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With small samples of discrete data
With small samples of discrete data, many statisticians prefer to use a different type
of P -value. Called the mid P -value, it adds only half the probability of the observed
result to the probability of the more extreme results. To illustrate, in the above example
with y = 9 successes in n = 10 trials, the ordinary P -value for Ha: π> 0.50 is
P(9) + P(10) = 0.010 + 0.001 = 0.011. The mid P -value is P(9)/2 + P(10) =
0.010/2 + 0.001 = 0.006. Table 1.2 also shows the mid P -values for the possible y
values when n = 10.
Tests using the mid P -value are, on the average, less conservative than tests using
the ordinary P -value. The mid P -value has a null expected value of 0.50, the same
as the regular P -value for continuous variates. Also, the two separate one-sided mid
P -values sum to 1.0. For example, for y = 9 when n = 10, for Ha: π> 0.50 the
ordinary P -value is
right-tail P -value = P(9) + P(10) = 0.011
and for Ha: π< 0.50 it is
left-tail P -value = P(0) + P(1) +···+ P(9) = 0.999
That is, P(9) gets counted in each tail for each P -value. By contrast, for Ha: π> 0.50,
the mid P -value is
right-tail mid P -value = P(9)/2 + P(10) = 0.006
and for Ha: π< 0.50 it is
left-tail mid P -value = P(0) + P(1) +···+ P(9)/2 = 0.994
and these one-sided mid P -values sum to 1.0.
The two-sided P -value for the large-sample z score test approximates the two-sided
mid P -value in the small-sample binomial test. For example, with y = 9in n = 10
trials for H0: π = 0.50, z = (0.90 − 0.50)/√[0.50(0.50)/10]= 2.53 has two-sided
P -value = 0.0114. The two-sided mid P -value is 2[P(9)/2 + P(10)]= 0.0117. For small samples, one can construct confidence intervals by inverting results of
significance tests that use the binomial distribution, rather than a normal approx-imation. Such inferences are very conservative when the test uses the ordinary
P -value. We recommend inverting instead the binomial test using the mid P -value. The mid-P confidence interval is the set of π0 values for a two-sided test
in which the mid P -value using the binomial distribution exceeds 0.05. This is
available in some software, such as an R function (written by A. Gottard) at
http://www.stat.ufl.edu/∼aa/cda/software.html.
of P -value. Called the mid P -value, it adds only half the probability of the observed
result to the probability of the more extreme results. To illustrate, in the above example
with y = 9 successes in n = 10 trials, the ordinary P -value for Ha: π> 0.50 is
P(9) + P(10) = 0.010 + 0.001 = 0.011. The mid P -value is P(9)/2 + P(10) =
0.010/2 + 0.001 = 0.006. Table 1.2 also shows the mid P -values for the possible y
values when n = 10.
Tests using the mid P -value are, on the average, less conservative than tests using
the ordinary P -value. The mid P -value has a null expected value of 0.50, the same
as the regular P -value for continuous variates. Also, the two separate one-sided mid
P -values sum to 1.0. For example, for y = 9 when n = 10, for Ha: π> 0.50 the
ordinary P -value is
right-tail P -value = P(9) + P(10) = 0.011
and for Ha: π< 0.50 it is
left-tail P -value = P(0) + P(1) +···+ P(9) = 0.999
That is, P(9) gets counted in each tail for each P -value. By contrast, for Ha: π> 0.50,
the mid P -value is
right-tail mid P -value = P(9)/2 + P(10) = 0.006
and for Ha: π< 0.50 it is
left-tail mid P -value = P(0) + P(1) +···+ P(9)/2 = 0.994
and these one-sided mid P -values sum to 1.0.
The two-sided P -value for the large-sample z score test approximates the two-sided
mid P -value in the small-sample binomial test. For example, with y = 9in n = 10
trials for H0: π = 0.50, z = (0.90 − 0.50)/√[0.50(0.50)/10]= 2.53 has two-sided
P -value = 0.0114. The two-sided mid P -value is 2[P(9)/2 + P(10)]= 0.0117. For small samples, one can construct confidence intervals by inverting results of
significance tests that use the binomial distribution, rather than a normal approx-imation. Such inferences are very conservative when the test uses the ordinary
P -value. We recommend inverting instead the binomial test using the mid P -value. The mid-P confidence interval is the set of π0 values for a two-sided test
in which the mid P -value using the binomial distribution exceeds 0.05. This is
available in some software, such as an R function (written by A. Gottard) at
http://www.stat.ufl.edu/∼aa/cda/software.html.
0/5000
Dengan sampel kecil data diskrit, banyak Statistik lebih memilih untuk menggunakan tipe
p-nilai. Disebut pertengahan P-nilai, ia menambahkan hanya separuh kemungkinan diamati
hasil kemungkinan hasil yang lebih ekstrim. Untuk mengilustrasikan, dalam contoh di atas
dengan y = 9 keberhasilan dalam n = 10 uji, yang biasa P-nilai untuk Ha: π mengatakan 0,50 is
P(9) P(10) = 0.010 0.001 = 0.011. Pertengahan P-nilai adalah P (9) / 2 P(10) =
0.010 / 2 0.001 = 0.006. 1.2 meja juga menunjukkan pertengahan P-nilai y mungkin
nilai ketika n = 10.
tes menggunakan P pertengahan-nilai yang rata-rata, kurang konservatif daripada tes menggunakan
biasa P-nilai. Pertengahan P-nilai memiliki nilai null diharapkan 0,50, sama
sebagai biasa P-nilai untuk terus-menerus variates. Juga, dua terpisah sepihak pertengahan
P-nilai jumlah 1.0. Misalnya, untuk y = 9 ketika n = 10, untuk Ha: π mengatakan 0,50
biasa P-nilai
kanan-ekor P-nilai = P(9) P(10) = 0.011
dan Ha: π < 0,50 itu
P kiri-ekor-nilai = P(0) P(1) ··· P(9) = 0.999
, P(9) mendapatkan dihitung dalam setiap ekor untuk P masing-masing-nilai. oleh kontras, untuk Ha: π mengatakan 0,50,
P pertengahan-nilai
kanan-ekor pertengahan P-nilai = P (9) / 2 P(10) = 0.006
dan Ha: π < 0.50 itu
kiri-ekor pertengahan P-nilai = P(0) P(1) ··· P (9) / 2 = 0.994
dan ini sepihak pertengahan P-nilai jumlah 1.0.
dua sisi P-nilai untuk skor z besar-sampel tes kira-kira dua sisi
pertengahan P-nilai dalam tes binomial sampel kecil. Sebagai contoh, dengan y = 9 in n = 10
uji untuk H0: π = 0,50, z = (0.90 − 0.50)/√[0.50 (0.50) / 10] = 2.53 memiliki dua sisi
P-nilai = 0.0114. Dua sisi pertengahan P-nilai adalah 2 [P (9) / 2 P(10)] = 0.0117. Untuk sampel kecil, satu dapat membangun interval keyakinan oleh membalik hasil
signifikansi tes yang menggunakan Distribusi binomial, daripada normal kira-kira-imation. Kesimpulan tersebut sangat konservatif ketika tes menggunakan biasa
P-nilai. Kami merekomendasikan membalik bukan tes binomial menggunakan pertengahan P-nilai. Interval kepercayaan pertengahan-P adalah serangkaian nilai-nilai π0 untuk tes dua sisi
di mana pertengahan P-nilai menggunakan Distribusi binomial melebihi 0,05. Ini adalah
tersedia dalam beberapa perangkat lunak, seperti fungsi R (ditulis oleh A. Gottard) di
http://www.stat.ufl.edu/ ∼aa/cda/software.html.
p-nilai. Disebut pertengahan P-nilai, ia menambahkan hanya separuh kemungkinan diamati
hasil kemungkinan hasil yang lebih ekstrim. Untuk mengilustrasikan, dalam contoh di atas
dengan y = 9 keberhasilan dalam n = 10 uji, yang biasa P-nilai untuk Ha: π mengatakan 0,50 is
P(9) P(10) = 0.010 0.001 = 0.011. Pertengahan P-nilai adalah P (9) / 2 P(10) =
0.010 / 2 0.001 = 0.006. 1.2 meja juga menunjukkan pertengahan P-nilai y mungkin
nilai ketika n = 10.
tes menggunakan P pertengahan-nilai yang rata-rata, kurang konservatif daripada tes menggunakan
biasa P-nilai. Pertengahan P-nilai memiliki nilai null diharapkan 0,50, sama
sebagai biasa P-nilai untuk terus-menerus variates. Juga, dua terpisah sepihak pertengahan
P-nilai jumlah 1.0. Misalnya, untuk y = 9 ketika n = 10, untuk Ha: π mengatakan 0,50
biasa P-nilai
kanan-ekor P-nilai = P(9) P(10) = 0.011
dan Ha: π < 0,50 itu
P kiri-ekor-nilai = P(0) P(1) ··· P(9) = 0.999
, P(9) mendapatkan dihitung dalam setiap ekor untuk P masing-masing-nilai. oleh kontras, untuk Ha: π mengatakan 0,50,
P pertengahan-nilai
kanan-ekor pertengahan P-nilai = P (9) / 2 P(10) = 0.006
dan Ha: π < 0.50 itu
kiri-ekor pertengahan P-nilai = P(0) P(1) ··· P (9) / 2 = 0.994
dan ini sepihak pertengahan P-nilai jumlah 1.0.
dua sisi P-nilai untuk skor z besar-sampel tes kira-kira dua sisi
pertengahan P-nilai dalam tes binomial sampel kecil. Sebagai contoh, dengan y = 9 in n = 10
uji untuk H0: π = 0,50, z = (0.90 − 0.50)/√[0.50 (0.50) / 10] = 2.53 memiliki dua sisi
P-nilai = 0.0114. Dua sisi pertengahan P-nilai adalah 2 [P (9) / 2 P(10)] = 0.0117. Untuk sampel kecil, satu dapat membangun interval keyakinan oleh membalik hasil
signifikansi tes yang menggunakan Distribusi binomial, daripada normal kira-kira-imation. Kesimpulan tersebut sangat konservatif ketika tes menggunakan biasa
P-nilai. Kami merekomendasikan membalik bukan tes binomial menggunakan pertengahan P-nilai. Interval kepercayaan pertengahan-P adalah serangkaian nilai-nilai π0 untuk tes dua sisi
di mana pertengahan P-nilai menggunakan Distribusi binomial melebihi 0,05. Ini adalah
tersedia dalam beberapa perangkat lunak, seperti fungsi R (ditulis oleh A. Gottard) di
http://www.stat.ufl.edu/ ∼aa/cda/software.html.
Sedang diterjemahkan, harap tunggu..
With small samples of discrete data, many statisticians prefer to use a different type
of P -value. Called the mid P -value, it adds only half the probability of the observed
result to the probability of the more extreme results. To illustrate, in the above example
with y = 9 successes in n = 10 trials, the ordinary P -value for Ha: π> 0.50 is
P(9) + P(10) = 0.010 + 0.001 = 0.011. The mid P -value is P(9)/2 + P(10) =
0.010/2 + 0.001 = 0.006. Table 1.2 also shows the mid P -values for the possible y
values when n = 10.
Tests using the mid P -value are, on the average, less conservative than tests using
the ordinary P -value. The mid P -value has a null expected value of 0.50, the same
as the regular P -value for continuous variates. Also, the two separate one-sided mid
P -values sum to 1.0. For example, for y = 9 when n = 10, for Ha: π> 0.50 the
ordinary P -value is
right-tail P -value = P(9) + P(10) = 0.011
and for Ha: π< 0.50 it is
left-tail P -value = P(0) + P(1) +···+ P(9) = 0.999
That is, P(9) gets counted in each tail for each P -value. By contrast, for Ha: π> 0.50,
the mid P -value is
right-tail mid P -value = P(9)/2 + P(10) = 0.006
and for Ha: π< 0.50 it is
left-tail mid P -value = P(0) + P(1) +···+ P(9)/2 = 0.994
and these one-sided mid P -values sum to 1.0.
The two-sided P -value for the large-sample z score test approximates the two-sided
mid P -value in the small-sample binomial test. For example, with y = 9in n = 10
trials for H0: π = 0.50, z = (0.90 − 0.50)/√[0.50(0.50)/10]= 2.53 has two-sided
P -value = 0.0114. The two-sided mid P -value is 2[P(9)/2 + P(10)]= 0.0117. For small samples, one can construct confidence intervals by inverting results of
significance tests that use the binomial distribution, rather than a normal approx-imation. Such inferences are very conservative when the test uses the ordinary
P -value. We recommend inverting instead the binomial test using the mid P -value. The mid-P confidence interval is the set of π0 values for a two-sided test
in which the mid P -value using the binomial distribution exceeds 0.05. This is
available in some software, such as an R function (written by A. Gottard) at
http://www.stat.ufl.edu/∼aa/cda/software.html.
of P -value. Called the mid P -value, it adds only half the probability of the observed
result to the probability of the more extreme results. To illustrate, in the above example
with y = 9 successes in n = 10 trials, the ordinary P -value for Ha: π> 0.50 is
P(9) + P(10) = 0.010 + 0.001 = 0.011. The mid P -value is P(9)/2 + P(10) =
0.010/2 + 0.001 = 0.006. Table 1.2 also shows the mid P -values for the possible y
values when n = 10.
Tests using the mid P -value are, on the average, less conservative than tests using
the ordinary P -value. The mid P -value has a null expected value of 0.50, the same
as the regular P -value for continuous variates. Also, the two separate one-sided mid
P -values sum to 1.0. For example, for y = 9 when n = 10, for Ha: π> 0.50 the
ordinary P -value is
right-tail P -value = P(9) + P(10) = 0.011
and for Ha: π< 0.50 it is
left-tail P -value = P(0) + P(1) +···+ P(9) = 0.999
That is, P(9) gets counted in each tail for each P -value. By contrast, for Ha: π> 0.50,
the mid P -value is
right-tail mid P -value = P(9)/2 + P(10) = 0.006
and for Ha: π< 0.50 it is
left-tail mid P -value = P(0) + P(1) +···+ P(9)/2 = 0.994
and these one-sided mid P -values sum to 1.0.
The two-sided P -value for the large-sample z score test approximates the two-sided
mid P -value in the small-sample binomial test. For example, with y = 9in n = 10
trials for H0: π = 0.50, z = (0.90 − 0.50)/√[0.50(0.50)/10]= 2.53 has two-sided
P -value = 0.0114. The two-sided mid P -value is 2[P(9)/2 + P(10)]= 0.0117. For small samples, one can construct confidence intervals by inverting results of
significance tests that use the binomial distribution, rather than a normal approx-imation. Such inferences are very conservative when the test uses the ordinary
P -value. We recommend inverting instead the binomial test using the mid P -value. The mid-P confidence interval is the set of π0 values for a two-sided test
in which the mid P -value using the binomial distribution exceeds 0.05. This is
available in some software, such as an R function (written by A. Gottard) at
http://www.stat.ufl.edu/∼aa/cda/software.html.
Sedang diterjemahkan, harap tunggu..
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