Tests and confidence intervals

We can do z-test, t-test and find confidence intervals for the mean of a normal distribution and do the elementary statistical inference.

binom.test(x, n, p=0.5, alternative="two.sided") Test hypothesises about the parameter p in a Binomial(n,p) model given x, the number of successes out of n trials. The argument alternative has 3 options: "two.sided" (not equal to p), "less" (less than p) or "greater" (greater than p)
chisq.test(x, y=NULL, correct=T ) Performs a Pearson's chi-square test on a two-dimensional contingency table.
chisq.gof(x, n.classes=ceiling(2 * (length(x)^(2/5))), cut.points=NULL, distribution="normal", n.param.est=0, ...) performs a chi square goodness-of-fit test.
cor.test(x, y, alternative="two.sided", method="pearson") tests whether two vectors are uncorrelated using Pearson's product moment correlation coefficient, Kendall's tau-statistic, or Spearman's rank correlation. The options of method are "pearson", "kendall", or "spearman", depending on what coefficient of correlation should be used in the test statistic. Only the first character is necessary.
fisher.test(x, y=NULL, node.stack.dim=1001, value.stack.dim=10000, hybrid=F) performs a Fisher's exact test on a two-dimensional contingency table.
friedman.test(y, groups, blocks) performs a Friedman rank sum test with unreplicated blocked data.
kruskal.test(y, groups) performs a Kruskal-Wallis rank sum test on data following a one-way layout.
ks.gof(x, y = NULL, alternative = "two.sided", distribution = "normal", ...) performs a one or two sample Kolmogorov-Smirnov test, which tests the relationship between two distributions.
mcnemar.test(x, y=NULL, correct=T) performs a McNemar's chi-square test on a two-dimensional contingency table.
prop.test(x, n, p=<>, alternative="two.sided", conf.level=.95, correct=T) compares proportions against hypothesized values. Alternately, tests whether underlying proportions are equal.
t.test(x, y=NULL, alternative="two.sided", mu=0, paired=F, var.equal=T, conf.level=.95) does the z-test and t-test. If y is not indicated, we get the one sample case. The argument alternative has the options: "greater", "less" or "two.sided".
var.test(x, y, alternative="two.sided", conf.level=.95) Performs an F test to compare variances of two samples from normal populations.
wilcox.test(x, y, alternative="two.sided", mu=0, paired=F, exact=T, correct=T) computes Wilcoxon rank sum test for two sample data (equivalent to the Mann-Whitney test) or the Wilcoxon signed rank test for paired or one sample data.

For example,

> x
[1] -1.7 -1.3 -5.0  0.2  6.0  1.5  2.3  2.7
> y
[1]   12   34    5   12    6    7 2345    2  
> t.test(x,mu=23,var=2)
        One-sample t-Test
data:  x
t = -19.0285, df = 7, p-value = 0
alternative hypothesis: true mean is not equal to 23
95 percent confidence interval:
 -2.197641  3.372641
sample estimates:
 mean of x
    0.5875        
> t.test(x,mu=2,alternative="greater")

        One-sample t-Test

data:  x
t = -1.1992, df = 7, p-value = 0.8653
alternative hypothesis: true mean is greater than 2
95 percent confidence interval:
 -1.644004        NA
sample estimates:
 mean of x
    0.5875

> t.test(x,mu=10)
        One-sample t-Test
data:  x
t = -7.9913, df = 7, p-value = 1e-04
alternative hypothesis: true mean is not equal to 10
95 percent confidence interval:
 -2.197641  3.372641
sample estimates:
 mean of x
    0.5875

> t.test(x,y)
        Standard Two-Sample t-Test
data:  x and y
t = -1.0361, df = 14, p-value = 0.3177
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -928.041  323.466
sample estimates:
 mean of x mean of y
    0.5875   302.875  
> t.test(x,y,var.equal=F)
        Welch Modified Two-Sample t-Test
data:  x and y
t = -1.0361, df = 7, p-value = 0.3346
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -992.1753  387.6003
sample estimates:
 mean of x mean of y
    0.5875   302.875
                     
> t.test(x,y,var.equal=T)
        Standard Two-Sample t-Test
data:  x and y
t = -1.0361, df = 14, p-value = 0.3177
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -928.041  323.466
sample estimates:
 mean of x mean of y
    0.5875   302.875
> t.test(x,y,paired=T)
        Paired t-Test
data:  x and y
t = -1.037, df = 7, p-value = 0.3342
alternative hypothesis: true mean of differences is not equal to 0
95 percent confidence interval:
 -991.6102  387.0352
sample estimates:
 mean of x - y
     -302.2875