One Sample Analysis in R

One sample analysis in R-In statistics, we can define the corresponding null hypothesis  (H0) as follow:

Hypothesis:

1.      H0:m=μ, 

2.      H0:m≤μ

3.      H0:m≥μ

The corresponding alternative hypotheses (Ha) are as follow:

1.      Ha:m≠μ (different)

2.      Ha:m>μ (greater)

3.      Ha:m<μ (less)

Outlier Detection:

Out.fun<-function{abs(x-mean(x,na.rm=TRUE))>3*sd(x,na.rm=TRUE)}
ddply(data,.(sample, variable),transform,outlier.team=out.fun(value))

column heading should be sample, variable, value

Check outlier detection based on the above formula and remove if any.

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Shapiro-Wilk test:

Ho: Null hypothesis: the data are normally distributed.

H1: Alternative hypothesis: the data are not normally distributed

shapiro.test(data$weight) 

From the output, the p-value is greater than the significance level of 0.05 implying that the distribution of the data is not significantly different from a normal distribution. In other words, we can assume normality.

Parametric Method:

one-sample t-test is used to compare the mean of one sample to a known standard (or theoretical/hypothetical) mean (μ). the one-sample t-test can be used only when the data are normally distributed.

One sample analysis in R

one-sample t-test

two.sided

To perform a one-sample t-test, the R function t.test() can be used as follow:

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t.test(x, mu = 0, alternative = “two.sided”)

one sided

t.test(data$weight, mu = 2, alternative = “less”)
t.test(data$weight, mu = 2, alternative = “greater”)

Non Parametric Method:

The one-sample Wilcoxon signed-rank test is a non-parametric alternative to a one-sample t-test when the data cannot be assumed to be normally distributed. It’s used to determine whether the median of the sample is equal to a known standard value (i.e. theoretical value).

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one-sample Wilcoxon test

two.sided

To perform a one-sample Wilcoxon-test, the R function wilcox.test() can be used as follow:

wilcox.test(x, mu = 0, alternative = “two.sided”)

one sided

wilcox.test(data$weight, mu = 2, alternative = “less”)
wilcox.test(data$weight, mu = 2, alternative = “greater”)

Interpretation

The p-value of the test is less than the significance level alpha = 0.05. We can conclude that the mean weight is significantly different from 2g with a p-value x.

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