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200107P - DATA SUMMARY AND PRESENTATION 1: DATA PRESENTATION AS DIAGRAMS

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Presentation to the Module I: Clinical Epidemiology at a Clinical Research Coordinator Course held on 5-9 January 2020 at Faculty of Medicine, King Fahad Medical City, Riyadh. by Professor Omar Hasan Kasule Sr. MB ChB (MUK), MPH (Harvard), DrPH (Harvard), Chairman of the KFMC IRB


DEFINITIONS 

Learning Objectives: 

  • Data grouping 
  • Data tabulation 
  • Data diagrams 


Key Words and Terms:

  • Bar diagram, bar chart, histogram
  • Class interval
  • Cumulative frequency
  • Data grouping
  • Data tabulation 
  • Diagram, line graph, pie chart, scattergram, stem, and leaf
  • Grouping error
  • Kurtosis
  • Modality 
  • Origin of a graph 
  • Shape of distribution 
  • Skewness 


DATA GROUPING:

  • Data grouping summarizes data but leads to loss of information due to grouping errors.
  • The suitable number of classes is 10-20. The bigger the class interval, the bigger the grouping error.
  • Classes should be mutually exclusive, of equal width, and cover all the data.
  • The upper and lower class limits can be true or approximate.
  • The approximate limits are easier to tabulate.
  • Data can be dichotomous (2 groups), trichotomous (3 groups), or polychotomous (>3 groups). 


ILLUSTRATION TABLE  


DATA TABULATION

  • Tabulation summarizes data in logical groupings for easy visual inspection.
  • A table shows cell frequency (cell number), cell number as a percentage of the overall total (cell %), cell number as a row percentage (row%), cell number as a column percentage (column %), cumulative frequency, cumulative frequency%, relative (proportional) frequency, and relative frequency %. 
  • Ideal tables are simple, easy to read, correctly scaled, titled, labeled, self-explanatory, with marginal and overall totals. 
  • The commonest table is the 2 x 2 contingency table. Other configurations are the 2 x k table and the r x c table. 


ILLUSTRATION – A HISTOGRAM


 

DATA DIAGRAMS - 1 

  • An ideal diagram is self-explanatory, simple, not crowded, of appropriate size, and emphasizes data and not graphics. 
  • The 1-way bar diagram, the stem and leaf, the pie chart, and a map are diagrams showing only 1 variable. 
  • A bar diagram uses ‘bars’ to indicate the frequency and is classified as a bar chart, a histogram, or a vertical line graph.
  • The bar chart, with spaces between bars, and the line graph, with vertical lines instead of bars, are used for discrete, nominal, or ordinal data. 
  • The histogram, with no spaces between bars, is used for continuous data. The area of the bar and not its height is proportional to frequency.
  • The bar diagram is intuitive for the non-specialist. 


ILLUSTRATION: PIE CHART, STEM & LEAF 


DATA DIAGRAMS - 2

  • The stem and leaf diagram shows actual numerical values with the aid of a key and not their representation as bars.
  • The pie chart (pie diagram) shows relative frequency % converted into angles of a circle (called sector angle). The area of each sector is proportional to the frequency.
  • A pictogram shows pictures of the variable being measured as used instead of bars.


ILLUSTRATION: A LINE GRAPH  


DATA DIAGRAMS - 3 

  • A line graph is produced when the frequency is plotted against the class interval midpoint. Joining the points by straight lines produces a frequency polygon and joining them with a smoothed line produces a frequency curve. 
  • A line graph shows cumulative frequency, cumulative frequency %, moving averages, time series, trends (cyclic and non-cyclic), medians, quartiles, and percentiles.
  • Plotting the line graph with the y-axis in logarithmic units and the x-axis as arithmetic units enables the representation of a wider variety than with a linear scale.
  • A dot plot uses dots instead of bars.
  • A time series plot is a graph of the value of a variable against time.
  • The scatter diagram is also called the x-y scatter or the scatter plot.


ILLUSTRATION: BELL-SHAPED GRAPH, RIGHT SKEW, LEFT SKEW

 


SHAPES OF DIAGRAMS 

  • Bar diagrams and line graphs are distributions. The unimodal shape is the commonest shape. The 2 humps of the bimodal need not be equal. More than 2 peaks are unusual.
  • A perfectly symmetrical distribution is bell-shaped and is centered on the mean.
  • Skew to right (+ve skew) is more common than skew to the left (-ve skew).
  • Leptokurtosis is a narrow sharp peak. 
  • Platykurtosis is a wide flat hump.
  • The common shapes are the normal, the s-curve (ogive), the reverse J-curve (exponential), and the uniform. 


MISLEADING DIAGRAMS

  • Poor labeling, 
  • Inappropriate scaling, 
  • Omitting the zero origins.