tValue

David Bourne david@boomer.org
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10 Feb 2016 v1.0.0 Approved

Unpaired t-test: Unequal or Equal variance and Unequal sample size

Example Data

  30.02 29.89
  29.99 29.93
  30.11 29.72
  29.97 29.98
  30.01 30.02
  29.99 29.98
  30.00  
  30.04  
Mean 30.01625 29.92
Std Dev 0.04340425 0.1078888
n 8 6

The result using R Studio and R

Using the Welch-Satterthwaite Method

> b1
 [1] 30.02 29.99 30.11 29.97 30.01 29.99 30.00 30.04
 > b2
 [1] 29.89 29.93 29.72 29.98 30.02 29.98
> sd(b1)
 [1] 0.04340425
 > sd(b2)
 [1] 0.1078888
> t.test(b1,b2)
 
 Welch Two Sample t-test
 
 data:  b1 and b2
 t = 2.0636, df = 6.2221, p-value = 0.08296
 alternative hypothesis: true difference in means is not equal to 0
 95 percent confidence interval:
 -0.01689914  0.20939914
 sample estimates:
 mean of x mean of y
 30.01625  29.92000

Using a Pooled mathod

 > t.test(b1,b2,var.equal = TRUE)
 
 Two Sample t-test
 
 data:  b1 and b2
 t = 2.3107, df = 12, p-value = 0.03943
 alternative hypothesis: true difference in means is not equal to 0
 95 percent confidence interval:
 0.005492236 0.187007764
 sample estimates:
 mean of x mean of y
 30.01625  29.92000
tValue Screenshot

One Sample t-test or Paired t-test

tValue can also be used to calculate a t value when only set of data is being compared with zero or another specified value. This method can also be used for a paired t-test once the difference between paired values is calculated.

Example Data

  0.213
  0.134
  0.043
  1.34
Mean 0.4325
Std Dev 0.6090
n 4

Leave the second set of values empty.

The result using R Studio and R

> a2 <- c(0.213,0.134,0.043,1.34)
> sd(a2)
 [1] 0.6089743
> t.test(a2)
 
 One Sample t-test
 
 data:  a2
 t = 1.4204, df = 3, p-value = 0.2506
 alternative hypothesis: true mean is not equal to 0
 95 percent confidence interval:
 -0.536514  1.401514
 sample estimates:
 mean of x
 0.4325

And data for a paired t-test

> b1
 [1] 30.02 29.99 30.11 29.97 30.01 29.99 30.00 30.04
> b2
 [1] 29.89 29.93 29.72 29.98 30.02 29.98 29.97 30.01
> c1 <- b1-b2
> c1
 [1]  0.13  0.06  0.39 -0.01 -0.01  0.01  0.03  0.03
> sd(c1)
 [1] 0.1336774
> t.test(b1,b2,var.equal = TRUE,paired = TRUE)
 
 Paired t-test
 
 data:  b1 and b2
 t = 1.6662, df = 7, p-value = 0.1396
 alternative hypothesis: true difference in means is not equal to 0
 95 percent confidence interval:
 -0.03300709  0.19050709
 sample estimates:
 mean of the differences
 0.07875
One sample t-test
tValue Screenshot
Paired t-test
tValue Screenshot

References

Localization

Please let me know if I've made a mistake with these translation or if additional translations can be added, e.g. for Std Dev or n, P or df. Thanks, David Bourne (david@boomer.org)

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David Bourne (david@boomer.org)