summarizing data (test 1)

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descriptive statistics (numerical data)

• measures of central tendency (typical)

  • mean

  • median

  • mode

• measures of dispersion (spread or variability)

  • range

  • interquartile range (IQR)

  • variance, standard deviation

  • skewness

mean

• average value of sample distribution achieved by…

  • sum of all values / # of all values

• sensitive to outliers and can be affected by “skew“ in the data

• should only be calculated for continuous data that is normally distributed

  • ex: BP/HF staging

median

• the “middle“ value of a sample distribution

• remember our sample distribution

  • 4 8 X 12 100

• given an even number:

  • (8+12) / 2 = 10

• so the mean was 31 but median was 10

  • strength of the mean is more appropriate with skewed data

  • may be used in not only continuous, but also ordinal data

mode

• # that most frequently occurs in a data set

• preferred in nominal data, wen central location if nonnumeric

  • nominal date is usually depicted by rate, %, and ratios

range

• difference between the highest and lowest values of a data set

• useful in setting limitations in the expectations of effect for a given intervention

• a measurement of precision or consistency of data set

  • large: the effects of in intervention may very greatly between individuals

  • small: we can predict with reasonable certainty the effect of our intervention

• let’s say we measure baseline % LDL for 1000 people, followed by giving them atorvastatin 20 mg for 3 months

  • highest reduction → 40%

  • lowest reduction → 5%

interquartile range

• difference between the 75th and 25th percentiles of the data

• useful graphical representations of a probability distribution

variance

• how far the values of a variable lie from the mean

• mathematically defined as the average squared distance of values from their means

standard deviation

• indicates how spread out the data is and to what degree the data is dispersed away from the mean

  • low, small range of values, and data is clustered around the mean

• it is the square root of the variance

  • is sensitive to outliers in the data

left skew

negative direction

normal (no skew)

normal curve represents a perfectly symmetrical distribution

right skew

positive direction

frequency table

the simplest for of visual representation

• it organize discrete or continuous data at any level of measurement

bar chart

graph discrete, categorical data (nominal/ordinal scale)

• shows the frequency counts of values for the different levels of a categorical or nominal variable

  • one axis represents a measured value, or show other statistics, i.e., percentages.

  • the other axis of the chart shows the specific categories

• can be plotted vertically or horizontally

histogram

graph continuous data that have been apportioned into discrete categories

• plots the distribution of a numeric variables values as a series of bars

  • each bar typically covers a range of numeric values called a bin or class

  • a bar’s height indicates the frequency of data points with a value within the corresponding bin

• has numerical groups ie age groups and bars touch

  • bar chart used categorical data ie your favorite color

pie chart

represents proportions or relative quantities of values

• limited to small number of categories

contingency table

observations are cross-classified according to their membership in the categories of the variables

we can use mode for nominal data

• how else can we describe nominal data?

• ratios

• proportions

• precentages

proportion

the # of observations (a) with a given characteristic divided by the total # of observations (a+b) in a given group

• (a) / (a+b)

• always defined as a part divided by the whole

percentage

simply a proportion x by 100

• [(a) / (a+b)] * 100

ratios

# of observations in a group with a given characteristic divided by the # of observations without the given characteristic

• (a) / (b)

• always defined as a part divided by another part