I'm assuming that the data are assumed to be paired as ordered in the two inputs in the non-formula signature of the t.test function t.test(x, y, paired=T) (x and y in the documentation).

However, how does the function associate observations in the two groups as pairs in the formula signature t.test(values groups, df, paired=T)? by sequence?

I make a dataframe with paired before and after data in the spreadsheet below. Then, I formatted it twice in long form (as would be appropriate for the t.test function): 1) List the "before" group in the order of observation, followed by the "after" group. 2) List every piece of information in random order.

On both sets of data, I conduct a paired t-test. It's rather clear that in two groups, the t.test function is making some kind of assumption.

```library(tidyverse)

df = data.frame(
observation = 1:20,
before = rnorm(20, 10, 2),
after = rnorm(20, 10.2, 2.3)
)

print.data.frame(df)
#>    observation    before     after
#> 1            1 10.930157 11.818216
#> 2            2 10.870749 10.699232
#> 3            3  9.603120 14.384484
#> 4            4  9.615291  8.777045
#> 5            5  6.714043  9.506421
#> 6            6  9.063117  5.574887
#> 7            7  8.152260 10.357455
#> 8            8  8.256237  8.660646
#> 9            9 12.641977  7.511760
#> 10          10 11.010290  9.391047
#> 11          11 12.545197  9.072856
#> 12          12 12.606526  9.110687
#> 13          13  8.659088 12.445071
#> 14          14  8.958959 10.783168
#> 15          15 11.635443  6.926802
#> 16          16  6.922437 12.419453
#> 17          17 10.326176 10.416757
#> 18          18  7.680960  9.836573
#> 19          19  9.458365  8.083777
#> 20          20  7.235837 12.094290

df_long =
df %>%
pivot_longer(
cols = c("before", "after"),
names_to = "time",
values_to="fabulousness"
)

print.data.frame(df_long)
#>    observation   time fabulousness
#> 1            1 before    10.930157
#> 2            1  after    11.818216
#> 3            2 before    10.870749
#> 4            2  after    10.699232
#> 5            3 before     9.603120
#> 6            3  after    14.384484
#> 7            4 before     9.615291
#> 8            4  after     8.777045
#> 9            5 before     6.714043
#> 10           5  after     9.506421
#> 11           6 before     9.063117
#> 12           6  after     5.574887
#> 13           7 before     8.152260
#> 14           7  after    10.357455
#> 15           8 before     8.256237
#> 16           8  after     8.660646
#> 17           9 before    12.641977
#> 18           9  after     7.511760
#> 19          10 before    11.010290
#> 20          10  after     9.391047
#> 21          11 before    12.545197
#> 22          11  after     9.072856
#> 23          12 before    12.606526
#> 24          12  after     9.110687
#> 25          13 before     8.659088
#> 26          13  after    12.445071
#> 27          14 before     8.958959
#> 28          14  after    10.783168
#> 29          15 before    11.635443
#> 30          15  after     6.926802
#> 31          16 before     6.922437
#> 32          16  after    12.419453
#> 33          17 before    10.326176
#> 34          17  after    10.416757
#> 35          18 before     7.680960
#> 36          18  after     9.836573
#> 37          19 before     9.458365
#> 38          19  after     8.083777
#> 39          20 before     7.235837
#> 40          20  after    12.094290

df_long_not_paired =
df_long %>%
arrange(fabulousness)

print.data.frame(df_long_not_paired)
#>    observation   time fabulousness
#> 1            6  after     5.574887
#> 2            5 before     6.714043
#> 3           16 before     6.922437
#> 4           15  after     6.926802
#> 5           20 before     7.235837
#> 6            9  after     7.511760
#> 7           18 before     7.680960
#> 8           19  after     8.083777
#> 9            7 before     8.152260
#> 10           8 before     8.256237
#> 11          13 before     8.659088
#> 12           8  after     8.660646
#> 13           4  after     8.777045
#> 14          14 before     8.958959
#> 15           6 before     9.063117
#> 16          11  after     9.072856
#> 17          12  after     9.110687
#> 18          10  after     9.391047
#> 19          19 before     9.458365
#> 20           5  after     9.506421
#> 21           3 before     9.603120
#> 22           4 before     9.615291
#> 23          18  after     9.836573
#> 24          17 before    10.326176
#> 25           7  after    10.357455
#> 26          17  after    10.416757
#> 27           2  after    10.699232
#> 28          14  after    10.783168
#> 29           2 before    10.870749
#> 30           1 before    10.930157
#> 31          10 before    11.010290
#> 32          15 before    11.635443
#> 33           1  after    11.818216
#> 34          20  after    12.094290
#> 35          16  after    12.419453
#> 36          13  after    12.445071
#> 37          11 before    12.545197
#> 38          12 before    12.606526
#> 39           9 before    12.641977
#> 40           3  after    14.384484

df_long_paired =
df_long %>%
arrange(desc(time))

print.data.frame(df_long_paired)
#>    observation   time fabulousness
#> 1            1 before    10.930157
#> 2            2 before    10.870749
#> 3            3 before     9.603120
#> 4            4 before     9.615291
#> 5            5 before     6.714043
#> 6            6 before     9.063117
#> 7            7 before     8.152260
#> 8            8 before     8.256237
#> 9            9 before    12.641977
#> 10          10 before    11.010290
#> 11          11 before    12.545197
#> 12          12 before    12.606526
#> 13          13 before     8.659088
#> 14          14 before     8.958959
#> 15          15 before    11.635443
#> 16          16 before     6.922437
#> 17          17 before    10.326176
#> 18          18 before     7.680960
#> 19          19 before     9.458365
#> 20          20 before     7.235837
#> 21           1  after    11.818216
#> 22           2  after    10.699232
#> 23           3  after    14.384484
#> 24           4  after     8.777045
#> 25           5  after     9.506421
#> 26           6  after     5.574887
#> 27           7  after    10.357455
#> 28           8  after     8.660646
#> 29           9  after     7.511760
#> 30          10  after     9.391047
#> 31          11  after     9.072856
#> 32          12  after     9.110687
#> 33          13  after    12.445071
#> 34          14  after    10.783168
#> 35          15  after     6.926802
#> 36          16  after    12.419453
#> 37          17  after    10.416757
#> 38          18  after     9.836573
#> 39          19  after     8.083777
#> 40          20  after    12.094290

df_long_not_paired %>%
t.test(fabulousness ~ time, ., paired=T)
#>
#>  Paired t-test
#>
#> data:  fabulousness by time
#> t = 2.0289, df = 19, p-value = 0.05672
#> alternative hypothesis: true difference in means is not equal to 0
#> 95 percent confidence interval:
#>  -0.007878376  0.506318062
#> sample estimates:
#> mean of the differences
#>               0.2492198

df_long_paired %>%
t.test(fabulousness ~ time, ., paired=T)
#>
#>  Paired t-test
#>
#> data:  fabulousness by time
#> t = 0.3422, df = 19, p-value = 0.736
#> alternative hypothesis: true difference in means is not equal to 0
#> 95 percent confidence interval:
#>  -1.27509  1.77353
#> sample estimates:
#> mean of the differences
#>               0.2492198```
Jul 22, 2022 678 views

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