Thanks! The assumptions of these procedures are very important, but are often ignored or only briefly touched on. That always seems a little curious to me, so I spend more time discussing assumptions than most instructors. This video is unlikely to set the world on fire, but I like it. I'm glad you like it too.
An assumption of the one-sample t test is that we are sampling from a normally distributed population. If you don't believe me, feel free to do a little googling. What statistic's sampling distribution are you referring to? The sampling distribution of the sample mean? The sampling distribution of the t test statistic? Understanding the normality assumption is definitely important for the purposes of understanding the concepts involved.
…(cont'd) Mathematically, a t distribution arises as the distribution of the ratio of a standard normal random variable, divided by the square root of an independent chi-square rv over its degrees of freedom. Our one-sample t statistic satisfies these conditions, provided we are sampling from a normally distributed population. It's not enough to simply require that the sample mean is approximately normal, but in practice that's usually not too far off the mark. Cheers.
Liking this video with a rating of 7 out of 10 representing a sample size of 1. So my mu(0) = 7, mu(alternative) =/= 7, alpha = .01 with a standard divination of 0. Z becomes infinity. I like the subtle nuances of stats you're covering :)
surprising to see the the rate of convergence of t-test percentage of rejection of null hypothesis is quite slow: while the exponential one drops from 11.6% to 5.7%, the percentage of rejection of null hypothesis only at 4.2%, a 0.8% difference when compared with 0.7% difference for the exponential one, while t distribution is supposingly more similar to normal than exponential distribution...
Great video... however, I believe the assumption is not of a normally distributed population but of a normally distributed sampling distribution. I don't mean to be pedantic, but I think the distinction is important for the purposes of understanding the concepts involved.
I am a huge patron of good statistics. I may be in need of some inference. We typically use "an introduction to error analysis" by Dr John R. Taylor to follow statistics in my thermodynamics class. Yet, after three varied stats classes ( My first from a great AP statistician) I have little faith in the power of the method we are using. I have two facts: a literature value of 1.29 and experimental-lit of 1.30 ± 0.02. I have ran an experiment and ruled out 2 outliers using Tompson's tau( with an alpha level .05) if i am even doing a legal action there. But I am still not sure how to really test these 20 values based on one of the two values above.We were using a goodness of fit Chi-square but after fitting it to cumulative distribution and getting an expected value. the Chi-squared and reduced Chi-squared values show me that this test may be the wrong test in general. Advice?
Firstly I have been watching your videos with a lot of ethusiasm, I think all of them very instructive. Could you please explain me, why do number of % of tests that rejected for population with a heavier tailed distributions is smaller than normal distribution ? Isn't distribution with have tails more resemble to uniform distribution than normal distribution itself ? Also It would be great IF you could understand the "reported p-value tend to be smaller' comment. Thank you!
While much of what you say is correct, it's oversimplifying the situation a little. In addition to the sample mean, we also use the sample standard deviation, and this complicates matters (ratios of statistics can have ugly distributions)…(cont'd)
The t-test uses the estimated standard error in it's formula. The population distribution (typically unknown) can be any shape but the sampling distribution will reflect that shape with small sample sizes and will approach a normal shape with increasing sample sizes (regardless of the population distribution shape).
one question, assume population var is known (no matter how unlikely it is), then we use z-test, how much it would be affected by the violation of normality in the population the sample is sampled from? compared with t-test? I'm bit clueless every time i see the sample data is kinda indicating violation to normal assumption
Timeywimey , The normal assumption of the population can be relaxed, if the sample size is large. This is due to central limit theorem. Alternatively the t distribution approaches normal distribution for large sample size(n), due to higher degrees of freedom (n-1).
Sorry, I did not mean to offend. Just trying to improve my own understanding. By sampling distribution, I meant the theoretical distribution of the means of an infinate(?) number of samples of a set size. The mean of that distribution would be identical to the population mean, and the standard deviation would be the standard error.
This is your most irritating video in my opinion. You need to explain WHY the significance levels are different. I’ve spent hours trying to understand and have failed. Why why why does heavier tails mean a more consented same mean distribution. WHY!!!! You can’t just not explain! What’s the point in even telling me if you don’t explain why! WHY! Ahhhhh!
Thanks! The assumptions of these procedures are very important, but are often ignored or only briefly touched on. That always seems a little curious to me, so I spend more time discussing assumptions than most instructors. This video is unlikely to set the world on fire, but I like it. I'm glad you like it too.
you set my word on fire homie
big claps to author, small claps for self for finishing the hypo test playlist :)
An assumption of the one-sample t test is that we are sampling from a normally distributed population. If you don't believe me, feel free to do a little googling.
What statistic's sampling distribution are you referring to? The sampling distribution of the sample mean? The sampling distribution of the t test statistic?
Understanding the normality assumption is definitely important for the purposes of understanding the concepts involved.
…(cont'd) Mathematically, a t distribution arises as the distribution of the ratio of a standard normal random variable, divided by the square root of an independent chi-square rv over its degrees of freedom. Our one-sample t statistic satisfies these conditions, provided we are sampling from a normally distributed population. It's not enough to simply require that the sample mean is approximately normal, but in practice that's usually not too far off the mark. Cheers.
Liking this video with a rating of 7 out of 10 representing a sample size of 1.
So my mu(0) = 7, mu(alternative) =/= 7, alpha = .01 with a standard divination of 0.
Z becomes infinity.
I like the subtle nuances of stats you're covering :)
This is the standard way for exploring finite sample properties. We also did something similar in our stats course.
surprising to see the the rate of convergence of t-test percentage of rejection of null hypothesis is quite slow: while the exponential one drops from 11.6% to 5.7%, the percentage of rejection of null hypothesis only at 4.2%, a 0.8% difference when compared with 0.7% difference for the exponential one, while t distribution is supposingly more similar to normal than exponential distribution...
Great video... however, I believe the assumption is not of a normally distributed population but of a normally distributed sampling distribution. I don't mean to be pedantic, but I think the distinction is important for the purposes of understanding the concepts involved.
I am a huge patron of good statistics. I may be in need of some inference. We typically use "an introduction to error analysis" by Dr John R. Taylor to follow statistics in my thermodynamics class. Yet, after three varied stats classes ( My first from a great AP statistician) I have little faith in the power of the method we are using. I have two facts: a literature value of 1.29 and experimental-lit of 1.30 ± 0.02. I have ran an experiment and ruled out 2 outliers using Tompson's tau( with an alpha level .05) if i am even doing a legal action there. But I am still not sure how to really test these 20 values based on one of the two values above.We were using a goodness of fit Chi-square but after fitting it to cumulative distribution and getting an expected value. the Chi-squared and reduced Chi-squared values show me that this test may be the wrong test in general. Advice?
Firstly I have been watching your videos with a lot of ethusiasm, I think all of them very instructive.
Could you please explain me, why do number of % of tests that rejected for population with a heavier tailed distributions is smaller than normal distribution ? Isn't distribution with have tails more resemble to uniform distribution than normal distribution itself ? Also It would be great IF you could understand the "reported p-value tend to be smaller' comment. Thank you!
While much of what you say is correct, it's oversimplifying the situation a little. In addition to the sample mean, we also use the sample standard deviation, and this complicates matters (ratios of statistics can have ugly distributions)…(cont'd)
The t-test uses the estimated standard error in it's formula.
The population distribution (typically unknown) can be any shape but the sampling distribution will reflect that shape with small sample sizes and will approach a normal shape with increasing sample sizes (regardless of the population distribution shape).
one question, assume population var is known (no matter how unlikely it is), then we use z-test, how much it would be affected by the violation of normality in the population the sample is sampled from? compared with t-test? I'm bit clueless every time i see the sample data is kinda indicating violation to normal assumption
Timeywimey , The normal assumption of the population can be relaxed, if the sample size is large. This is due to central limit theorem. Alternatively the t distribution approaches normal distribution for large sample size(n), due to higher degrees of freedom (n-1).
Sorry, I did not mean to offend. Just trying to improve my own understanding. By sampling distribution, I meant the theoretical distribution of the means of an infinate(?) number of samples of a set size. The mean of that distribution would be identical to the population mean, and the standard deviation would be the standard error.
wrg
This is your most irritating video in my opinion. You need to explain WHY the significance levels are different. I’ve spent hours trying to understand and have failed. Why why why does heavier tails mean a more consented same mean distribution. WHY!!!! You can’t just not explain! What’s the point in even telling me if you don’t explain why! WHY! Ahhhhh!