Frequency Distribution a systematic arrangement of data values (transforms a mass of unmanageable details of data into manageable summaries) a count of how many times each value occurred in a dataset Frequency is a statistical term for a count of how many cases there are in a particular category of a variable, thus the frequency distribution is the list of frequencies for each category of the variable

Constructing a Frequency Distribution List each data value in a sequence (usually, ascending order) 1, 2, 3, 4, 5… Tally each occurrence of the value Total the frequencies for each value (f) The sum of fs for all data values must equal the sample size: Σf = N

Elements of a Typical Frequency Distribution Data values Absolute frequencies (counts) Relative frequencies (percentages) % = (f / N) x100 Cumulative relative frequencies (the percentage for a given score value, combined with percentages for all preceding values)

Bar Graphs Bar graphs: Used for nominal (and many ordinal) level variables Bar graphs have a horizontal dimension (X axis) that specifies categories (i.e., data values) The vertical dimension (Y axis) specifies either frequencies or percentages Bars for each category drawn to the height that indicates the frequency or % Note the bars do not touch each other

Bar Graph example In 32 of the 65 participants with ADL difficulty at baseline, these difficulties persisted or worsened at follow-up. The ADL impairment most likely to persist was transferring, followed by bathing and dressing (Figure). Among the 32 participants with persistent or worsened ADL impairment, 11 participants had improvement in the original impairment but onset of 1 or more other impairments. Cimino T, Steinman MA, Mitchell SL, Miao Y, Bharel M, Barnhart CE, Brown RT. The Course of Functional Impairment in Older Homeless Adults: Disabled on the Street. JAMA Intern Med. 2015 May 26. doi: 10.1001/jamainternmed.2015.1562. Figure. Changes in Activities of Daily Living (ADL) Function After 1 Year Among 65 Older Homeless Adults With ADL Difficulty at Baseline Persistent difficulty was defined as an ADL difficulty present at both baseline and follow-up. The combined length of each set of paired bars represents the number of participants with that ADL difficulty present at baseline.

Pie Chart Pie Charts: Also used for nominal (and many ordinal) level variables Circle is divided into pie- shaped wedges corresponding to percentages for a given category or data value All pieces add up to 100% Place wedges in order, with biggest wedge starting at “12 o’clock”

Pie Chart example Tait AR, Voepel-Lewis T, Brennan-Martinez C, McGonegal M, Levine R. Using animated computer-generated text and graphics to depict the risks and benefits of medical treatment. Am J Med. 2012 Nov;125(11):1103-10. doi: 10.1016/j.amjmed.2012.04.040. Epub 2012 Aug 28.

Histograms frequency Heart rate in bpm Histograms: Used for interval- and ratio-level data Similar to a bar graph, with an X and Y axis—but adjacent values are on a continuum so bars touch one another [indicate that the items are non-discrete, unlike the items shown in a bar graph] Data values on X axis are arranged from lowest to highest Bars are drawn to height to show frequency or percentage (Y axis) frequency Heart rate in bpm

Histogram example Our study was prompted by a re-examination of the published data from the Candesartan in Heart Failure—Assessment of Mortality and Morbidity (CHARM) program. As a part of that program, the CHARM investigators published a histogram showing the distribution of EF in their HF population.4 This histogram illustrates the effect of a loaded distribution in which the greater number of patients with a low EF drives the shape of the distribution plot (Figure 1); approximately 60% of the total population had an EF <0.40. To adjust for this loaded distribution, we proportionately reduced each of the low EF bins so the number of patients with an EF <0.40 was equal to those with an EF >0.40 (Figure 1). Visual inspection of the resulting histogram suggested a bimodal distribution. This hypothesis-generating plot prompted us to examine the EF distribution in 2 other HF trials. Figure 1. Distribution of EF in 7,599 patients with HF in the CHARM program.4(A) Unimodal distribution, but after adjustment to correct for loaded distribution, (B) histogram suggests a bimodal distribution. See text for details. Gaasch WH1, Delorey DE, Kueffer FJ, Zile MR. Distribution of left ventricular ejection fraction in patients with ischemic and hypertensive heart disease and chronic heart failure. Am J Cardiol. 2009 Nov 15;104(10):1413-5. doi: 10.1016/j.amjcard.2009.06.064.