summaryStats: Summary Statistics

Description Usage Arguments Value Author(s) References See Also Examples

Description

summaryStats is a generic function used to produce summary statistics, confidence intervals, and results of hypothesis tests. The function invokes particular methods which depend on the class of the first argument.

The summary statistics include: sample size, number of missing values, mean, standard deviation, median, min, and max. Optional additional summary statistics include 1st quartile, 3rd quartile, and stadard error.

Usage

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summaryStats(object, ...)

## S3 method for class 'formula'
summaryStats(object, data = NULL, subset, 
  na.action = na.pass, ...)

## Default S3 method:
summaryStats(object, group = NULL, 
    drop.unused.levels = TRUE, se = FALSE, quartiles = FALSE, 
    digits = max(3, getOption("digits") - 3), 
    digit.type = "round", drop0trailing = TRUE, 
    show.na = TRUE, show.0.na = FALSE, p.value = FALSE, 
    p.value.digits = 2, p.value.digit.type = "signif", 
    test = "parametric", paired = FALSE, test.arg.list = NULL, 
    combine.groups = p.value, rm.group.na = TRUE, 
    group.p.value.type = NULL, alternative = "two.sided", 
    ci = NULL, ci.between = NULL, conf.level = 0.95, 
    stats.in.rows = FALSE, 
    data.name = deparse(substitute(object)), ...)

## S3 method for class 'factor'
summaryStats(object, group = NULL, 
    drop.unused.levels = TRUE, 
    digits = max(3, getOption("digits") - 3), 
    digit.type = "round", drop0trailing = TRUE,  
    show.na = TRUE, show.0.na = FALSE, p.value = FALSE, 
    p.value.digits = 2, p.value.digit.type = "signif", 
    test = "chisq", test.arg.list = NULL, combine.levels = TRUE, 
    combine.groups = FALSE, rm.group.na = TRUE, 
    ci = p.value & test != "chisq", conf.level = 0.95, 
    stats.in.rows = FALSE, ...)

## S3 method for class 'character'
summaryStats(object, ...)

## S3 method for class 'logical'
summaryStats(object, ...)

## S3 method for class 'data.frame'
summaryStats(object, ...)

## S3 method for class 'matrix'
summaryStats(object, ...)

## S3 method for class 'list'
summaryStats(object, ...)

Arguments

object

an object for which summary statistics are desired. In the default method, the argument object can be a numeric vector, factor, character vector, logical vector, data frame, matrix, or list. When object is a character or logical vector, it is coerced to be a factor. When object is a data frame, all columns must be numeric or all columns must be factors. When object is a matrix, it must be a numeric or character matrix. When object is a list, all components must be numeric vectors or all components must be factors. In the formula method, a symbolic specification of the form y ~ g can be given, indicating the observations in the vector y are to be grouped according to the levels of the factor g (the form y ~ 1 indicates no grouping). NAs are allowed in the data.

data

when object is a formula, data specifies an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which
summaryStats is called.

subset

when object is a formula, subset specifies an optional vector specifying a subset of observations to be used.

na.action

when object is a formula, na.action specifies a function which indicates what should happen when the data contain NAs. The default is na.pass.

group

when object is a numeric vector or factor, group is a factor or character vector indicating which group each observation belongs to. When object is a matrix or data frame this argument is ignored and the columns define the groups. When object is a formula, this argument is ignored and the right-hand side of the formula specifies the grouping variable.

drop.unused.levels

when drop.unused.levels=TRUE, groups with no observations are dropped.

se

for numeric data, logical scalar indicating whether to include the standard error of the mean in the summary statistics. The default value is se=FALSE.

quartiles

for numeric data, logical scalar indicating whether to include the estimated 25th and 75th percentiles in the summary statistics. The default value is
quartiles=FALSE.

digits

integer indicating the number of digits to use for the summary statistics. When digit.type="signif", digits indicates the number of significant digits. When digit.type="round", digits indicates the number of decimal places to round to. The default value is max(3, getOption("digits") - 3), that is, the maximum of 3 versus the current setting of the "digits" component of .Options minus 3.

digit.type

character string indicating whether the digits argument refers to significant digits (digit.type="signif"), or how many decimal places to round to
(digit.type="round", the default).

drop0trailing

logical scalar indicating whether to drop trailing 0's when printing the summary statistics. The value of this argument is added as an attribute to the returned list and is used by the print.summaryStats function. The default value is TRUE.

show.na

logical scalar indicating whether to return the number of missing values. The default value is show.na=TRUE.

show.0.na

logical scalar indicating whether to diplay the number of missing values in the case when there are no missing values. The default value is
show.0.na=FALSE.

p.value

logical scalar indicating whether to return the p-value associated with a test of hypothesis. The default value is p.value=FALSE. Numeric data: if there are no groups the p-value is associated with the t-test to test whether the mean is different from 0; if there are groups see the explanation for the argument group.p.value.type below. Factors: the p-value is associated with the test specified by the argument test (see below).

p.value.digits

integer indicating the number of digits to use for the p-value. When
p.value.digit.type="signif", p.value.digits indicates the number of significant digits. When p.value.digit.type="round", p.value.digits indicates the number of decimal places to round to. The default value is
p.value.digits=2.

p.value.digit.type

character string indicating whether the p.value.digits argument refers to significant digits (p.value.digit.type="signif", the default), or how many decimal places to round to (p.value.digit.type="round").

test

Numeric data: character string indicating whether to compute p-values and confidence intervals based on parametric (test="parametric"; the default) or nonparametric (test="nonparametric") tests when p.value=TRUE and/or ci=TRUE. When test="parametric", confidence intervals are based on the t-test (see t.test) and p-values are based on the t-test or F-test (see anova.lm). When test="nonparametric", confidence intervals are based on the Wilcoxon rank sum test (see wilcox.test) and p-values are based on the Wilcoxon rank sum test or the Kruskal-Wallis rank sum test
(see kruskal.test).

Factors: character string indicating which test to perform when
p.value=TRUE. Possible values are test="chisq" for the chi-squared test as performed by the function chisq.test (the default), test="prop" for the chi-squared test as performed by the function prop.test, test="fisher" for Fisher's exact test as performed by the function fisher.test, and
test="binom" for the one-sample exact binomial test as performed by
binom.test. The chi-squared test as performed by prop.test is only available when the number of levels in object is 2 and either group is not supplied or the number of levels in group is 2. Fisher's exact test is only available when the number of levels in group is ≥ 2. The exact binomial test is only available when group is not supplied and the number of levels in object is 2.

paired

applicable only to the case when there are two groups:
logical scalar indicating whether the observations in the first group are paired with those in the second group. The default is paired=FALSE. NOTE: If the argument test.arg.list (see below) contains a component named paired, the value of that component is set to the value of the argument paired.

test.arg.list

a list with additional arguments to pass to the test used to compute p-values and confidence intervals. For numeric data, when test="parametric",
p.value=TRUE, group.p.value.type="between" and there are two groups, if this argument is NULL or does not contain a component named
var.equal, it will be modified to contain the component var.equal=TRUE. Note that this overrides the default behavior of t.test when there are two groups.
NOTE: If test.arg.list contains a component named paired, the value of that component is set to the value of the argument paired (see above).

combine.groups

logical scalar indicating whether to show summary statistics for all groups combined. Numeric data: the default value is TRUE if p.value=TRUE, otherwise FALSE. Factors: the default value is FALSE.

rm.group.na

logical scalar indicating whether to remove missing values from the group argument. If rm.group.na=FALSE and group contains missing values then an error is returned. If rm.group.na=TRUE and group contains missing values then a warning is issued. By default rm.group.na=TRUE.

group.p.value.type

for numeric data, character string indicating which p-value(s) to compute when there is more than one group. When group.p.value.type="between" (the default when combine.groups=TRUE), the p-value is associated with the two-sample t-test (or the Wilcoxon rank sum test) in the case of two groups, and the one-way analysis of variance F-test (or Krukal-Wallis test) in the case of three or more groups to test whether the group means (locations) are different from each other. When group.p.value.type="within" (the default when combine.groups=FALSE), the computed p-values for each group are associated with the one-sample t-test (or Wilcox signed rank test) to test whether the group mean (location) is different from 0.

alternative

for numeric data, character string indicating which alternative to assume for p-values and confidence intervals. Possible values are "two.sided" (the default), "less", and "greater". This argument is ignored for p-values in the case of three or more groups when group.p.value.type="between", and is ignored for confidence intervals in the case of three or more groups when
ci.between=TRUE.

ci

Numeric data: logical scalar indicating whether to compute a confidence interval for the mean or each group mean. The default value is FALSE unless p.value=TRUE and there are no groups, or when p.value=TRUE and there are groups and group.p.value.type="within".

Factors: logical scalar indicating whether to compute a confidence interval. A confidence interval is computed only if the number of levels in object is 2. When group is not supplied, if ci=TRUE and test="prop" or
test="binom", a confidence interval for the percent (not probability) of the first level of object is computed. When group is supplied and the number of levels in group is 2, if ci=TRUE and test="prop", a confidence interval for the difference between percents (not proportions) is computed, and if test="fisher" a confidence interval for the odds ratio is computed.

ci.between

for numeric data, logical scalar indicating whether to compute a confidence interval for the difference between group means when there are two groups. The default value is ci.between=TRUE when p.value=TRUE and
group.p.value.type="between", otherwise this argument is ignored.

conf.level

numeric scalar between 0 and 1 indicating the confidence level associated with the confidence intervals. The default value is conf.level=0.95.

stats.in.rows

logical scalar indicating whether to show the summary statistics in the rows or columns of the output. The default is stats.in.rows=FALSE.

data.name

character string indicating the name of the data used for the summary statistics.

combine.levels

for factors, a logical scalar indicating whether to compute summary statistics based on combining all levels of a factor.

...

additional arguments affecting the summary statistics produced.

Value

an object of class "summaryStats" (see summaryStats.object. Objects of class "summaryStats" are numeric matrices that contain the summary statisics produced by a call to summaryStats or summaryFull. These objects have a special printing method that by default removes trailing zeros for sample size entries and prints blanks for statistics that are normally displayed as NA (see print.summaryStats).

Summary statistics for numeric data include sample size, mean, standard deviation, median, min, and max. Options include the standard error of the mean (when se=TRUE), the estimated quartiles (when quartiles=TRUE), p-values (when p.value=TRUE), and/or confidence intervals (when ci=TRUE and/or ci.between=TRUE).

Summary statistics for factors include the sample size for each level of the factor and the percent of the total for that level. Options include a p-value (when p.value=TRUE).

Note that unlike the R function summary and the EnvStats function summaryFull, by default the digits argument for the EnvStats function summaryStats refers to how many decimal places to round to, not how many significant digits to use (see the explanation of the argument digit.type above).

Author(s)

Steven P. Millard (EnvStats@ProbStatInfo.com)

References

Berthouex, P.M., and L.C. Brown. (2002). Statistics for Environmental Engineers, Second Edition. Lewis Publishers, Boca Raton, FL.

Millard, S.P., and N.K. Neerchal. (2001). Environmental Statistics with S-PLUS. CRC Press, Boca Raton, FL.

Zar, J.H. (2010). Biostatistical Analysis. Fifth Edition. Prentice-Hall, Upper Saddle River, NJ, Chapter 24.

See Also

summary, summaryFull, t.test, anova.lm, wilcox.test, kruskal.test, chisq.test,
fisher.test, binom.test.

Examples

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  # The guidance document USEPA (1994b, pp. 6.22--6.25)
  # contains measures of 1,2,3,4-Tetrachlorobenzene (TcCB)
  # concentrations (in parts per billion) from soil samples
  # at a Reference area and a Cleanup area. These data are strored
  # in the data frame EPA.94b.tccb.df.

  #----------
  # First, create summary statistics by area based on the log-transformed data. 

  summaryStats(log10(TcCB) ~ Area, data = EPA.94b.tccb.df)
  #           N    Mean     SD  Median     Min    Max
  #Cleanup   77 -0.2377 0.5908 -0.3665 -1.0458 2.2270
  #Reference 47 -0.2691 0.2032 -0.2676 -0.6576 0.1239

  #----------
  # Now create summary statistics by area based on the log-transformed data 
  # and use the t-test to compare the areas.

  summaryStats(log10(TcCB) ~ Area, data = EPA.94b.tccb.df, p.value = TRUE)

  summaryStats(log10(TcCB) ~ Area, data = EPA.94b.tccb.df, 
    p.value = TRUE, stats.in.rows = TRUE)
  #                Cleanup  Reference Combined
  #N                77       47       124     
  #Mean             -0.2377  -0.2691   -0.2496
  #SD                0.5908   0.2032    0.481 
  #Median           -0.3665  -0.2676   -0.3143
  #Min              -1.0458  -0.6576   -1.0458
  #Max               2.227    0.1239    2.227 
  #Diff                                -0.0313
  #p.value.between                      0.73  
  #95%.LCL.between                     -0.2082
  #95%.UCL.between                      0.1456

  #====================================================================

  # Page 9-3 of USEPA (2009) lists trichloroethene 
  # concentrations (TCE; mg/L) collected from groundwater at two wells.
  # Here, the seven non-detects have been set to their detection limit.

  #----------
  # First, compute summary statistics for all TCE observations.

  summaryStats(TCE.mg.per.L ~ 1, data = EPA.09.Table.9.1.TCE.df, 
    digits = 3, data.name = "TCE")
  #     N Mean    SD Median   Min  Max NA's N.Total
  #TCE 27 0.09 0.064    0.1 0.004 0.25    3      30

  summaryStats(TCE.mg.per.L ~ 1, data = EPA.09.Table.9.1.TCE.df,
    se = TRUE, quartiles = TRUE, digits = 3, data.name = "TCE")
  #     N Mean    SD    SE Median   Min  Max 1st Qu. 3rd Qu. NA's N.Total
  #TCE 27 0.09 0.064 0.012    0.1 0.004 0.25   0.031    0.12    3      30

  #----------
  # Now compute summary statistics by well.

  summaryStats(TCE.mg.per.L ~ Well, data = EPA.09.Table.9.1.TCE.df, 
    digits = 3)
  #        N  Mean    SD Median   Min  Max NA's N.Total
  #Well.1 14 0.063 0.079  0.031 0.004 0.25    1      15
  #Well.2 13 0.118 0.020  0.110 0.099 0.17    2      15

  summaryStats(TCE.mg.per.L ~ Well, data = EPA.09.Table.9.1.TCE.df,
    digits = 3, stats.in.rows = TRUE)
  #        Well.1 Well.2
  #N       14     13    
  #Mean     0.063  0.118
  #SD       0.079  0.02 
  #Median   0.031  0.11 
  #Min      0.004  0.099
  #Max      0.25   0.17 
  #NA's     1      2    
  #N.Total 15     15 

  # If you want to keep trailing 0's, use the drop0trailing argument:
  summaryStats(TCE.mg.per.L ~ Well, data = EPA.09.Table.9.1.TCE.df,
    digits = 3, stats.in.rows = TRUE, drop0trailing = FALSE)
  #        Well.1 Well.2
  #N       14.000 13.000
  #Mean     0.063  0.118
  #SD       0.079  0.020
  #Median   0.031  0.110
  #Min      0.004  0.099
  #Max      0.250  0.170
  #NA's     1.000  2.000
  #N.Total 15.000 15.000

  #====================================================================

  # Page 13-3 of USEPA (2009) lists iron concentrations (ppm) in 
  # groundwater collected from 6 wells.  

  #----------
  # First, compute summary statistics for each well.

  summaryStats(Iron.ppm ~ Well, data = EPA.09.Ex.13.1.iron.df, 
    combine.groups = FALSE, digits = 2, stats.in.rows = TRUE)
  #       Well.1 Well.2 Well.3 Well.4 Well.5 Well.6
  #N        4      4      4      4      4      4   
  #Mean    47.01  55.73  90.86  70.43 145.24 156.32
  #SD      12.4   20.34  59.35  25.95  92.16  51.2 
  #Median  50.05  57.05  76.73  76.95 137.66 171.93
  #Min     29.96  32.14  39.25  34.12  60.95  83.1 
  #Max     57.97  76.71 170.72  93.69 244.69 198.34

  #----------
  # Note the large differences in standard deviations between wells.
  # Compute summary statistics for log(Iron), by Well.

  summaryStats(log(Iron.ppm) ~ Well, data = EPA.09.Ex.13.1.iron.df, 
    combine.groups = FALSE, digits = 2, stats.in.rows = TRUE)
  #       Well.1 Well.2 Well.3 Well.4 Well.5 Well.6
  #N      4      4      4      4      4      4     
  #Mean   3.82   3.97   4.35   4.19   4.8    5     
  #SD     0.3    0.4    0.66   0.45   0.7    0.4   
  #Median 3.91   4.02   4.29   4.34   4.8    5.14  
  #Min    3.4    3.47   3.67   3.53   4.11   4.42  
  #Max    4.06   4.34   5.14   4.54   5.5    5.29

  #----------
  # Include confidence intervals for the mean log(Fe) concentration
  # at each well, and also the p-value from the one-way 
  # analysis of variance to test for a difference in well means.

  summaryStats(log(Iron.ppm) ~ Well, data = EPA.09.Ex.13.1.iron.df, 
    digits = 1, ci = TRUE, p.value = TRUE, stats.in.rows = TRUE)
  #                Well.1 Well.2 Well.3 Well.4 Well.5 Well.6 Combined
  #N                4      4      4      4      4      4     24      
  #Mean             3.8    4      4.3    4.2    4.8    5      4.4    
  #SD               0.3    0.4    0.7    0.5    0.7    0.4    0.6    
  #Median           3.9    4      4.3    4.3    4.8    5.1    4.3    
  #Min              3.4    3.5    3.7    3.5    4.1    4.4    3.4    
  #Max              4.1    4.3    5.1    4.5    5.5    5.3    5.5    
  #95%.LCL          3.3    3.3    3.3    3.5    3.7    4.4    4.1    
  #95%.UCL          4.3    4.6    5.4    4.9    5.9    5.6    4.6    
  #p.value.between                                            0.025 

  #====================================================================

  # Using the built-in dataset HairEyeColor, summarize the frequencies 
  # of hair color and test whether there is a difference in proportions.
  # NOTE:  The data that was originally factor data has already been 
  #        collapsed into frequency counts by catetory in the object 
  #        HairEyeColor.  In the examples in this section, we recreate 
  #        the factor objects in order to show how summaryStats works 
  #        for factor objects.

  Hair <- apply(HairEyeColor, 1, sum)
  Hair
  #Black Brown   Red Blond 
  #  108   286    71   127

  Hair.color <- names(Hair)
  Hair.fac <- factor(rep(Hair.color, times = Hair), 
    levels = Hair.color)

  #----------

  # Compute summary statistics and perform the chi-square test 
  # for equal proportions of hair color

  summaryStats(Hair.fac, digits = 1, p.value = TRUE)
  #           N   Pct ChiSq_p
  #Black    108  18.2        
  #Brown    286  48.3        
  #Red       71  12.0        
  #Blond    127  21.5        
  #Combined 592 100.0 2.5e-39

  #----------
  # Now test the hypothesis that 10% of the population from which 
  # this sample was drawn has Red hair, and compute a 95% confidence 
  # interval for the percent of subjects with red hair.

  Red.Hair.fac <- factor(Hair.fac == "Red", levels = c(TRUE, FALSE), 
    labels = c("Red", "Not Red"))

  summaryStats(Red.Hair.fac, digits = 1, p.value = TRUE, 
    ci = TRUE, test = "binom", test.arg.list = list(p = 0.1))
  #           N Pct Exact_p 95%.LCL 95%.UCL
  #Red       71  12             9.5    14.9
  #Not Red  521  88                        
  #Combined 592 100    0.11

  #----------
  # Now test whether the percent of people with Green eyes is the 
  # same for people with and without Red hair.

  HairEye <- apply(HairEyeColor, 1:2, sum)
  Hair.color <- rownames(HairEye)
  Eye.color  <- colnames(HairEye)

  n11 <-     HairEye[Hair.color == "Red", Eye.color == "Green"]
  n12 <- sum(HairEye[Hair.color == "Red", Eye.color != "Green"])
  n21 <- sum(HairEye[Hair.color != "Red", Eye.color == "Green"])
  n22 <- sum(HairEye[Hair.color != "Red", Eye.color != "Green"])

  Hair.fac <- factor(rep(c("Red", "Not Red"), c(n11+n12, n21+n22)), 
    levels = c("Red", "Not Red"))
  Eye.fac  <- factor(c(rep("Green", n11), rep("Not Green", n12), 
    rep("Green", n21), rep("Not Green", n22)), 
    levels = c("Green", "Not Green"))


  #----------
  # Here are the results using the chi-square test and computing 
  # confidence limits for the difference between the two percentages

  summaryStats(Eye.fac, group = Hair.fac, digits = 1, 
    p.value = TRUE, ci = TRUE, test = "prop", 
    stats.in.rows = TRUE, test.arg.list = list(correct = FALSE))
  #                Green Not Green Combined
  #Red(N)           14    57        71     
  #Red(Pct)         19.7  80.3     100     
  #Not Red(N)       50   471       521     
  #Not Red(Pct)      9.6  90.4     100     
  #ChiSq_p                           0.01  
  #95%.LCL.between                   0.5   
  #95%.UCL.between                  19.7

  #----------
  # Here are the results using Fisher's exact test and computing 
  # confidence limits for the odds ratio

  summaryStats(Eye.fac, group = Hair.fac, digits = 1, 
    p.value = TRUE, ci = TRUE, test = "fisher", 
    stats.in.rows = TRUE)
  #             Green Not Green Combined
  #Red(N)        14    57        71     
  #Red(Pct)      19.7  80.3     100     
  #Not Red(N)    50   471       521     
  #Not Red(Pct)   9.6  90.4     100     
  #Fisher_p                       0.015 
  #95%.LCL.OR                     1.1   
  #95%.UCL.OR                     4.6 

  rm(Hair, Hair.color, Hair.fac, Red.Hair.fac, HairEye, Eye.color, 
    n11, n12, n21, n22, Eye.fac)

  #====================================================================

  # The data set EPA.89b.cadmium.df contains information on 
  # cadmium concentrations in groundwater collected from a
  # background and compliance well.  Compare detection frequencies 
  # between the well types and test for a difference using 
  # Fisher's exact test.

  summaryStats(factor(Censored) ~ Well.type, data = EPA.89b.cadmium.df, 
    digits = 1, p.value = TRUE, test = "fisher")


  summaryStats(factor(Censored) ~ Well.type, data = EPA.89b.cadmium.df, 
    digits = 1, p.value = TRUE, test = "fisher", stats.in.rows = TRUE)
  #                FALSE TRUE  Combined
  #Background(N)     8    16    24     
  #Background(Pct)  33.3  66.7 100     
  #Compliance(N)    24    40    64     
  #Compliance(Pct)  37.5  62.5 100     
  #Fisher_p                      0.81  
  #95%.LCL.OR                    0.3   
  #95%.UCL.OR                    2.5

  #====================================================================

  #--------------------
  # Paired Observations
  #--------------------

  # The data frame ACE.13.TCE.df contians paired observations of 
  # trichloroethylene (TCE; mg/L) at 10 groundwater monitoring wells 
  # before and after remediation.
  #
  # Compare TCE concentrations before and after remediation and 
  # use a paired t-test to test for a difference between periods.

  summaryStats(TCE.mg.per.L ~ Period, data = ACE.13.TCE.df, 
    p.value = TRUE, paired = TRUE)


  summaryStats(TCE.mg.per.L ~ Period, data = ACE.13.TCE.df, 
    p.value = TRUE, paired = TRUE, stats.in.rows = TRUE)
  #                       Before   After    Combined
  #N                       10       10       20     
  #Mean                    21.624    3.6329  12.6284
  #SD                      13.5113   3.5544  13.3281
  #Median                  20.3      2.48     8.475 
  #Min                      5.96     0.272    0.272 
  #Max                     41.5     10.7     41.5   
  #Diff                                     -17.9911
  #paired.p.value.between                     0.0027
  #95%.LCL.between                          -27.9097
  #95%.UCL.between                           -8.0725

  #==========

  # Repeat the last example, but use a one-sided alternative since 
  # remediation should decrease TCE concentration.

  summaryStats(TCE.mg.per.L ~ Period, data = ACE.13.TCE.df, 
    p.value = TRUE, paired = TRUE, alternative = "less")


  summaryStats(TCE.mg.per.L ~ Period, data = ACE.13.TCE.df, 
    p.value = TRUE, paired = TRUE, alternative = "less", 
    stats.in.rows = TRUE)
  #                            Before   After    Combined
  #N                            10       10       20     
  #Mean                         21.624    3.6329  12.6284
  #SD                           13.5113   3.5544  13.3281
  #Median                       20.3      2.48     8.475 
  #Min                           5.96     0.272    0.272 
  #Max                          41.5     10.7     41.5   
  #Diff                                          -17.9911
  #paired.p.value.between.less                     0.0013
  #95%.LCL.between                                   -Inf
  #95%.UCL.between                                -9.9537

EnvStats documentation built on Oct. 23, 2020, 6:41 p.m.