Introduction to data display Useful questions to ask when - PowerPoint PPT Presentation

Chi-square • The most commonly used statistical test. • Used to test if two or more percentages are different. • For example, suppose that in a study of 933 patients with a hip fracture, 10% of the men (22/219) of the men develop pneumonia compared with 5% of the women (36/714). • What is the probability that this could happen by chance alone? • Univariate, difference, unmatched, nominal, =>2 groups, n=>20. 64

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Fisher’s Exact Test • This test can be used for 2 by 2 tables when the number of cases is too small to satisfy the assumptions of the chi-square. – Total number of cases is <20 or – The expected number of cases in any cell is <1 or – More than 25% of the cells have expected frequencies <5. 66

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Student’s t -test • Used to compare the average (mean) in one group with the average in another group. • Is the average age of patients significantly different between those who developed pneumonia and those who did not? • Univariate, Difference, Unmatched, Interval, Normal, 2 groups. 68

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Mann-Whitney U test • Same as the Wilcoxon rank-sum test • Used in place of the Student’s t-test when the data are skewed. • A nonparametric test that uses the rank of the value rather than the actual value. • Univariate, Difference, Unmatched, Interval, Nonnormal, 2 groups. 70

Paired t-test • Used to compare the average for measurements made twice within the same person - before vs. after. • Used to compare a treatment group and a matched control group. • For example, Did the systolic blood pressure change significantly from the scene of the injury to admission? • Univariate, Difference, Matched, Interval, Normal, 2 groups. 71

Wilcoxon signed-rank test • Used to compare two skewed continuous variables that are paired or matched. • Nonparametric equivalent of the paired t-test. • For example, “Was the Glasgow Coma Scale score different between the scene and admission?” • Univariate, Difference, Matched, Interval, Nonnormal, 2 group. 72

ANOVA One-way used to compare more than 3 means from independent groups. “Is the age different between White, Black, Hispanic patients?” Two-way used to compare 2 or more means by 2 or more factors. “Is the age different between Males and Females, With and Without Pnuemonia?” 73

Tests of Between-Subjects Effects Dependent Variable: AGE Ty pe III Sum of Mean Source Squares df Square F Sig. 944 a Model 5769 4 1442 486 8664 .775 .000 SEX 1981 .683 1 1981 .683 11.904 .001 PNEUMON 1299 .320 1 1299 .320 7.8 05 .005 SEX * PNEUMON 519.282 1 519.282 3.1 19 .078 Error 1546 57.2 929 166.477 Total 5924 601 933 a. R Squa red = .974 (Adjusted R Sq uared = .974) 74

Kruskal-Wallis One-Way ANOVA • Used to compare continuous variables that are not normally distributed between more than 2 groups. • Nonparametric equivalent to the one-way ANOVA. • Is the length of stay different by ethnicity? • Analyze, nonparametric tests, K independent samples. 75

Repeated-Measures ANOVA • Used to assess the change in 2 or more continuous measurement made on the same person. Can also compare groups and adjust for covariates. • Do changes in the vital signs within the first 24 hours of a hip fracture predict which patients will develop pneumonia? • Analyze, General Linear Model, Repeated Measures. 76

Pearson Correlation • Used to assess the linear association between two continuous variables. – r=1.0 perfect correlation – r=0.0 no correlation – r=-1.0 perfect inverse correlation • Univariate, Association, Interval 77

Correlations 35-SYSTO NUMBER 43-TOT AL LIC OF NUMBER BLOOD 35-GLASG 49-DAYS COMORB OF PRESSU OW COMA IN IDITES COMPLIC RE FIRST SCALE 35-PULSE AGE HOSPITAL (0-9 ) ATIONS ER FIRST ER FIRST ER AGE Pearson Correlation 1.0 00 .088** .211** .137** .149** -.030 -.008 Sig. (2-ta il e d) . .007 .000 .000 .000 .356 .809 N 933 933 933 933 925 926 923 49-DAYS IN HOSPITAL Pearson Correlation .088** 1.0 00 .167** .453** .039 .016 .022 Sig. (2-ta il e d) .007 . .000 .000 .237 .633 .499 N 933 933 933 933 925 926 923 NUMBER OF Pearson Correlation .211** .167** 1.0 00 .222** .034 -.079* .055 COMORBIDITES (0-9 ) Sig. (2-ta il e d) .000 .000 . .000 .296 .017 .093 N 933 933 933 933 925 926 923 43-TOT AL NUMBER Pearson Correlation .137** .453** .222** 1.0 00 -.033 -.028 .046 OF COMPLICATIONS Sig. (2-ta il e d) .000 .000 .000 . .310 .393 .161 N 933 933 933 933 925 926 923 35-SYSTOLIC BLOOD Pearson Correlation .149** .039 .034 -.033 1.0 00 .043 .069* PRESSURE FIRST ER Sig. (2-ta il e d) .000 .237 .296 .310 . .196 .035 N 925 925 925 925 925 925 923 35-GLASGOW COMA Pearson Correlation -.030 .016 -.079* -.028 .043 1.0 00 -.100** SCALE FIRST ER Sig. (2-ta il e d) .356 .633 .017 .393 .196 . .002 N 926 926 926 926 925 926 923 35-PULSE FIRST ER Pearson Correlation -.008 .022 .055 .046 .069* -.100** 1.0 00 Sig. (2-ta il e d) .809 .499 .093 .161 .035 .002 . N 923 923 923 923 923 923 923 **. Correlation is signif ican t at the 0.0 1 lev el (2-ta il e d). *. Correlation is signif ican t at the 0.0 5 lev el (2-ta il e d). 78

Spearman rank-order correlation • Use to assess the relationship between two ordinal variables or two skewed continuous variables. • Nonparametric equivalent of the Pearson correlation. • Univariate, Association, Ordinal (or skewed). 79

Correlations 35-SYSTO NUMBER 43-TOT AL LIC OF NUMBER BLOOD 35-GLASG 49-DAYS COMORB OF PRESSU OW COMA IN IDITES COMPLIC RE FIRST SCALE 35-PULSE AGE HOSPITAL (0-9 ) ATIONS ER FIRST ER FIRST ER Spearman's rho AGE Correlation Coef f icient 1.0 00 .089** .158** .145** .091** -.146** -.008 Sig. (2-ta il e d) . .007 .000 .000 .005 .000 .806 N 933 933 933 933 925 926 923 49-DAYS IN HOSPITAL Correlation Coef f icient .089** 1.0 00 .142** .389** .073* .048 .037 Sig. (2-ta il e d) .007 . .000 .000 .027 .149 .268 N 933 933 933 933 925 926 923 NUMBER OF Correlation Coef f icient .158** .142** 1.0 00 .229** .037 -.091** .042 COMORBIDITES (0-9 ) Sig. (2-ta il e d) .000 .000 . .000 .257 .006 .202 N 933 933 933 933 925 926 923 43-TOT AL NUMBER Correlation Coef f icient .145** .389** .229** 1.0 00 -.014 -.076* .043 OF COMPLICATIONS Sig. (2-ta il e d) .000 .000 .000 . .676 .020 .196 N 933 933 933 933 925 926 923 35-SYSTOLIC BLOOD Correlation Coef f icient .091** .073* .037 -.014 1.0 00 .079* .080* PRESSURE FIRST ER Sig. (2-ta il e d) .005 .027 .257 .676 . .017 .015 N 925 925 925 925 925 925 923 35-GLASGOW COMA Correlation Coef f icient -.146** .048 -.091** -.076* .079* 1.0 00 -.038 SCALE FIRST ER Sig. (2-ta il e d) .000 .149 .006 .020 .017 . .252 N 926 926 926 926 925 926 923 35-PULSE FIRST ER Correlation Coef f icient -.008 .037 .042 .043 .080* -.038 1.0 00 Sig. (2-ta il e d) .806 .268 .202 .196 .015 .252 . N 923 923 923 923 923 923 923 **. Correlation is signif ican t at the .01 lev el ( 2-ta il e d). *. Correlation is signif ican t at the .05 lev el ( 2-ta il e d). 80

Summary of Inferential Tests 81

Unpaired vs. Paired • Student’s t -test • Paired t-test • Chi-square • McNemar’s test • One-way ANOVA • Repeated-measures • Mann-Whitney U test • Wilcoxon signed-rank • Kruskal-Wallis H test • Friedman ANOVA 82

Parametric vs. Nonparametric • Student’s t -test • Mann-Whitney U test • One-way ANOVA • Kruskal-Wallis test • Paired t-test • Wilcoxon signed-rank • Pearson correlation • Spearman’s r • Correlated F ratio • Friedman ANOVA (repeatedmeasures ANOVA) 83

A Good Rule to Follow • Always check your results with a nonparametric. • If you test your null hypothesis with a Student’s t -test, also check it with a Mann- Whitney U test. • It will only take an extra 25 seconds. 84

Linear Regression • Used to assess how one or more predictor variables can be used to predict a continuous outcome variable. • “Do age, number of comorbidities, or admission vital signs predict the length of stay in the hospital after a hip fracture?” • Multivariate, Association, Interval/Ordinal dependent variable. 85

a Coefficients Standardi zed Unstandardized Coeff icien Coeff icients ts Model B Std. Error Beta t Sig. 1 (Constant) -4.4 51 18.889 -.236 .814 AGE 7.1 36E-02 .045 .053 1.5 71 .117 NUMBER OF 2.6 06 .548 .159 4.7 57 .000 COMORBIDITES (0-9 ) 35-SYSTOLIC BLOOD 1.5 62E-02 .022 .024 .726 .468 PRESSURE FIRST ER 35-GLASGOW COMA 1.0 67 1.1 70 .030 .912 .362 SCALE FIRST ER 35-PULSE FIRST ER 2.5 81E-02 .047 .019 .554 .580 35-RESPIRATION -8.0 0E-02 .188 -.014 -.425 .671 RATE FIRST ER 86 a. Depe ndent Variable: 49-DAYS IN HOSPIT AL

Logistic Regression • Used to assess the predictive value of one or more variables on an outcome that is a yes/no question. • “Do age, gender, and comorbidities predict which hip fracture patients will develop pneumonia?” • Multivariate, Difference, Nominal dependent variable, not time-dependent, 2 groups. 87

1 Total number of comorbidities 2 Cirrhosis 3 COPD 4 Gender 5 Age 88

Draw Conclusions • We reject the null hypothesis. • Patients who are at high risk of developing pneumonia during their hospitalization for a hip fracture can be identified by: – total number of pre-existing conditions – cirrhosis – COPD – male gender 89

Survival Analysis • Kaplan-Meier method – Used to plot cumulative survival • Log-rank test – Used to compare survival curves • Cox proportional-hazards – Used to adjust for covariates in survival analysis 90

Thanks for your attention

Introduction to Statistics Descriptive Analysis

Review of Descriptive Stats. • Descriptive Statistics are used to present quantitative descriptions in a manageable form. • This method works by reducing lots of data into a simpler summary.

Univariate Analysis • This is the examination across cases of one variable at a time. • Frequency distributions are used to group data. • One may set up margins that allow us to group cases into categories. • Examples include: – age categories – price categories – temperature categories.

Distributions Two ways to describe a univariate distribution • a table • a graph (histogram, bar chart)

Distributions (con’t) Sex No % Men 12 60 Women 8 40 Ditribution of participants of the research methodology workshop by sex total 20 100 70% 60% 50% 40% 30% 20% 10% 0% Men Women

Distributions (con’t) Workshop participants by specialty Others Workshop participants by specialty Nursing Microbiology Env ironmental sciences Fishery Fishery Nursing Environmental Other sciences Microbiology 0% 5% 10 % 15 % 20 % 25 % 30 % 35 % 40 %

Distributions (cont.) A Frequency Distribution Table Category Percent Under 35 9 36-45 21 46-55 45 56-65 19 66+ 6

Distributions (cont.) A Histogram 50 40 30 Percent 20 10 0 Under 36-45 46-55 56-65 66+ 35

Central Tendency • An estimate of the “center” of a distribution • Three different types of estimates: – Mean – Median – Mode