Statistical Editor, Health & Social Care in the Community 26 March 2008 Statistical presentation in international scientific publications 4. Reporting numbers Malcolm Campbell Lecturer in Statistics, School of Nursing, Midwifery & Social Work, The University of Manchester Statistical Editor, Health & Social Care in the Community Statistical presentation - 4. Reporting numbers

4. Reporting numbers Contents 26 March 2008 4. Reporting numbers Contents 4.1 Introduction 4.2 Reporting numbers and percentages 4.3 Reporting statistics 4.4 Reporting test results 4.5 Terminology and notation 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

4.1 Introduction Rationale for statistical reporting 26 March 2008 4.1 Introduction Rationale for statistical reporting Be consistent and give the reader clear, concise but complete information find a compromise between giving too little and too much information this compromise may depend on the readership of the journal There are general conventions for reporting numbers percentages statistics hypothesis tests 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

Statistical presentation - 4. Reporting numbers 26 March 2008 Reporting results in the Results section What should be reported (where applicable) numbers and percentages participating by group if applicable characteristics of participants also by group if applicable characteristics of non-participants comparison with participants baseline values of key variables preliminary analyses analyses for individual variables involved in primary analyses, especially if the latter is multivariate assessment of assumptions for primary analyses primary analyses those involved with main research questions secondary analyses those involved with supporting research questions 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

Statistical presentation - 4. Reporting numbers 26 March 2008 4.2 Reporting numbers… Conventions (see BMJ stylebook; Lang and Secic, 1997) Use text for zero, one to nine and use digits from 10 onwards, unless an age, a date or with a unit of measurement eg a 5 year old child; 7 June; 5 ml; 8 mm Hg; 6 weeks the start of a sentence eg Twenty-five patients failed to attend. reporting large general numbers eg five hundred; a thousand Report ranges of numbers using “to” without repeating units eg 5 to 10 ml 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

… and percentages More conventions 26 March 2008 … and percentages More conventions Reader should be aware of denominator explicitly via the total, or implicitly via the numerator Use same number of decimal places consistently usually none (eg 12%) or one (12.3%) Use numbers followed by “%” (eg 5%) unless the start of a sentence eg Twenty-five percent of patients failed to attend. report ranges of percentages using “to”, repeating “%” eg 5% to 10% usually best to use the style “number (percent%)” eg Of those responding, 123 (45.6%) said … 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

Statistical presentation - 4. Reporting numbers 26 March 2008 Numerical precision for percentages How many decimal places? (Lang and Secic, 1997) If the sample is “moderate” to “large”, use one decimal place eg Out of 150 patients, 75 (50.0%) said this … “small”, round to nearest integer eg Out of 80 patients, 40 (50%) said that … “very small”, eg < 20, use actual numbers instead eg Out of 30 patients, 15 said the other … Try to use same number of decimal places throughout the paper perhaps outside Results and tables, use whole numbers (BMJ stylebook) 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

How to round to n decimal places How software does it 26 March 2008 How to round to n decimal places How software does it Values with digits from 0 to 4 in (n+1)st decimal place are rounded downwards eg, to one decimal place, round 2.345 to 2.3 Values with digits from 5 to 9 in (n+1)st decimal place are rounded upwards eg, to one decimal place, round 3.450 to 3.5 If after rounding, nth decimal place is 0, report it eg if one decimal place is used, report 21.0, not 21 “21.0” is in the range 20.05 inclusive to 21.05 exclusive “21” is in the range 20.5 inclusive to 21.5 exclusive 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

The Bad Inconsistent percentages 26 March 2008 The Bad Inconsistent percentages Papanikolaou et al (2003) [again] Pressure ulcer risk assessment: application of logistic analysis, J Advanced Nursing 44(2), 128-136 Table 2 reports percentages counts should have been reported too, at least for each column (25 and 473) varying number of decimal places for percentages (0, 1 or 2) percentages such as 16.0 and 4.0 reported as 16 and 4 [does not follow IMRaD structure (see earlier)] [no sample size calculation and p-values of “0.00”] 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

Statistical presentation - 4. Reporting numbers 26 March 2008 Numerical precision for statistics How many decimal places? (Altman et al, 2000) For summary statistics such as means, standard deviations, standard errors, and confidence limits, use one more decimal place than the raw values for medians and quartiles, possibly use raw value For most test statistics, use at most 2 decimal places Where possible, try to use same number of decimal places consistently throughout paper for each type of value 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

4.3 Reporting statistics 1 Some parametric statistics … 26 March 2008 4.3 Reporting statistics 1 Some parametric statistics … Report means with SD, SE or CI: if SD high compared to mean, distribution is skewed… report means and standard deviations or standard errors as “mean (SD standard deviation)” or “mean (SE standard error)” eg 23.4 (SD 5.6); 8.9 (SE 0.1) avoid using “±” as this does not differentiate between SD, SE or other measures report confidence intervals as “CI lower to upper” or “CI lower, upper” eg 95% CI 1.2 to 3.4 or 95% CI 1.2, 3.4 “CI lower – upper” is tricky if lower or upper is negative 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

Reporting statistics 2 … and some order/nonparametric statistics 26 March 2008 Reporting statistics 2 … and some order/nonparametric statistics … And if the distribution is skewed, report medians with ranges or interquartile ranges report ranges as “range minimum to maximum” or “range minimum, maximum” eg range 5 to 67 or range 5, 67 and not as the arithmetic difference 62 report medians and central percentile ranges (such as interquartile range [IQR]) in the form “median (IQR lower to upper)” or “median (IQR lower, upper)” eg 45.6 (IQR 12.3 to 89.0) or 45.6 (IQR 12.3, 89.0) do not report arithmetic difference for the range if not IQR, identify the percentile range used 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

The Bad Means without SDs 26 March 2008 The Bad Means without SDs Saarikoski et al (2002) Clinical learning environment and supervision: testing a research instrument in an international comparative study, Nurse Education Today 22, 340-349 [does not follow IMRaD structure] [no sample size calculation, no test statistics but “P-value <0.000***” reported twice] subscale means reported without SDs; ANOVA used for two-group comparison instead of t-test if group SDs had been different, unequal variance t-test might have been better, given different group sizes not clear whether differences between means were clinically important (statistical significance may be due to large sample sizes) 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

Statistical presentation - 4. Reporting numbers 26 March 2008 4.4 Reporting test results How to report results of tests (Lang and Secic, 1997) Do not give p-values in isolation; if readable, test results in text or tables should include value of the test statistic (eg to two decimal places) state explicitly if one-tailed (default is two-tailed) degrees of freedom (where applicable) eg df = 30; or t[30] = …; df = 1, 30; or F[1,30] = … if sufficient space, the actual p-value to three decimal places or two significant figures (check the journal!) eg p = 0.012 or p = 0.34 (ranges like “p < 0.05” hide info) unless p < 0.001, conventionally report “p < 0.001” if not (in tables), “* p<0.05, ** p<0.01, *** p<0.001” but not at the same time as actual p-values! 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

Statistical presentation - 4. Reporting numbers 26 March 2008 Report supporting statistics Show what the test result means (Altman et al, 2000) p-value does not show the “size” of any effect Include supporting statistics to indicate the clinical importance of the result estimated group proportions, group means/SDs, mean/SD of (paired) difference or confidence interval for difference between group proportions or means especially for main outcome measures or effect size odds ratio, phi statistic/Cramér’s V statistic (Cohen’s w), standardised difference between means (Cohen’s d or Glass’ g), standardised mean (paired) difference, correlation coefficient 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

Non-significant results It’s not the end of the world 26 March 2008 Non-significant results It’s not the end of the world A non-significant test does not mean failure! just that there is insufficient evidence to show a statistically significant difference or relationship not enough data, or no difference or relationship this might be interesting in its own right sometimes the pattern of results is more important If a main analysis, give results and supporting statistics in full reader still needs to know that the test has been performed correctly supporting statistics may help interpreting overall pattern 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

The Bad P-values in isolation 26 March 2008 The Bad P-values in isolation Abayomi and Hackett (2004) Assessment of malnutrition in mental health clients: nurses’ judgement vs. a nutrition risk tool J Advanced Nursing 45(4), 430-437 [“Data were collated and analysed using the Statistical Package for the Social Sciences (SPSS). The chi square test was used to assess relationships between variables…”] [main comparison is risk assessment by tool (yes/no) v risk assessment by nurse (yes/no), which should have been measured using kappa statistic, not chi-square] actual p-values given but no test statistics; no supporting statistics when comparing either risk assessment with reason for admission, gender, age (<40, >40) 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

The Ugly P-values ranges only – not sure about the tests 26 March 2008 The Ugly P-values ranges only – not sure about the tests Paxton et al (1996) [again] Evaluating the workload of practice nurses: a study, Nursing Standard 10(21), 33-38 study comparing workload of same 34 practice-employed and health board attached nurses before and after introduction of the New General Practitioner Contract [no sample size calculations] [chi square statistic said to be used for categorical variables, ignoring paired nature of data (see earlier)] [statistical methods for other variables (% of time, hours per FTE) not described] no test statistics reported – only p-value ranges – so can’t identify tests being used 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

The Ugly Generally poor reporting of results 26 March 2008 The Ugly Generally poor reporting of results Zeitoun et al (2003) A prospective, randomized study of ventilator-assisted pneumonia in patients using a closed vs. open suction system, J Clinical Nursing 12(4), 484-489 [not randomised, no justification for small sample size (24 open suction v 23 closed suction) and probably not enough for logistic regression] actual p-values (some 1.000s) but no test statistics entries in two tables not clear probably mean(range) days of use of drugs no details of how logistic regression applied details of “final” model shown in table odds ratio from logistic regression mistakenly interpreted as risk ratio (“a 0.014 less chance of developing VAP”) 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

4.5 Terminology and notation Yet more conventions 26 March 2008 4.5 Terminology and notation Yet more conventions There are common conventions on the use of reserved terminology standard statistical notation, including common abbreviations Roman characters Greek characters 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

Reserved terminology Some words should only be used statistically 26 March 2008 Reserved terminology Some words should only be used statistically Avoid using the following except in their statistical sense (eg Altman et al, 2000): correlation, dependent, incidence, independent, normal, parameter, population, power, prevalence, random, sample, sensitivity, significance/significant, specificity, variance Suggest using “clinical importance” instead of “clinical significance” 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

Statistical abbreviations Commonly used in text or tables 26 March 2008 Statistical abbreviations Commonly used in text or tables ANACOVA, ANCOVA – analysis of covariance ANOVA – analysis of variance CI – confidence interval ICC – intra-class correlation IQR – interquartile range MANOVA – multivariate analysis of variance NNT – number needed to treat SD - standard deviation SE - standard error 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

Statistical presentation - 4. Reporting numbers 26 March 2008 Standard statistical notation 1 Commonly used Roman characters (Lang and Secic, 1997) F - statistic for F test H0 – null hypothesis H1, Ha – alternative hypothesis n, N - sample size p, P - probability r, R - Pearson product-moment correlation r2, R2 – coefficient of determination Sample and test statistics are usually in italics s - sample standard deviation t - statistic for t test U - statistic for Mann-Whitney (Wilcoxon rank-sum) test – sample mean z, Z - statistic for Z test (standard Normal distribution) 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers

Statistical presentation - 4. Reporting numbers 26 March 2008 Standard statistical notation 2 Commonly used Greek characters (Lang and Secic, 1997)  - probability of Type I error (significance level)  - probability of Type II error (1 - power) 2 - chi-square (test or statistic)  - Cohen’s kappa statistic  - population mean  - Spearman’s rank order correlation (rho)  - population standard deviation  - summation  - Kendall’s concordance correlation (tau) 26 March 2008 Statistical presentation - 4. Reporting numbers Statistical presentation - 4. Reporting numbers