Mixing
Likelihood Ratio tests
$begingroup$
I am trying to figure out how to calculate an LRT for a question, but my problem seems to start with the fact that I have no idea how this is possible:
$$ln L1 = ln(100/63) + 63 ln(1/2) +(100-63)ln(1-1/2) = -5.92.$$
Regardless of which calculator I send it to, I do not get this answer.
What am I doing wrong, I am at a complete loss.
maximum-likelihood
edited Jan 17 at 21:33
Dog_69
6421523
asked Jan 17 at 21:12
SomeoneSomeone
11
$endgroup$
add a comment |
$begingroup$
I am trying to figure out how to calculate an LRT for a question, but my problem seems to start with the fact that I have no idea how this is possible:
$$ln L1 = ln(100/63) + 63 ln(1/2) +(100-63)ln(1-1/2) = -5.92.$$
Regardless of which calculator I send it to, I do not get this answer.
What am I doing wrong, I am at a complete loss.
maximum-likelihood
edited Jan 17 at 21:33
Dog_69
6421523
asked Jan 17 at 21:12
SomeoneSomeone
11
$endgroup$
$begingroup$
The expression does not equal $-5.92$ so the error must be somewhere else. Without further information, it is difficult to help you.
$endgroup$
– angryavian
Jan 17 at 21:19
$begingroup$
The assignment is to calculate a likelihood ratio test. In our scenario, our coin lands on heads 63 times out of 100. The equation given to us to solve this was: LRT = -2(lnL1 - lnL2) For L1 the above equation was supplied to solve its value. Thanks for trying to help btw.
$endgroup$
– Someone
Jan 17 at 21:30
add a comment |
$begingroup$
I am trying to figure out how to calculate an LRT for a question, but my problem seems to start with the fact that I have no idea how this is possible:
$$ln L1 = ln(100/63) + 63 ln(1/2) +(100-63)ln(1-1/2) = -5.92.$$
Regardless of which calculator I send it to, I do not get this answer.
What am I doing wrong, I am at a complete loss.
maximum-likelihood
edited Jan 17 at 21:33
Dog_69
6421523
asked Jan 17 at 21:12
SomeoneSomeone
11
$endgroup$
I am trying to figure out how to calculate an LRT for a question, but my problem seems to start with the fact that I have no idea how this is possible:
$$ln L1 = ln(100/63) + 63 ln(1/2) +(100-63)ln(1-1/2) = -5.92.$$
Regardless of which calculator I send it to, I do not get this answer.
What am I doing wrong, I am at a complete loss.
maximum-likelihood
maximum-likelihood
edited Jan 17 at 21:33
Dog_69
6421523
asked Jan 17 at 21:12
SomeoneSomeone
11
edited Jan 17 at 21:33
Dog_69
6421523
asked Jan 17 at 21:12
SomeoneSomeone
11
edited Jan 17 at 21:33
Dog_69
6421523
edited Jan 17 at 21:33
Dog_69
6421523
edited Jan 17 at 21:33
Dog_69
6421523
6421523
asked Jan 17 at 21:12
SomeoneSomeone
11
asked Jan 17 at 21:12
SomeoneSomeone
11
asked Jan 17 at 21:12
SomeoneSomeone
11
11
$begingroup$
The expression does not equal $-5.92$ so the error must be somewhere else. Without further information, it is difficult to help you.
$endgroup$
– angryavian
Jan 17 at 21:19
$begingroup$
The assignment is to calculate a likelihood ratio test. In our scenario, our coin lands on heads 63 times out of 100. The equation given to us to solve this was: LRT = -2(lnL1 - lnL2) For L1 the above equation was supplied to solve its value. Thanks for trying to help btw.
$endgroup$
– Someone
Jan 17 at 21:30
add a comment |
$begingroup$
The expression does not equal $-5.92$ so the error must be somewhere else. Without further information, it is difficult to help you.
$endgroup$
– angryavian
Jan 17 at 21:19
$begingroup$
The assignment is to calculate a likelihood ratio test. In our scenario, our coin lands on heads 63 times out of 100. The equation given to us to solve this was: LRT = -2(lnL1 - lnL2) For L1 the above equation was supplied to solve its value. Thanks for trying to help btw.
$endgroup$
– Someone
Jan 17 at 21:30
$begingroup$
The expression does not equal $-5.92$ so the error must be somewhere else. Without further information, it is difficult to help you.
$endgroup$
– angryavian
Jan 17 at 21:19
$begingroup$
The expression does not equal $-5.92$ so the error must be somewhere else. Without further information, it is difficult to help you.
$endgroup$
– angryavian
Jan 17 at 21:19
$begingroup$
The assignment is to calculate a likelihood ratio test. In our scenario, our coin lands on heads 63 times out of 100. The equation given to us to solve this was: LRT = -2(lnL1 - lnL2) For L1 the above equation was supplied to solve its value. Thanks for trying to help btw.
$endgroup$
– Someone
Jan 17 at 21:30
$begingroup$
The assignment is to calculate a likelihood ratio test. In our scenario, our coin lands on heads 63 times out of 100. The equation given to us to solve this was: LRT = -2(lnL1 - lnL2) For L1 the above equation was supplied to solve its value. Thanks for trying to help btw.
$endgroup$
– Someone
Jan 17 at 21:30
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
What is the probability that you get exactly $63$ heads in $100$ flips of a fair coin? [Then take the logarithm.] For some reason you thought it was $frac{63}{100} (1/2)^{63} (1/2)^{100-63}$ or something, which is wrong.
$$ln L_1 = ln left(binom{100}{63} 2^{-100}right) = - 100 ln 2 + sum_{k=64}^{100} ln(k) - sum_{k=1}^{37} ln(k) = -5.92$$
answered Jan 17 at 21:38
angryavianangryavian
41.7k23381
$endgroup$
$begingroup$
Hi thank you!!! I copied it straight out of our textbook in exactly the same format. I would love to post a screenshot. Additionally, none of us in this class are math majors and the examples are not explained, so we are kind of drifting. Thank you very much for clearing that up!!!
$endgroup$
– Someone
Jan 17 at 21:42
$begingroup$
@DormantPerson I now see the confusion: you mistook $binom{100}{63}$ for $left(frac{100}{63}right)$. If you are not familiar with this notation, read about the binomial coefficient.
$endgroup$
– angryavian
Jan 17 at 22:00
$begingroup$
I just checked the original text to make sure I was not confusing things as you suggested. The text says (100/63) with a division line. Is there any reason why a text book would display the equation in this incorrect format?
$endgroup$
– Someone
Jan 20 at 17:39
$begingroup$
@Someone Must be a typo then.
$endgroup$
– angryavian
Jan 20 at 17:50
add a comment |
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1 Answer
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$begingroup$
What is the probability that you get exactly $63$ heads in $100$ flips of a fair coin? [Then take the logarithm.] For some reason you thought it was $frac{63}{100} (1/2)^{63} (1/2)^{100-63}$ or something, which is wrong.
$$ln L_1 = ln left(binom{100}{63} 2^{-100}right) = - 100 ln 2 + sum_{k=64}^{100} ln(k) - sum_{k=1}^{37} ln(k) = -5.92$$
answered Jan 17 at 21:38
angryavianangryavian
41.7k23381
$endgroup$
$begingroup$
Hi thank you!!! I copied it straight out of our textbook in exactly the same format. I would love to post a screenshot. Additionally, none of us in this class are math majors and the examples are not explained, so we are kind of drifting. Thank you very much for clearing that up!!!
$endgroup$
– Someone
Jan 17 at 21:42
$begingroup$
@DormantPerson I now see the confusion: you mistook $binom{100}{63}$ for $left(frac{100}{63}right)$. If you are not familiar with this notation, read about the binomial coefficient.
$endgroup$
– angryavian
Jan 17 at 22:00
$begingroup$
I just checked the original text to make sure I was not confusing things as you suggested. The text says (100/63) with a division line. Is there any reason why a text book would display the equation in this incorrect format?
$endgroup$
– Someone
Jan 20 at 17:39
$begingroup$
@Someone Must be a typo then.
$endgroup$
– angryavian
Jan 20 at 17:50
add a comment |
$begingroup$
What is the probability that you get exactly $63$ heads in $100$ flips of a fair coin? [Then take the logarithm.] For some reason you thought it was $frac{63}{100} (1/2)^{63} (1/2)^{100-63}$ or something, which is wrong.
$$ln L_1 = ln left(binom{100}{63} 2^{-100}right) = - 100 ln 2 + sum_{k=64}^{100} ln(k) - sum_{k=1}^{37} ln(k) = -5.92$$
answered Jan 17 at 21:38
angryavianangryavian
41.7k23381
$endgroup$
$begingroup$
Hi thank you!!! I copied it straight out of our textbook in exactly the same format. I would love to post a screenshot. Additionally, none of us in this class are math majors and the examples are not explained, so we are kind of drifting. Thank you very much for clearing that up!!!
$endgroup$
– Someone
Jan 17 at 21:42
$begingroup$
@DormantPerson I now see the confusion: you mistook $binom{100}{63}$ for $left(frac{100}{63}right)$. If you are not familiar with this notation, read about the binomial coefficient.
$endgroup$
– angryavian
Jan 17 at 22:00
$begingroup$
I just checked the original text to make sure I was not confusing things as you suggested. The text says (100/63) with a division line. Is there any reason why a text book would display the equation in this incorrect format?
$endgroup$
– Someone
Jan 20 at 17:39
$begingroup$
@Someone Must be a typo then.
$endgroup$
– angryavian
Jan 20 at 17:50
add a comment |
$begingroup$
What is the probability that you get exactly $63$ heads in $100$ flips of a fair coin? [Then take the logarithm.] For some reason you thought it was $frac{63}{100} (1/2)^{63} (1/2)^{100-63}$ or something, which is wrong.
$$ln L_1 = ln left(binom{100}{63} 2^{-100}right) = - 100 ln 2 + sum_{k=64}^{100} ln(k) - sum_{k=1}^{37} ln(k) = -5.92$$
answered Jan 17 at 21:38
angryavianangryavian
41.7k23381
$endgroup$
What is the probability that you get exactly $63$ heads in $100$ flips of a fair coin? [Then take the logarithm.] For some reason you thought it was $frac{63}{100} (1/2)^{63} (1/2)^{100-63}$ or something, which is wrong.
$$ln L_1 = ln left(binom{100}{63} 2^{-100}right) = - 100 ln 2 + sum_{k=64}^{100} ln(k) - sum_{k=1}^{37} ln(k) = -5.92$$
answered Jan 17 at 21:38
angryavianangryavian
41.7k23381
answered Jan 17 at 21:38
angryavianangryavian
41.7k23381
answered Jan 17 at 21:38
angryavianangryavian
41.7k23381
answered Jan 17 at 21:38
angryavianangryavian
41.7k23381
41.7k23381
$begingroup$
Hi thank you!!! I copied it straight out of our textbook in exactly the same format. I would love to post a screenshot. Additionally, none of us in this class are math majors and the examples are not explained, so we are kind of drifting. Thank you very much for clearing that up!!!
$endgroup$
– Someone
Jan 17 at 21:42
$begingroup$
@DormantPerson I now see the confusion: you mistook $binom{100}{63}$ for $left(frac{100}{63}right)$. If you are not familiar with this notation, read about the binomial coefficient.
$endgroup$
– angryavian
Jan 17 at 22:00
$begingroup$
I just checked the original text to make sure I was not confusing things as you suggested. The text says (100/63) with a division line. Is there any reason why a text book would display the equation in this incorrect format?
$endgroup$
– Someone
Jan 20 at 17:39
$begingroup$
@Someone Must be a typo then.
$endgroup$
– angryavian
Jan 20 at 17:50
add a comment |
$begingroup$
Hi thank you!!! I copied it straight out of our textbook in exactly the same format. I would love to post a screenshot. Additionally, none of us in this class are math majors and the examples are not explained, so we are kind of drifting. Thank you very much for clearing that up!!!
$endgroup$
– Someone
Jan 17 at 21:42
$begingroup$
@DormantPerson I now see the confusion: you mistook $binom{100}{63}$ for $left(frac{100}{63}right)$. If you are not familiar with this notation, read about the binomial coefficient.
$endgroup$
– angryavian
Jan 17 at 22:00
$begingroup$
I just checked the original text to make sure I was not confusing things as you suggested. The text says (100/63) with a division line. Is there any reason why a text book would display the equation in this incorrect format?
$endgroup$
– Someone
Jan 20 at 17:39
$begingroup$
@Someone Must be a typo then.
$endgroup$
– angryavian
Jan 20 at 17:50
$begingroup$
Hi thank you!!! I copied it straight out of our textbook in exactly the same format. I would love to post a screenshot. Additionally, none of us in this class are math majors and the examples are not explained, so we are kind of drifting. Thank you very much for clearing that up!!!
$endgroup$
– Someone
Jan 17 at 21:42
$begingroup$
Hi thank you!!! I copied it straight out of our textbook in exactly the same format. I would love to post a screenshot. Additionally, none of us in this class are math majors and the examples are not explained, so we are kind of drifting. Thank you very much for clearing that up!!!
$endgroup$
– Someone
Jan 17 at 21:42
$begingroup$
@DormantPerson I now see the confusion: you mistook $binom{100}{63}$ for $left(frac{100}{63}right)$. If you are not familiar with this notation, read about the binomial coefficient.
$endgroup$
– angryavian
Jan 17 at 22:00
$begingroup$
@DormantPerson I now see the confusion: you mistook $binom{100}{63}$ for $left(frac{100}{63}right)$. If you are not familiar with this notation, read about the binomial coefficient.
$endgroup$
– angryavian
Jan 17 at 22:00
$begingroup$
I just checked the original text to make sure I was not confusing things as you suggested. The text says (100/63) with a division line. Is there any reason why a text book would display the equation in this incorrect format?
$endgroup$
– Someone
Jan 20 at 17:39
$begingroup$
I just checked the original text to make sure I was not confusing things as you suggested. The text says (100/63) with a division line. Is there any reason why a text book would display the equation in this incorrect format?
$endgroup$
– Someone
Jan 20 at 17:39
$begingroup$
@Someone Must be a typo then.
$endgroup$
– angryavian
Jan 20 at 17:50
$begingroup$
@Someone Must be a typo then.
$endgroup$
– angryavian
Jan 20 at 17:50
add a comment |
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$begingroup$
The expression does not equal $-5.92$ so the error must be somewhere else. Without further information, it is difficult to help you.
$endgroup$
– angryavian
Jan 17 at 21:19
$begingroup$
The assignment is to calculate a likelihood ratio test. In our scenario, our coin lands on heads 63 times out of 100. The equation given to us to solve this was: LRT = -2(lnL1 - lnL2) For L1 the above equation was supplied to solve its value. Thanks for trying to help btw.
$endgroup$
– Someone
Jan 17 at 21:30