Why is the critical value for a goodness of fit test at a 99% significance level higher than that of one at a...
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I am doing a chi squared goodness of fit test. I have found the chi squared test statistic to be 1.88. From what I understand, if the test statistic is lower than the critical values given in the tables, then we conclude that the model is a good fit for the data. But when I looked at the table of critical values I realised I didn’t understand quite what the values meant.
Instead of 1.88, say I got a value of 13.
I have 6 degrees of freedom. Looking at the tables, I see that at the 95% level the value given is 12.59. From what I understand this would mean I would conclude the model was not a good fit at the 95% significance level as 13 is greater than 12.59. However, at 99%, the value given is 16.81. By my logic, since 13 < 16.81 that would mean I would conclude that the model was a good fit at the 99% significance level.
But the idea of rejecting the null hypothesisthat the model was a good fit at a 95% significance level but accepting it at a 99% significance level makes no sense.
What have I done wrong?
statistics
asked Nov 20 at 20:16
user3047368
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I am doing a chi squared goodness of fit test. I have found the chi squared test statistic to be 1.88. From what I understand, if the test statistic is lower than the critical values given in the tables, then we conclude that the model is a good fit for the data. But when I looked at the table of critical values I realised I didn’t understand quite what the values meant.
Instead of 1.88, say I got a value of 13.
I have 6 degrees of freedom. Looking at the tables, I see that at the 95% level the value given is 12.59. From what I understand this would mean I would conclude the model was not a good fit at the 95% significance level as 13 is greater than 12.59. However, at 99%, the value given is 16.81. By my logic, since 13 < 16.81 that would mean I would conclude that the model was a good fit at the 99% significance level.
But the idea of rejecting the null hypothesisthat the model was a good fit at a 95% significance level but accepting it at a 99% significance level makes no sense.
What have I done wrong?
statistics
asked Nov 20 at 20:16
user3047368
336
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am doing a chi squared goodness of fit test. I have found the chi squared test statistic to be 1.88. From what I understand, if the test statistic is lower than the critical values given in the tables, then we conclude that the model is a good fit for the data. But when I looked at the table of critical values I realised I didn’t understand quite what the values meant.
Instead of 1.88, say I got a value of 13.
I have 6 degrees of freedom. Looking at the tables, I see that at the 95% level the value given is 12.59. From what I understand this would mean I would conclude the model was not a good fit at the 95% significance level as 13 is greater than 12.59. However, at 99%, the value given is 16.81. By my logic, since 13 < 16.81 that would mean I would conclude that the model was a good fit at the 99% significance level.
But the idea of rejecting the null hypothesisthat the model was a good fit at a 95% significance level but accepting it at a 99% significance level makes no sense.
What have I done wrong?
statistics
asked Nov 20 at 20:16
user3047368
336
I am doing a chi squared goodness of fit test. I have found the chi squared test statistic to be 1.88. From what I understand, if the test statistic is lower than the critical values given in the tables, then we conclude that the model is a good fit for the data. But when I looked at the table of critical values I realised I didn’t understand quite what the values meant.
Instead of 1.88, say I got a value of 13.
I have 6 degrees of freedom. Looking at the tables, I see that at the 95% level the value given is 12.59. From what I understand this would mean I would conclude the model was not a good fit at the 95% significance level as 13 is greater than 12.59. However, at 99%, the value given is 16.81. By my logic, since 13 < 16.81 that would mean I would conclude that the model was a good fit at the 99% significance level.
But the idea of rejecting the null hypothesisthat the model was a good fit at a 95% significance level but accepting it at a 99% significance level makes no sense.
What have I done wrong?
statistics
statistics
asked Nov 20 at 20:16
user3047368
336
asked Nov 20 at 20:16
user3047368
336
asked Nov 20 at 20:16
user3047368
336
asked Nov 20 at 20:16
user3047368
336
asked Nov 20 at 20:16
user3047368
336
336
add a comment |
add a comment |
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