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Inference for Means

means.Rmd

One Sample t-test 

one_t_inference(wt ~ 1, data = mtcars2)
response n mean SE df conf.low conf.high
wt 32 3.22 0.17 31 2.86 3.57
One Sample t-test (two.sided), with 95% confidence intervals.

Separately by another categorical variable 

one_t_inference(wt ~ am, data = mtcars2)
response variable n mean SE df conf.low conf.high
wt am = automatic 19 3.77 0.18 18 3.39 4.14
wt am = manual 13 2.41 0.17 12 2.04 2.78
One Sample t-test (two.sided), with 95% confidence intervals.

Two Sample t-test 

two_t_inference(wt ~ am, data = mtcars2)
response variable difference SE df conf.low conf.high null t.value p.value
wt am: automatic - manual 1.36 0.25 29.2 0.85 1.86 0.000 5.49 < 0.0001
Welch Two Sample t-test (two.sided), with 95% confidence intervals.

together in one table 

combine_tests(
  one_t_inference(wt ~ am, data = mtcars2),
  two_t_inference(wt ~ am, data = mtcars2))
response variable n mean difference SE df conf.low conf.high null t.value p.value footnote
wt am = automatic 19 3.77
0.18 18.0 3.39 4.14


1 
wt am = manual 13 2.41
0.17 12.0 2.04 2.78


1 
wt am: automatic - manual

1.36 0.25 29.2 0.85 1.86 0.000 5.49 < 0.0001 2 
1 One Sample t-test (two.sided), with 95% confidence intervals.
2 Welch Two Sample t-test (two.sided), with 95% confidence intervals.

Pairwise t-tests 

combine_tests(
  one_t_inference(wt ~ cyl, data = mtcars2),
  pairwise_t_inference(wt ~ cyl, data = mtcars2))
response variable n mean difference SE df conf.low conf.high null t.value p.value p.adjust footnote
wt cyl = 4 11 2.29
0.17 10.0   1.90  2.67



1 
wt cyl = 6 7 3.12
0.13  6.00  2.79  3.45



1 
wt cyl = 8 14 4.00
0.20 13.0   3.56  4.44



1 
wt cyl: 4 - 6

−0.83 0.22 16.0  −1.41 −0.25 0.000 -3.81   0.0015   0.0046 2,3 
wt cyl: 4 - 8

−1.71 0.27 23.0  −2.40 −1.03 0.000 -6.44 < 0.0001 < 0.0001 2,3 
wt cyl: 6 - 8

−0.88 0.24 19.0  −1.52 −0.24 0.000 -3.62   0.0018   0.0055 2,3 
1 One Sample t-test (two.sided), with 95% confidence intervals.
2 Welch Two Sample t-test (two.sided), with 95% confidence intervals, adjusted for 3 comparisons using the Bonferroni method.
3 p-values adjusted for 3 multiple comparisons using the Bonferroni method.

Paired t-test 

combine_tests(
  one_t_inference(score1 + score2 ~ 1, data = passfail),
  paired_t_inference(score2 - score1 ~ 1, data = passfail))
response n mean difference SE df conf.low conf.high null t.value p.value footnote
score1 50 81.85
0.90 49 80.05 83.66


1 
score2 50 84.6 
1.0  49 82.5  86.7 


1 
score2 - score1

2.7 1.3  49  0.2   5.3  0.000 2.17   0.035 2 
1 One Sample t-test (two.sided), with 95% confidence intervals.
2 Paired t-test (two.sided), with 95% confidence intervals.

Log transformations

By default, responses using log(...) are back-transformed. To keep the result on the log scale, use backtransform = FALSE.

combine_tests(
  one_t_inference(log(wt) ~ am, data = mtcars2, backtransform = FALSE),
  two_t_inference(log(wt) ~ am, data = mtcars2, backtransform = FALSE),
  one_t_inference(log(wt) ~ am, data = mtcars2),
  two_t_inference(log(wt) ~ am, data = mtcars2))
response variable n mean difference ratio SE df conf.low conf.high null t.value p.value footnote
log(wt) am = automatic 19 1.308

0.045 18.0 1.215 1.402


1 
log(wt) am = manual 13 0.849

0.072 12.0 0.691 1.007


1 
log(wt) am: automatic - manual

0.459
0.085 20.8 0.282 0.636 0.000 5.40 < 0.0001 2 
wt am = automatic 19 3.70 

0.16  18.0 3.37  4.06 


1,3 
wt am = manual 13 2.34 

0.17  12.0 2.00  2.74 


1,3 
wt am: automatic / manual


1.58 0.13  20.8 1.33  1.89  1.00  5.40 < 0.0001 2,4 
1 One Sample t-test (two.sided), with 95% confidence intervals.
2 Welch Two Sample t-test (two.sided), with 95% confidence intervals.
3 Results are backtransformed from the log scale (that is, the geometric mean is reported), and the standard error is estimated using the delta method.
4 Results are backtransformed from the log scale (that is, the ratio is reported), and the standard error is estimated using the delta method. 

combine_tests(
  one_t_inference(log(score1) + log(score2) ~ 1, data = passfail),
  paired_t_inference(log(score2) - log(score1) ~ 1, data = passfail))
response n mean ratio SE df conf.low conf.high null t.value p.value footnote
score1 50 81.61
0.90  49 79.82  83.44 


1,2 
score2 50 84.3 
1.0   49 82.2   86.4  


1,2 
score2 / score1

1.033 0.016 49  1.001  1.065 1.00 2.09   0.042 3,4 
1 One Sample t-test (two.sided), with 95% confidence intervals.
2 Results are backtransformed from the log scale (that is, the geometric mean is reported), and the standard error is estimated using the delta method.
3 Paired t-test (two.sided), with 95% confidence intervals.
4 Results are backtransformed from the log scale (that is, the ratio is reported), and the standard error is estimated using the delta method.