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Two sided or one sided interval estimation of mu1-mu2 of two normal samples

interval_estimate5.Rd

Compute the two sided or one sided interval estimation of mu1-mu2 of two normal samples when the population variances are known, unknown equal, or unknown unequal.

Usage

interval_estimate5(x, y, sigma = c(-1, -1), var.equal = FALSE, side = 0, alpha = 0.05)

Arguments

x

A numeric vector.

y

A numeric vector.

sigma

A numeric vector of length 2, which contains the standard deviations of two populations. When the standard deviations are known, input it, then the function computes the interval endpoints using normal population; when the standard deviations are unknown, ignore it, now we need to consider whether the two populations have equal variances. See var.equal below.

var.equal

A logical variable indicating whether to treat the two variances as being equal. If TRUE then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used.

side

A parameter used to control whether to compute two sided or one sided interval estimation. When computing the one sided upper limit, input side = -1; when computing the one sided lower limit, input side = 1; when computing the two sided limits, input side = 0 (default).

alpha

The significance level, a real number in [0, 1]. Default to 0.05. 1-alpha is the degree of confidence.

Value

A data.frame with variables:

mean

The difference of sample means xb-yb.

df

The degree of freedom.

a

The confidence lower limit.

b

The confidence upper limit.

References

Zhang, Y. Y., Wei, Y. (2013), One and two samples using only an R funtion, doi:10.2991/asshm-13.2013.29 .

Author

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

Examples

x=rnorm(10, mean = 1, sd = 0.2); x
#>  [1] 0.8441429 1.3078899 1.1400111 1.0235185 0.9432755 1.0995818 1.3219886
#>  [8] 1.3722272 1.0772498 0.7062713
y=rnorm(20, mean = 2, sd = 0.3); y
#>  [1] 2.215257 2.039573 1.440223 1.723801 2.361209 2.080180 1.459922 1.605099
#>  [9] 1.928436 1.657061 1.764657 1.751669 2.283301 1.808092 1.347131 1.934857
#> [17] 2.173974 2.587151 1.714219 1.439784

interval_estimate5(x, y, sigma = c(0.2, 0.3), side = -1)
#>         mean df    a          b
#> 1 -0.7821642 30 -Inf -0.6305162
interval_estimate5(x, y, var.equal = TRUE)
#>         mean df         a          b
#> 1 -0.7821642 28 -1.025611 -0.5387177
interval_estimate5(x, y)
#>         mean       df         a          b
#> 1 -0.7821642 26.24205 -0.992436 -0.5718925