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Why the t.test returns a smallest p-value of 2.2e – 16 in R?
When we perform a t test in R and the difference between two groups is very large then the p-value of the test is printed as 2.2e – 16 which is a printing behaviour of R for hypothesis testing procedures. The actual p-value can be extracted by using the t test function as t.test(“Var1”,”Var2”,var.equal=FALSE)$p.value. This p-value is not likely to be the same as 2.2e – 16.
Example1
> x1<-1:100 > y1<-100001:110000 > t.test(x1,y1,var.equal=FALSE)
Output
Welch Two Sample t-test data: x1 and y1 t = -3617.2, df = 10098, p-value < 2.2e-16 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -105006.9 -104893.1 sample estimates: mean of x mean of y 50.5 105000.5
> t.test(x1,y1,var.equal=FALSE)$p.value [1] 0
Example2
> x2<-sample(1:10,50,replace=TRUE) > y2<-sample(500:510,replace=TRUE) > t.test(x2,y2,var.equal=FALSE)
Output
Welch Two Sample t-test data: x2 and y2 t = -427.61, df = 12.789, p-value < 2.2e-16 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -500.4179 -495.3785 sample estimates: mean of x mean of y 5.9200 503.8182
> t.test(x2,y2,var.equal=FALSE)$p.value [1] 5.881324e-28
Example3
> x3<-sample(101:110,50,replace=TRUE) > y3<-sample(1001:1010,50,replace=TRUE) > t.test(x3,y3,var.equal=FALSE)
Output
Welch Two Sample t-test data: x3 and y3 t = -1730.7, df = 97.907, p-value < 2.2e-16 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -901.4725 -899.4075 sample estimates: mean of x mean of y 105.38 1005.82
> t.test(x3,y3,var.equal=FALSE)$p.value [1] 2.07048e-221
Example4
> x4<-sample(1001:1010,50,replace=TRUE) > y4<-sample(100001:1000010,50) > t.test(x4,y4,var.equal=FALSE)
Output
Welch Two Sample t-test data: x4 and y4 t = -14.798, df = 49, p-value < 2.2e-16 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -620129.5 -471835.6 sample estimates: mean of x mean of y 1005.6 546988.1
> t.test(x4,y4,var.equal=FALSE)$p.value [1] 1.043251e-19
Updated on: 04-Sep-2020
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