Index

Note: Page numbers in bold type refer to figures; those in italic refer to tables or boxed material.

A bin widths, 10 absolute risk difference (ARD), 26 blocked randomization, 42 absolute risk reduction (ARR), 26 Bonferroni correction, 92, 149 absolute risks, 28 bootstrap, 56 accuracy, 42 box-whisker plot, 7, 8, 10 alternative hypothesis, 65 C B case–control study, 31–3, 145–6 bar charts, 8–9, 10 categorical variables, 9 bar chart/histogram distinction, 9 binary, 1, 2 see also binary Bayes factors, 69 variables Bayes’ Theorem, 68 nominal, 1, 2 binary data, 24–35 ordinal, 1, 2 common questions, 35–6 censored observation, 133, 134, binary variable, 2 136, 141 binary variables, summarizing central limit theorem, 43–4 relationship between CHI, 155, 167 examples chi-squared (χ2) test, 86–99 hay fever and eczema, 30–1 common questions, 98 post-hemorrhagic ventricular comparing proportions, 90–2 dilatation (PHVD), 28, 29 extensions, 98 number needed to harm (NNH), formula appreciation, 98–9 26–7, 35 fourfold tables, 89–90 number needed to treat (NNT), McNemar’s test see McNemar’s COPYRIGHTED26–7, 35 MATERIALtest odds ratios see also odds ratios observed/theoretical distribution (OR) comparision, 95–6 and case–control studies, 31–3 in OpenEpi, 159–61, 160, 161, 162 paired alternatives, 33–5 procedure, 87–9 relative risks versus, 29–31 reading/reporting, 99 one variable, 24–5 splitting, 92–3 risks, 29–31 see also risks trends, 93–5 two variables, 25–9 Yates’ correction, 90

183 184 Index cluster study, 144 dynamite plunger plot, 9 coeffi cient of variation (CV%), 21 histograms, 8, 8, 9 , 145 bar chart/histogram distinction, 9 computer software see software in papers, 10–11 confi dence interval (CI), 50–2, 56 stem and leaf plots, 3–4, 4 for an , 54–5 data dredging, 70 bootstrap, 56 data summary, 1–11 common questions, 56–8 common questions, 9–10 for a difference in proportions or data types, 1, 1–3 percentages, 54 , 4–5, 5 range, 4 large sample differences, 52–3 variation measurement, 5–6 small sample, 73–4 see also data display percentages or proportions, 53–4 dependent variable, 120, 121, 123 reading and reporting, 57 design, 143–6 for a , 56 matched parallel, 144 confi rmatory hypotheses, 148 parallel group, 144 continuous variable, 1, 1, 2 quasi-experimental, 145 correlation, 119–25 reading/reporting, 145 causality, 123 see also, study coeffi cient, 119 diagnostic tests, 102–9 calculation, 121–3 diagnosis/screening, 107–8 common questions, 129–30 likelihood ratio, 106 formula appreciation, 131 in OpenEpi, 161, 162, 163 reading/reporting, 131 prevalence, 103, 105, 105, 106, 107 scatter diagrams, 119–21 reading/reporting, 109 signifi cance test, 123–4 ROC curve, 107, 108 Spearman’s rank, 124–5 sensitivity, 103–4, 104, 105, 106, Cox regression, 140 107, 108 cross-sectional study, 146 specifi city, 104, 104, 105, 106, 107, 108 D standard table, 102 data difference binary, 24–35 ranked see rank score tests grouped, standard deviation t tests, 72–3 from, 18, 18–19 distribution paired, 13, 97–8, 149 normal see normal distribution transformation, 19, 19–20, 20 skewed see skewed distribution geometric mean, 20 dot plots, 7, 20 types, 1–3 double blinded study, 144 categorical variables, 1, 2 dynamite plunger plot, 9 cut-off points, 2 quantitative variables, 1, 1–2 E ungrouped, standard deviation empirical normal range, 50 from, 16–17, 17 equation, regression, 125–9 data display error bar charts, 8–9, 10 type I, 60–1 box–whisker plot, 7, 8 type II, 65–6 common questions, 9–10 exploratory hypotheses, 148 Index 185

F and t test, 117 Fisher’s exact test, 90, 159 Mantel–Haenszel method, 94 common questions, 98–9 matched parallel design, 144 mid P-value, 90, 98 McNemar’s test, 97–8 reading and reporting, 99 in OpenEpi, 162 fourfold tables, chi-squared (χ) test, mean 89–90 confi dence interval for, 72–4 defi nition, 13 G standard error of, 52 Gaussian distribution see normal and standard deviation, 13–15 distribution standard error of, 43–5 geometric mean, 20 measured variables, 1 measurement error, 21 H measure of location see mean, median histograms, 8 median bar chart/histogram distinction, 9 comparison by non-parametric bin widths, 10 tests, 116–17 group requirement in a, 10 data summary, 4, 4–5 hypothesis midpoint see median alternative, 65 mid P-value, 90, 98 confi rmatory, 148 mode, 21 null, 53, 60–1 multiple regression, 129 study, 65

I N incidence rate, 25 nominal variables, 2, 66 incidence rate ratio (IRR), 27 non-parametric test, 110, 116–17 independent variable, 120, 121 non-random samples inference, 68–9 common questions, 46–7 interquartile range (IQR), 5 problems with, 45–6 data display in papers, 10 reading and reporting populations and samples, 47 K normal distribution, 14–15, 15, 180 Kaplan–Meier survival curve, 133–4 curve, 14, 15 normal range, 50 L null hypothesis least squares estimate, 127 and alternative hypotheses, 66 likelihood ratio of a diagnostic test, and type I error, 60–1 106 number needed to harm (NNH), Liket scale, 2 26–7, 35 logged data, 19, 20, 20, 79 number needed to treat (NNT), log transform, 20 26–7, 35 logistic regression, 98 log rank test, 137–40 O odds, 25 M odds ratio (OR), 28 Mann–Whitney U test, 113–16 and case–control studies, 31–3 comparing /, 116–17 confi dence interval for, 54–5 in OpenStat, 162, 163, 165 in OpenEpi, 157, 158 in , 163, 165 versus relative risks, 29–31, 35 186 Index one-sided test, 67–8 probability one way , 83 Fisher’s exact test, 90 OpenEpi, 27, 154, 155, 167 P value, 63–5 χ2 test, 159–61, 160, 161, 162 statement of, 49–50 diagnostic tests in, 161, 162, 163 proportional hazards assumption, odds ratio in, 157, 158 survival analysis, 137 risks analysis in, 157, 157 proportions OpenOffi ce Calc, 153, 167 χ2 comparisons, 90–2 OpenStat, 154, 155, 167 confi dence interval for a comparison of two means, 158, difference in, 54 158–9, 159 standard error of, 45 kurtosis, 156 standard error of difference Mann–Whitney U test, 162, 163, between, 53–4 165 prospective studies, 143 mean, 157 P-value, 63–5 regression data analysis, 163, common questions, 66–9 164, 166, 166 confi dence intervals, and skewness, 156 clinically important survival analysis, 166, 166 results, 64–5 Wilcoxon test, 162, 163, 164 mid P-value, 90, 98 ordinal variables, 1, 2 one-sided P-value, 64, 69, 90 outliers, 5, 83 reading/reporting, 69–70

P Q paired alternatives, 33–5 quantitative variables paired data, 13, 97–8, 149 continuous, 1, 2 paired samples, rank score tests, counted, 1, 1, 2 110–13 measured, 1, 1, 2 Wilcoxon test, 111–13 quartiles, 5 parallel group design, 144 quasi-experimental design, Pearson’s correlation coeffi cient, 145 119–23 percentages R confi dence interval for a randomization, 42–3, 143–4 difference in, 54 random sampling, 40–1, 148 standard error of difference stratifi ed, 41 between, 45, 53–4 systematic, 41 pie charts, 11 rank score tests, 110 populations common questions, 116–17 common questions, 46–7 paired samples, 110–13 defi ned, 39 Wilcoxon test, 111–13 parameter, 39–40 reading/reporting, 117 reading and reporting, 47 unpaired samples, 113–16 samples, 40–1 Mann–Whitney U test, positive predictive value (PPV), 105 113–16 power, of study, 65 rate, 24 PPV see positive predictive value (PPV) recall bias, 146 precision, 42 receiver operating characteristics prevalence, 24 (ROC) curve, 107, 108 diagnostic tests, 103, 105, 105, reference ranges, 49–50 106, 107 confi dence interval, 56–7 Index 187 regression correlation, 123–4 analysis in OpenStat, 163, 164, difference in two proportions, 53–4 166, 166 single blind study, 144 assumption testing, 128 SISA, 155 common questions, 129–30 skewed distribution, 19 equation, 125–9 software least squares estimate, 127 CHI, 155 line, 127–9 OpenEpi see OpenEpi multiple, 129 OpenOffi ce Calc, 153 reading/reporting, 131 OpenStat see OpenStat relative risk reduction (RRR), 27 R program, 155, 167 relative risks versus odds ratios, 29–31 SISA, 155 risks , 153 absolute risk difference (ARD), 26 Websites, 167 absolute risk reduction (ARR), 26 Xycoon, 155 analysis in OpenEpi, 157, 157 Spearman’s rank correlation, ratio or relative risk (RR), 27 124–5 ROC see receiver operating specifi city, diagnostic tests, 104, 104, characteristics (ROC) curve 105, 106, 107, 108 R program, software, 155 splitting, χ2 test, 92–3 Wilcoxon test, 163, 164, 165 standard deviation, 14 calculation of, 17 S from count data, 18 sample size, 146–8 from grouped data, 18–19 samples, 40–6 between subjects and within accuracy, 42 subjects, 21 central limit theorem, 43–4 from ungrouped data, 16–17 convenience, 45 standard error (SE) mean common questions, 66–9 confi dence interval, 52–3, of difference between means, 52 72–4 of difference between percentages differences see t test or proportions, 53–4 standard error of, 43–5 of the mean, 43–5 non-random, problems, 45–6 of a proportion or a percentage, 45 paired, 110–13 reading and reporting P-values, population mean differences 69–70 see t test Stata, 153, 167 precision, 42 stem and leaf plots, 3–4, 4 random, 40–1, 148 stratifi ed random sampling, 41 reading/reporting, 47 Student’s t test see t test response rate, 46 study stratifi ed random, 41 carryover effect, 144 systematic random, 41 case–control, 145–6 unbiased, 42 cluster, 144 unpaired, 113–16 cohort, 145 variation between, 43 control, 143, 144 scatter diagrams, 119–21, 122, 127 cross-sectional, 146 sensitivity, diagnostic tests, 103–4, double blinded, 144 104, 105, 106, 107, 108 placebo effects, 144 sequential study, 144 prospective, 143 signifi cance test randomization, 143–4 188 Index

Study (contd) formula appreciation, 84 randomized controlled trial, 143 and Mann-Whitney U test, 117 reading/reporting, 151 reading and reporting, 84 recall bias, 146 signifi cance test of correlation, sample size, 146–8 123–4 sequential, 144 unequal standard deviations, 79–80 statistical test selection, 148–51, Tukey’s hinges, 6 149, 150 two sided tests, 67–8 study hypothesis, 65 type I error summary see also interquar- and null hypothesis, 60–1 tile range (IQR); median relation with type II error, 66 for binary data from a type II error, 65 non-matched study relation with type I error, 66 common questions, 35–6 reading and displaying U summary statistics, 36 unbiased samples, 42 defi ned, 13 unpaired samples reading and displaying, 23 rank score tests, 113–16 survival analysis Mann-Whitney U test, 113–16 censored observation, 133, 134, t test, 75–78 136, 141 common questions, 141 V Kaplan–Meier survival curve, variables 133–4 correlation/causality, 123 long rank test, 137–40 dependent, 120, 121, 123 in OpenStat, 166 independent, 120, 121 proportional hazards input, 150 assumption, 137 outcome, 150–1 reading/reporting, 141 test selection, 149 survival curve calculation, 134–6 variance, 16–17 systematic random sampling, 41 variation, coeffi cient of (CV%), 21 variation measurement, 5–6 T data summary, 5–6 testing interquartile range (IQR), 5 for a difference in two outliers, 5 proportions, 62–3 quartiles, 5 for differences of two means, samples, 43 61–2 test selection, 148–51, 149, 150 W trends, χ2 test, 93–5 Welch test, 79 t test Wilcoxon test, 111–13 common questions, 83–4 in OpenStat, 162, 163, 164 confi dence interval for the mean in R, 163, 164, 165 from a small sample, 73–4 difference between means of X paired samples (paired t test), Xycoon software, 155, 167 80–2 difference between means of two Y samples, 75–8 Yates’ correction, χ2 test, 90 difference of sample mean from population mean, 74–5