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Why does the $t$-test result depend on the sample set sizes?
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The $t$-test is applied to determine if two distributions of data are significantly different from each other. Accordingly, the result of the test should not change with different sample sizes (still sufficient). However, considering the formula, its results significantly change for different values of $N1$ and $N2$.
statistics probability-distributions
edited 3 hours ago
Daniel Buck
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asked 4 hours ago
Reza_va
479
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up vote
-1
down vote
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The $t$-test is applied to determine if two distributions of data are significantly different from each other. Accordingly, the result of the test should not change with different sample sizes (still sufficient). However, considering the formula, its results significantly change for different values of $N1$ and $N2$.
statistics probability-distributions
edited 3 hours ago
Daniel Buck
2,2541523
asked 4 hours ago
Reza_va
479
1
It would be great if the sample size didn't matter. Taking a sample size of 1 for both $N_1$ and $N_2$ is generally a lot less expensive than a sample size of 1,000. Would you elaborate on why you think sample size or differences in sample sizes shouldn't matter?
– JimB
3 hours ago
@JimB, I think it tests two distributions, accordingly, it shouldn't be much different when the sample mean and sample std are equal to their expected values. however, for instance when testing with m1=6E-3, s1=8E-2, m2=1E-1, and s2=8E-1, the result of the tests varies with different values of N.
– Reza_va
3 hours ago
Maybe if you did some simulations with known means and variances from a normal distribution and varied the sample size, you'd see that sample size (and differences in sample size) matters. Then you'd need to determine why you think it shouldn't matter. Maybe en.wikipedia.org/wiki/Student%27s_t-test would help.
– JimB
3 hours ago
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
The $t$-test is applied to determine if two distributions of data are significantly different from each other. Accordingly, the result of the test should not change with different sample sizes (still sufficient). However, considering the formula, its results significantly change for different values of $N1$ and $N2$.
statistics probability-distributions
edited 3 hours ago
Daniel Buck
2,2541523
asked 4 hours ago
Reza_va
479
The $t$-test is applied to determine if two distributions of data are significantly different from each other. Accordingly, the result of the test should not change with different sample sizes (still sufficient). However, considering the formula, its results significantly change for different values of $N1$ and $N2$.
statistics probability-distributions
edited 3 hours ago
Daniel Buck
2,2541523
asked 4 hours ago
Reza_va
479
edited 3 hours ago
Daniel Buck
2,2541523
edited 3 hours ago
Daniel Buck
2,2541523
edited 3 hours ago
Daniel Buck
2,2541523
2,2541523
asked 4 hours ago
Reza_va
479
asked 4 hours ago
Reza_va
479
asked 4 hours ago
Reza_va
479
479
1
It would be great if the sample size didn't matter. Taking a sample size of 1 for both $N_1$ and $N_2$ is generally a lot less expensive than a sample size of 1,000. Would you elaborate on why you think sample size or differences in sample sizes shouldn't matter?
– JimB
3 hours ago
@JimB, I think it tests two distributions, accordingly, it shouldn't be much different when the sample mean and sample std are equal to their expected values. however, for instance when testing with m1=6E-3, s1=8E-2, m2=1E-1, and s2=8E-1, the result of the tests varies with different values of N.
– Reza_va
3 hours ago
Maybe if you did some simulations with known means and variances from a normal distribution and varied the sample size, you'd see that sample size (and differences in sample size) matters. Then you'd need to determine why you think it shouldn't matter. Maybe en.wikipedia.org/wiki/Student%27s_t-test would help.
– JimB
3 hours ago
add a comment |Â
1
It would be great if the sample size didn't matter. Taking a sample size of 1 for both $N_1$ and $N_2$ is generally a lot less expensive than a sample size of 1,000. Would you elaborate on why you think sample size or differences in sample sizes shouldn't matter?
– JimB
3 hours ago
@JimB, I think it tests two distributions, accordingly, it shouldn't be much different when the sample mean and sample std are equal to their expected values. however, for instance when testing with m1=6E-3, s1=8E-2, m2=1E-1, and s2=8E-1, the result of the tests varies with different values of N.
– Reza_va
3 hours ago
Maybe if you did some simulations with known means and variances from a normal distribution and varied the sample size, you'd see that sample size (and differences in sample size) matters. Then you'd need to determine why you think it shouldn't matter. Maybe en.wikipedia.org/wiki/Student%27s_t-test would help.
– JimB
3 hours ago
1
1
It would be great if the sample size didn't matter. Taking a sample size of 1 for both $N_1$ and $N_2$ is generally a lot less expensive than a sample size of 1,000. Would you elaborate on why you think sample size or differences in sample sizes shouldn't matter?
– JimB
3 hours ago
It would be great if the sample size didn't matter. Taking a sample size of 1 for both $N_1$ and $N_2$ is generally a lot less expensive than a sample size of 1,000. Would you elaborate on why you think sample size or differences in sample sizes shouldn't matter?
– JimB
3 hours ago
@JimB, I think it tests two distributions, accordingly, it shouldn't be much different when the sample mean and sample std are equal to their expected values. however, for instance when testing with m1=6E-3, s1=8E-2, m2=1E-1, and s2=8E-1, the result of the tests varies with different values of N.
– Reza_va
3 hours ago
@JimB, I think it tests two distributions, accordingly, it shouldn't be much different when the sample mean and sample std are equal to their expected values. however, for instance when testing with m1=6E-3, s1=8E-2, m2=1E-1, and s2=8E-1, the result of the tests varies with different values of N.
– Reza_va
3 hours ago
Maybe if you did some simulations with known means and variances from a normal distribution and varied the sample size, you'd see that sample size (and differences in sample size) matters. Then you'd need to determine why you think it shouldn't matter. Maybe en.wikipedia.org/wiki/Student%27s_t-test would help.
– JimB
3 hours ago
Maybe if you did some simulations with known means and variances from a normal distribution and varied the sample size, you'd see that sample size (and differences in sample size) matters. Then you'd need to determine why you think it shouldn't matter. Maybe en.wikipedia.org/wiki/Student%27s_t-test would help.
– JimB
3 hours ago
add a comment |Â
1 Answer
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oldest
votes
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0
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As sample size increases, the difference between two samples gets closer to the actual difference (if any) of the population or populations they came from. And so too does the sample standard deviation in moving closer to the population standard deviation. So yes, the result will probably change. Consider also, the probability of making a type II error (not rejecting the null when you should) is higher with smaller sample sizes.
answered 34 mins ago
Phil H
1,7882211
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
As sample size increases, the difference between two samples gets closer to the actual difference (if any) of the population or populations they came from. And so too does the sample standard deviation in moving closer to the population standard deviation. So yes, the result will probably change. Consider also, the probability of making a type II error (not rejecting the null when you should) is higher with smaller sample sizes.
answered 34 mins ago
Phil H
1,7882211
add a comment |Â
up vote
0
down vote
As sample size increases, the difference between two samples gets closer to the actual difference (if any) of the population or populations they came from. And so too does the sample standard deviation in moving closer to the population standard deviation. So yes, the result will probably change. Consider also, the probability of making a type II error (not rejecting the null when you should) is higher with smaller sample sizes.
answered 34 mins ago
Phil H
1,7882211
add a comment |Â
up vote
0
down vote
up vote
0
down vote
As sample size increases, the difference between two samples gets closer to the actual difference (if any) of the population or populations they came from. And so too does the sample standard deviation in moving closer to the population standard deviation. So yes, the result will probably change. Consider also, the probability of making a type II error (not rejecting the null when you should) is higher with smaller sample sizes.
answered 34 mins ago
Phil H
1,7882211
As sample size increases, the difference between two samples gets closer to the actual difference (if any) of the population or populations they came from. And so too does the sample standard deviation in moving closer to the population standard deviation. So yes, the result will probably change. Consider also, the probability of making a type II error (not rejecting the null when you should) is higher with smaller sample sizes.
answered 34 mins ago
Phil H
1,7882211
answered 34 mins ago
Phil H
1,7882211
answered 34 mins ago
Phil H
1,7882211
answered 34 mins ago
Phil H
1,7882211
1,7882211
add a comment |Â
add a comment |Â
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1
It would be great if the sample size didn't matter. Taking a sample size of 1 for both $N_1$ and $N_2$ is generally a lot less expensive than a sample size of 1,000. Would you elaborate on why you think sample size or differences in sample sizes shouldn't matter?
– JimB
3 hours ago
@JimB, I think it tests two distributions, accordingly, it shouldn't be much different when the sample mean and sample std are equal to their expected values. however, for instance when testing with m1=6E-3, s1=8E-2, m2=1E-1, and s2=8E-1, the result of the tests varies with different values of N.
– Reza_va
3 hours ago
Maybe if you did some simulations with known means and variances from a normal distribution and varied the sample size, you'd see that sample size (and differences in sample size) matters. Then you'd need to determine why you think it shouldn't matter. Maybe en.wikipedia.org/wiki/Student%27s_t-test would help.
– JimB
3 hours ago