Water pH levels of 75 water samples taken in the Great Smoky Mountains

Data for Exercises 6.40, 6.59, 7.10, and 7.35

Smokyph

Format

A data frame/tibble with 75 observations on three variables

waterph

water sample pH level

code

charater variable with values low (elevation below 0.6 miles), and high (elevation above 0.6 miles)

elev

elevation in miles

Source

Schmoyer, R. L. (1994), Permutation Tests for Correlation in Regression Errors, Journal of the American Statistical Association, 89, 1507-1516.

References

Kitchens, L. J. (2003) Basic Statistics and Data Analysis. Pacific Grove, CA: Brooks/Cole, a division of Thomson Learning.

Examples

summary(Smokyph$waterph)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   6.380   6.880   7.030   7.140   7.235   8.430 
tapply(Smokyph$waterph, Smokyph$code, mean)
#>     high      low 
#> 7.039697 7.218095 
stripchart(waterph ~ code, data = Smokyph, method = "stack",
           pch = 19, col = c("red", "blue"))

           t.test(Smokyph$waterph, mu = 7)
#> 
#> 	One Sample t-test
#> 
#> data:  Smokyph$waterph
#> t = 2.7516, df = 74, p-value = 0.007452
#> alternative hypothesis: true mean is not equal to 7
#> 95 percent confidence interval:
#>  7.038511 7.240689
#> sample estimates:
#> mean of x 
#>    7.1396 
#> 
           SIGN.test(Smokyph$waterph, md = 7)
#> 
#> 	One-sample Sign-Test
#> 
#> data:  Smokyph$waterph
#> s = 42, p-value = 0.2954
#> alternative hypothesis: true median is not equal to 7
#> 95 percent confidence interval:
#>  6.954832 7.085168
#> sample estimates:
#> median of x 
#>        7.03 
#> 
#> Achieved and Interpolated Confidence Intervals: 
#> 
#>                   Conf.Level L.E.pt U.E.pt
#> Lower Achieved CI     0.9361 6.9600 7.0800
#> Interpolated CI       0.9500 6.9548 7.0852
#> Upper Achieved CI     0.9630 6.9500 7.0900
#> 
           t.test(waterph ~ code, data = Smokyph, alternative = "less")
#> 
#> 	Welch Two Sample t-test
#> 
#> data:  waterph by code
#> t = -1.859, df = 70.875, p-value = 0.03359
#> alternative hypothesis: true difference in means between group high and group low is less than 0
#> 95 percent confidence interval:
#>         -Inf -0.01845818
#> sample estimates:
#> mean in group high  mean in group low 
#>           7.039697           7.218095 
#> 
           t.test(waterph ~ code, data = Smokyph, conf.level = 0.90)
#> 
#> 	Welch Two Sample t-test
#> 
#> data:  waterph by code
#> t = -1.859, df = 70.875, p-value = 0.06718
#> alternative hypothesis: true difference in means between group high and group low is not equal to 0
#> 90 percent confidence interval:
#>  -0.33833836 -0.01845818
#> sample estimates:
#> mean in group high  mean in group low 
#>           7.039697           7.218095 
#> 
 if (FALSE) {
 library(ggplot2)
 ggplot2::ggplot(data = Smokyph, aes(x = waterph, fill = code)) + 
            geom_dotplot() + 
            facet_grid(code ~ .) + 
            guides(fill = FALSE)
}