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Cell and Systems Biology

CSB345H1

William Navarre

Fall

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HMB325H © Lisa | Page 13
L E C T U R E 1 : H O W T O S U M M A R I Z E D ATA ( C H A P T E R 2 )
LEARNING OBJECTIVES
1. list, recognize, describe the characteristics of the 5 main levels/types of data measurement
used in biomedical studies
2. list and describe the descriptive statistics (ex. measures of central tendency, variability)
3. describe the situations & circumstances in which each of these descriptive statistics should &
should not be used
4. create & critique graphical displays of data distributions
5. describe the characteristics of normal & skewed distributions
6. describe what the standard of error of the mean measures & the 2 factors that affect its size
7. calculate & interpret applicable confidence intervals
THE 3 MAIN TASKS OF STATISTICS
1. to describe/summarize a set of data – data reduction
2. to estimate how close a result might be to the ‘true’ (unobserved) value
3. to estimate the probability that random variation (‘chance’) explains the observed results –
inferential statistics
1. hypothetical example on a community health survey:
During the past 24 hours, how many cigarettes have you smoked?
1. significance of this question (why?): smoking has understood adverse health
effects
2. who should be studied: hope that sample/subgroup is representative of the whole
pop (randomly selected)
1. statistics tells us that on avg, the random sample will be representative
3. what is measured/counted?: a number
LEVELS OF DATA MEASUREMENT
2. what ‘level/type of data measurement’ is ‘number of cigarettes smoked’?
1. continuous – no breaks bw two numbers (decimals & fractions are infinite bw them)
2. discrete – whole numbers, ex. # of pregnancies, teeth, stairs climbed
1. mostly discrete – depends on how variables are collected from indiv respondents
3. what other ‘levels/types of data measurement’ are there?
3. categorical
1) nominal – categories w names, no natural order, ex. eye colour, blood type, birth
country
2) dichotomous (binary) – only 2 choices, ex. have/don’t have the disease (special kind
of nominal variable)
3) ordinal – categories are ordered, ex. a 5-point scale
DESCRIPTIVE STATISTICS
4. descriptive statistics is used to turn a set of data (ex. of random numbers) into
something more meaningful
5. types of descriptive statistics
1. graphical displays – “a picture’s worth a thousand words”, ex. line graph, stem & leaf
plot, number line
2. quantitative measures (descriptive statistics)
1) measures of central tendency (mean, median, mode) – ‘representative’ (central)
value
1. mean: adding up the values & dividing the sample by the number (count)
of values in the sample
2. median: the middle value of a sequential set of data (the 50 percentile –
50% of the values are less than it & 50% are greater)
3. mode: the most frequently occurring value(s) in a set of data HMB325H © Lisa Z| Page 2
2) measures of variability – ‘dispersion/spread’ of the data
4. range: interval/difference from the lowest to the highest value in a set of
data (maps out the extremes but not how the data are dispersed bw them)
th
5. interquartile range (IQR): the range th the data’s first quartile (25
percentile) & its third quartile (75 percentile)
(p/100)(n+1); p = percentile, n = number of data points
ex. the 75 percentile of 14 data points would be the (75/100)(14+1) = 11.25
th th th
observation; the 75 percentile is the average of the 11 & 12 observation, ex. 34 &
40, (34+40)/2 = 37, IQR = 0 – 37
1. 50 percentile = median = avg bw the 50 data point & the 51 st
6. standard deviation (SD): the ‘average’ distance each data point is from
the sample’s mean
6. computing the standard deviation of 5 example data values: 71, 75, 79, 83, 92
1. Compute the mean: 400/5 = 80.0
2. Subtract the mean from each value: -9.0, -5.0, -1.0, 3.0, 12.0
3. Square each of the differences (“squared deviations”): 81.0, 25.0, 1.0, 9.0,
144.0
4. Add the squares & divide by n–1: 260/4 = 65.0 (the “variance”)
divide by n–1 bc any sample will underestimate the true amount of
variability for the whole pop (make denominator 1 unit smaller to mak

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