Describe the scope of biostatistics, the types of data and their presentation.

Scope and Types of Data

• The sources of variation must be understood before any statistic means anything:
• Biological variation between individuals — no two people are alike
• Biological variation within the same individual — blood pressure differs between morning and evening in the same person
• Measurement (observer and instrument) variation — the same observer measuring twice, or two observers measuring once
• Sampling variation — different samples from the same population give different results by chance alone
• The last of these is what statistical inference exists to handle
• The uses of biostatistics — to define what is normal; to test whether a difference is real; to study the association between variables; to calculate sample size; to evaluate the efficacy of treatments and programmes; to measure the health of a community; and to read the medical literature critically
• The types of data determine which statistic and which test may be used, so this classification is the practical foundation of everything else:
• Qualitative (categorical) data:
• Nominal — categories with NO natural order: sex, blood group, religion, presence or absence of disease. Only counting and proportion are meaningful
• Ordinal — categories with a natural order but unequal or unknown intervals: pain scored mild, moderate or severe; social class; tumour grade. The order is real but the distance between categories is not, which is why a mean of an ordinal scale is meaningless and the median must be used
• Quantitative (numerical) data:
• Discrete — whole numbers only: number of children, pulse rate, number of episodes
• Continuous — any value within a range, limited only by the precision of measurement: height, weight, blood pressure, haemoglobin
• The distinction between interval and ratio scales — a ratio scale has a true zero (weight, height), so ratios are meaningful; an interval scale has an arbitrary zero (temperature in Celsius), so 40°C is not "twice as hot" as 20°C
• Converting data downward (continuous to ordinal to nominal) is always possible but loses information — dichotomising blood pressure into hypertensive or not discards everything about how high it was, and reduces statistical power. Converting upward is impossible
• Hence the practical rule: collect data in its most detailed form and categorise later if needed

Presentation of Data

• Data are presented in three ways — as text, as tables, and as diagrams, each suited to a different purpose
• Tabulation is the first step, and the rules of a good table are examined directly:
• A clear, complete title stating what, where and when
• Clearly labelled rows and columns with units
• Totals given
• The source of the data cited, and footnotes explaining any abbreviation or exclusion
• Simple enough to be understood without reference to the text
• Data arranged meaningfully — by magnitude, time or category, not arbitrarily
• A frequency distribution groups continuous data into class intervals, which should be mutually exclusive, exhaustive and of equal width, and numerous enough (usually 5 to 15) not to conceal the shape
• The choice of diagram depends on the type of data, and getting this right is the most examinable part of the topic:
• For qualitative data — the bar diagram (simple, multiple or component), in which the bars are separated by gaps because the categories are distinct; and the pie chart, showing proportions of a whole, best limited to a few categories
• For quantitative continuous data — the histogram, in which the bars touch because the variable is continuous, and the area of each bar represents the frequency; the frequency polygon, joining the mid-points of the histogram tops, which allows two distributions to be compared on one figure; the frequency curve; and the ogive (cumulative frequency curve), from which medians and percentiles can be read directly
• The bar diagram versus histogram distinction IS the classic examination point — bars are separated in a bar diagram (discrete categories) and touch in a histogram (continuous variable), and the width of a histogram bar has meaning while that of a bar-diagram bar does not
• For data over time — the line diagram (time series), which shows trends and is used for epidemic curves and secular trends
• For the relationship between two continuous variables — the scatter diagram, which should always be drawn before calculating a correlation coefficient
• For geographical data — the spot (dot) map, showing the location of individual cases, and the shaded (choropleth) map, showing rates by area
• Other forms — the pictogram, useful for lay audiences; the box-and-whisker plot, which displays median, quartiles and outliers and is excellent for comparing groups; and the stem-and-leaf plot, which shows the shape while retaining the original values
• The principles OF honest presentation deserve stating, because misleading graphs are common:
• The vertical axis should normally start at zero; truncating it exaggerates differences and is the commonest form of graphical deception
• Do not use a three-dimensional effect on a two-dimensional quantity, since it distorts the visual comparison
• Label axes with units, give the sample size, and show variability (error bars or confidence intervals) rather than means alone
• A diagram should replace a table, not duplicate it; and a diagram is for impression, a table for precise values — which is the clearest way to decide which to use
• Bars touch in a histogram and are separated in a bar diagram, because one shows a continuous variable and the other distinct categories
• Histogram bar width has meaning; bar diagram bar width does not, which is why area represents frequency in the first
• Collect data in its most detailed form; categorising later is always possible and recovering detail never is
• Dichotomising a continuous variable loses power as well as information, which is a statistical cost not merely an aesthetic one
• A mean of an ordinal scale is meaningless, since the intervals between categories are unknown
• Forty degrees is not twice twenty, because Celsius is an interval scale with an arbitrary zero
• Always draw the scatter diagram first, before calculating any correlation coefficient
• Truncating the vertical axis exaggerates differences, and is the commonest form of graphical deception
• Avoid three-dimensional effects on two-dimensional quantities, since they distort visual comparison
• Show variability, not means alone, with error bars or confidence intervals on every figure
• A table gives precise values and a diagram an impression, which is the cleanest way to choose between them
• A diagram should replace a table, not duplicate it, or the reader is made to do the same work twice
• An ogive allows medians and percentiles to be read directly off the cumulative curve
• A frequency polygon compares two distributions on one figure, which a histogram cannot do cleanly
• Box plots display median, quartiles and outliers, and are excellent for comparing several groups at once
• Stem-and-leaf plots retain the original values while still showing the shape of the distribution
• Spot maps show cases and shaded maps show rates, and confusing the two misleads about population denominators
• A table should stand without the text, with a title stating what, where and when
• Class intervals must be equal and exhaustive, and numerous enough not to conceal the shape of the distribution
• Biological variation occurs within one person as well as between people, which affects how measurements are taken
• Sampling variation is what inference handles, and is the reason statistical tests exist at all
• Cite the source and footnote exclusions, without which a table cannot be interpreted or checked