An Introduction to R 2.1 Descriptive statistics
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1 An Introduction to R 2.1 Descriptive statistics Dan Navarro (daniel.navarro@adelaide.edu.au) School of Psychology, University of Adelaide ua.edu.au/ccs/people/dan DSTO R Workshop, 27-Apr-2015
2 Central tendency
3 Central tendency Commands: Calculate means using mean() Calculate medians using median() Find the mode using modeof() [lsr package]
4 Central tendency Commands: Calculate means using mean() Calculate medians using median() Find the mode using modeof() [lsr package] > mean( expt$age ) [1] 25.25
5 Central tendency Commands: Calculate means using mean() Calculate medians using median() Find the mode using modeof() [lsr package] > mean( expt$age ) [1] > median( expt$age ) [1] 25
6 Central tendency Commands: Calculate means using mean() Calculate medians using median() Find the mode using modeof() [lsr package] > mean( expt$age ) [1] > median( expt$age ) [1] 25 > library(lsr) > modeof( expt$age ) [1] 25
7 What if there are missing data? Sometimes there are missing data These are represented as NA values Different functions handle NA values differently
8 What if there are missing data? Sometimes there are missing data These are represented as NA values Different functions handle NA values differently What is the mean of 3, 4, 5 and NA? Pragmatic answer: ignore the missing data, and calculate the average of 3,4 and 5... i.e., mean = 4 Cautious answer: we don t know the missing value, so we don t know the mean either... i.e. mean = NA
9 What if there are missing data? > age <- c( 32, 19, NA, 64 ) > mean( age ) [1] NA By default, mean() gives the conservative don t know answer
10 What if there are missing data? > age <- c( 32, 19, NA, 64 ) > mean( age ) [1] NA > mean( age, na.rm=true ) [1] But we can force it to be a pragmatist: tell R to remove the NA values by specifying na.rm=true (the na.rm argument shows up in quite a lot of functions)
11 Calculating a trimmed mean > score <- c( 3, 2, 1, 5, 7, 12, 3, 1, 4, ) > mean( score ) [1] > mean( score, trim=.1 ) [1] Sometimes the mean isn t a compelling measure of central tendency, but we d prefer not to resort to the median because the sample size is so small
12 Calculating a trimmed mean > score <- c( 3, 2, 1, 5, 7, 12, 3, 1, 4, ) > mean( score ) [1] > mean( score, trim=.1 ) [1] This gives the 10% trimmed mean, a more robust measure of central tendency than the mean
13 Try it yourself (Exercise 2.1.1)
14 Spread
15 Spread Standard deviation: sd() Range: range() Interquartile range: IQR() Specific quantiles: quantile()
16 Spread Standard deviation: sd() Range: range() Interquartile range: IQR() Specific quantiles: quantile() > sd( expt$age ) [1]
17 Spread Standard deviation: sd() Range: range() Interquartile range: IQR() Specific quantiles: quantile() > sd( expt$age ) [1] > range( expt$age ) [1] 19 30
18 Spread Standard deviation: sd() Range: range() Interquartile range: IQR() Specific quantiles: quantile() > sd( expt$age ) [1] > range( expt$age ) [1] > IQR( expt$age ) [1] 4.25
19 Spread Standard deviation: sd() Range: range() Interquartile range: IQR() Specific quantiles: quantile() > sd( expt$age ) [1] > range( expt$age ) [1] > IQR( expt$age ) [1] 4.25 > quantile( expt$age, probs=c(.05,.25,.5,.75,.95)) 5% 25% 50% 75% 95%
20 Try it yourself (Exercise 2.1.2)
21 Higher order moments: Skew and kurtosis (briefly)
22 Skewness = asymmetry positive skewness the data skews out to the right (i.e. a long tail of large values) negative skewness the data skews out to the left (i.e. a long tail of small values)
23 Kurtosis = pointiness Platykurtic ("too flat") Mesokurtic Leptokurtic ("too pointy") kurtosis < 0 kurtosis = 0 kurtosis > 0
24 Skew and kurtosis Skew: skew() [psych package] Kurtosis: kurtosi() [psych package]
25 Skew and kurtosis Skew: skew() [psych package] Kurtosis: kurtosi() [psych package] > library(psych) > skew( expt$age ) [1] > kurtosi( expt$age ) [1]
26 Tabulating and cross-tabulating categorical variables
27 R always has lots of ways to do things Here are two ways to tabulate variables The table() function The xtabs() function Normally I wouldn t bother showing both, but there s a very good reason in this case...
28 Tabulating using table() > table( expt$treatment ) control drug1 drug Frequency table for the treatments > table( expt$treatment, expt$gender ) male female control 2 2 drug1 2 2 drug2 2 2
29 Tabulating using table() > table( expt$treatment ) control drug1 drug > table( expt$treatment, expt$gender ) male female control 2 2 drug1 2 2 drug2 2 2 We can get a cross tabulation simply by listing more variables in the input
30 > table( expt$age, expt$treatment, expt$gender ),, = male control drug1 drug Adding a third variable gives a three way cross-tabulation,, = female control drug1 drug
31 Try it yourself (Exercise 2.1.3)
32 table() versus xtabs() > table( expt$treatment, expt$gender ) male female control 2 2 drug1 2 2 drug2 2 2 When we do the cross tabulation using table(), we type in a list of variable names
33 table() versus xtabs() > table( expt$treatment, expt$gender ) male female control 2 2 drug1 2 2 drug2 2 2 > xtabs( formula = ~ treatment + gender, data = expt ) gender treatment male female control 2 2 drug1 2 2 drug2 2 2 xtabs() works a bit differently. We specify the name of the data frame (ie. expt), and a formula that indicates which variables need to be crosstabulated
34 Digression: Formulas
35 Formulas A formula is an abstract way to write down variable relationships The precise meaning depends on the context Formulas get used a lot in R, so it s helpful to see some examples...
36 Examples In xtabs(), a one-sided formula is used to specify a set of variables to cross tabulate... ~ variable1 + variable2 ~ variable1
37 Examples In xtabs(), a one-sided formula is used to specify a set of variables to cross tabulate... ~ variable1 + variable2 ~ variable1 In lm(), a two-sided formula is used to specify a regression model... outcome ~ predictor1 + predictor2 outcome ~ predictor1 * predictor2
38 Try it yourself (Exercise 2.1.4)
39 Getting lots of descriptive statistics quickly and easily...
40 Useful commands Getting lots of descriptive information for several variables at once: describe() [psych package] summary() Getting descriptive statistics separately for several groups: describeby() [psych package] by() and summary() aggregate()
41 Describe > library( psych ) > describe( expt ) var n mean sd median trimmed mad min max range skew kurtosis se id age gender* treatment* hormone happy sad
42 Describe > library( psych ) > describe( expt ) var n mean sd median trimmed mad min max range skew kurtosis se id age gender* treatment* hormone happy sad Each row contains descriptive statistics for one of the variables in the data frame. Variables with asterisks next to the names are factors: the asterisk here is a reminder that most of these measures are inappropriate for nominal scale variables
43 Describe > library( psych ) > describe( expt ) var n mean sd median trimmed mad min max range skew kurtosis se id age gender* treatment* hormone happy sad Number of observations
44 Describe > library( psych ) > describe( expt ) var n mean sd median trimmed mad min max range skew kurtosis se id age gender* treatment* hormone happy sad Mean, standard deviation and median
45 Describe > library( psych ) > describe( expt ) var n mean sd median trimmed mad min max range skew kurtosis se id age gender* treatment* hormone happy sad % trimmed mean
46 Describe > library( psych ) > describe( expt ) var n mean sd median trimmed mad min max range skew kurtosis se id age gender* treatment* hormone happy sad A robust estimator of the standard deviation that is computed by a transformation of the median absolute deviation (mad) from the sample median
47 Describe > library( psych ) > describe( expt ) var n mean sd median trimmed mad min max range skew kurtosis se id age gender* treatment* hormone happy sad Information about the range
48 Describe > library( psych ) > describe( expt ) var n mean sd median trimmed mad min max range skew kurtosis se id age gender* treatment* hormone happy sad Skew and kurtosis
49 Describe > library( psych ) > describe( expt ) var n mean sd median trimmed mad min max range skew kurtosis se id age gender* treatment* hormone happy sad Standard error of the mean (computed by the usual normal theory estimate)
50 Summary > summary( expt ) id age gender treatment Min. : 1.00 Min. :19.00 male :6 control:4 1st Qu.: st Qu.:23.75 female:6 drug1 :4 Median : 6.50 Median :25.00 drug2 :4 Mean : 6.50 Mean : rd Qu.: rd Qu.:28.00 Max. :12.00 Max. :30.00 hormone happy sad Min. : 6.70 Min. :2.000 Min. : st Qu.: st Qu.: st Qu.:2.540 Median :42.15 Median :3.425 Median :3.235 Mean :43.59 Mean :3.712 Mean : rd Qu.: rd Qu.: rd Qu.:4.633 Max. :98.40 Max. :5.690 Max. :6.120
51 Summary > summary( expt ) id age gender treatment Min. : 1.00 Min. :19.00 male :6 control:4 1st Qu.: st Qu.:23.75 female:6 drug1 :4 Median : 6.50 Median :25.00 drug2 :4 Mean : 6.50 Mean : rd Qu.: rd Qu.:28.00 Max. :12.00 Max. :30.00 Summary produces a frequency table for the factor variables hormone happy sad Min. : 6.70 Min. :2.000 Min. : st Qu.: st Qu.: st Qu.:2.540 Median :42.15 Median :3.425 Median :3.235 Mean :43.59 Mean :3.712 Mean : rd Qu.: rd Qu.: rd Qu.:4.633 Max. :98.40 Max. :5.690 Max. :6.120
52 Summary > summary( expt ) id age gender treatment Min. : 1.00 Min. :19.00 male :6 control:4 1st Qu.: st Qu.:23.75 female:6 drug1 :4 Median : 6.50 Median :25.00 drug2 :4 Mean : 6.50 Mean : rd Qu.: rd Qu.:28.00 Max. :12.00 Max. :30.00 hormone happy sad Min. : 6.70 Min. :2.000 Min. : st Qu.: st Qu.: st Qu.:2.540 Median :42.15 Median :3.425 Median :3.235 Mean :43.59 Mean :3.712 Mean : rd Qu.: rd Qu.: rd Qu.:4.633 Max. :98.40 Max. :5.690 Max. :6.120 For numeric variables it gives the mean, plus the 0th, 25th, 50th, 75th and 100th percentiles
53 Try it yourself (Exercise 2.1.5)
54 Useful commands Getting lots of descriptive information for several variables at once: describe() [psych package] summary() Getting descriptive statistics separately for several groups: describeby() [psych package] by() and summary() aggregate()
55 describeby() > describeby( expt, group=expt$gender ) group: male var n mean sd median trimmed mad min max range skew kurtosis se id age gender* data frame containing all the the variable used to NaN NaN 0.00 treatment* variables to 4 be 6 described define 2.00 the groups hormone happy sad group: female var n mean sd median trimmed mad min max range skew kurtosis se id age gender* NaN NaN 0.00 treatment* hormone happy sad
56 describeby() > describeby( expt, group=expt$gender ) group: male var n mean sd median trimmed mad min max range skew kurtosis se id age gender* NaN NaN 0.00 treatment* hormone happy sad group: female var n mean sd median trimmed mad min max range skew kurtosis se id age gender* NaN NaN 0.00 treatment* hormone happy sad
57 Using aggregate() > aggregate( formula = age ~ gender + treatment, data = expt, FUN = mean ) gender treatment age 1 male control female control male drug female drug male drug female drug2 25.5
58 Using aggregate() > aggregate( formula = age ~ gender + treatment, data = expt, FUN = mean ) gender treatment age 1 male Tells R you control want to 26.5 summarise age, broken 2 female down separately control by gender 25.5 and treatment 3 male drug female drug male drug female drug2 25.5
59 Using aggregate() > aggregate( formula = age ~ gender + treatment, data = expt, FUN = mean ) gender treatment age 1 male Tells R that control the variables 26.5 are all stored in the 2 female control data frame 25.5 called expt 3 male drug female drug male drug female drug2 25.5
60 Using aggregate() > aggregate( formula = age ~ gender + treatment, data = expt, FUN = mean ) gender treatment age 1 male The name control of the function 26.5 that produces the 2 female descriptive control statistic that 25.5 you want... e.g., mean, 3 male drug1 sd, 23.5 IQR, etc 4 female drug male drug female drug2 25.5
61 Using aggregate() > aggregate( formula = age ~ gender + treatment, data = expt, FUN = mean ) gender treatment age 1 male control female control male drug female drug male drug female drug The output contains the mean age for every group
62 Try it yourself (Exercise 2.1.6)
63 Briefly... another trick is to use by() > by( expt, INDICES=expt$gender, summary ) expt$gender: male id age gender treatment hormone happy sad Min. :1.00 Min. :23.00 male :6 control:2 Min. : 6.70 Min. :2.000 Min. : st Qu.:2.25 1st Qu.:24.25 female:0 drug1 :2 1st Qu.: st Qu.: st Qu.:3.768 Median :3.50 Median :25.00 drug2 :2 Median :31.75 Median :3.380 Median :4.525 Mean :3.50 Mean :25.50 Mean :38.55 Mean :3.650 Mean : rd Qu.:4.75 3rd Qu.: rd Qu.: rd Qu.: rd Qu.:4.758 Max. :6.00 Max. :28.00 Max. :98.40 Max. :5.690 Max. : expt$gender: female id age gender treatment hormone happy sad Min. : 7.00 Min. :19.00 male :0 control:2 Min. :18.50 Min. :2.830 Min. : st Qu.: st Qu.:22.00 female:6 drug1 :2 1st Qu.: st Qu.: st Qu.:2.340 Median : 9.50 Median :25.50 drug2 :2 Median :54.90 Median :3.675 Median :2.675 Mean : 9.50 Mean :25.00 Mean :48.63 Mean :3.775 Mean : rd Qu.: rd Qu.: rd Qu.: rd Qu.: rd Qu.:2.882 Max. :12.00 Max. :30.00 Max. :65.20 Max. :4.780 Max. :4.820
64 Descriptives 2: Correlating two variables
65 Correlations > cor( expt$happy, expt$sad ) [1] Pearson correlation
66 Correlations > cor( expt$happy, expt$sad ) [1] > cor( expt$happy, expt$sad, method="spearman" ) [1] Spearman correlation
67 Correlations > cor( expt$happy, expt$sad ) [1] > cor( expt$happy, expt$sad, method="spearman" ) [1] > cor( expt$happy, expt$sad, method="kendall" ) [1] Kendall s tau
68 All pairwise correlations > library( lsr ) > correlate( expt ) Just a reminder that you need to have the lsr package loaded for this command to work! CORRELATIONS ============ The - correlate correlation command type: itself pearson - correlations shown only when both variables are numeric id age gender treatment hormone happy sad id age gender treatment hormone happy sad
69 All pairwise correlations > library( lsr ) > correlate( expt ) CORRELATIONS ============ - correlation type: pearson - correlations shown only when both variables are numeric id age gender treatment hormone happy sad id age gender treatment hormone happy sad
70 Try it yourself (Exercise 2.1.7)
71 End of this section
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