources for Statist
39、ics Students http:/research.ed.asu.edu/msms/multimedia/multimedia.cfm,Statistics and Statistical Graphics Resources http:/www.math.yorku.ca/SCS/StatResource.html,Without data, all you are is just another person with an opinion. Unknown,Statistical Power Analysis,Prior to conducting a study, it is ad
40、visable to conduct a statistical power analysis.Power is the probability that a statistical test will detect a significant effect that exists.The power analysis will suggest an adequate sample size for the study.,Four parameters related to the power of a test:,Significance level (a)Sample size (n)Ef
41、fect size (ES)Power (1 - b),Relationship between power and other parameters:,As significance level (a) decreases numerically, power decreases As effect size increases, power increases As sample size increases, power increases,Conventions commonly used:,Examples of Effect Size:,Testing a mean against
42、 a true alternative: 1 slightly larger than 0 (“small effect”),0,Critical value,1,Region of nonrejection,Region of rejection,Testing a mean against a true alternative: 1 quite a bit larger than 0 (“large effect”),0,Critical value,Region of nonrejection,Region of rejection,1,Relationship Between Alph
43、a(a), Sample Size (n), and Power (1-b),The Power Analysis “Bible”,There are a lot of statistical power analysis resources (including interactive “power calculators”) on the World Wide Web.,For example, see the StatP web site at: http:/ using a WWW search engine like Yahoo or Google, use the search s
44、tring: statistical power analysis,Getting Help,For course assignments involving statistics, see your instructor or teaching assistant. For help related to a masters thesis or applied project, see your faculty advisor. Your instructor or advisor may confer with or make an appointment as needed with a
45、 statistician in the College of Nursing Center for Research and Scholarship.,Getting Help,The Statistics Hotline is sponsored by a joint effort of the ASU Committee on Statistics, the Department of Mathematics and Statistics, and the Division of Graduate Studies. Its services are available to anyone
46、 affiliated with ASU and needs assistance with their ASU-related research.,http:/www.asu.edu/graduate/statistics/hotline/,An approximate answer to the right question is worth a great deal more than a precise answer to the wrong question. The first golden rule of mathematics, sometimes attributed to John Tukey,Statistical Terms Crossword Solution,This presentation is available online in Microsoft PowerPoint format at:http:/www.public.asu.edu/eagle/stat_sampler.ppt,On the Web,
