Session 1 - Descriptive Statistics.docx

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Cell and Systems Biology
William Navarre

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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