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I want to plot some confidence interval graphs in MATLAB but I don't have any idea at all how to do it. Not the answer you're looking for?Browse other questions tagged matlab plot confidence-interval or ask your own question.

My questions are, iv_l and iv_u are the upper and lower confidence intervals or prediction intervals?? Prediction interval is the confidence interval for an observation and includes the estimate of the error.

Not the answer you're looking for?Browse other questions tagged python statistics statsmodels or ask your own question. Is there any truth to interpreting definition of a second as corresponding to oscillations?

Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.

Given a 95% confidence level, how do I demonstrate 95% of the intervals actually contain the population mean? Let me say first off that I'm consistently impressed with the quality of responses on this site. My basic goal is to prove that confidence intervals actually work, and by work I mean that that a certain percentage of them, say 95%, actually include the population mean (assuming that we know the population mean in the first place).

A) I’ve generated a data set in Excel consisting of 20 samples with 64 observations each (i.e.

C) Below is the best Excel formula I found that can generate something approaching a normal distribution. As you might have already guessed, here’s the issue: theoretically if 95% of these intervals contained the population mean, then only 1 interval out of 20 would have failed to include it. In case someone happens to see this thread, here are screen shots of the 2 main excel spreadsheets; one version with just the values, the other version with just the formulas.

Compared to your population standard deviation of 12, the width of your confidence intervals looks too narrow in many cases. Use meaningful names for ranges and variables rather than cell references wherever possible. To illustrate, let me share a spreadsheet I created long ago for exactly this purpose: to show, via simulation, how confidence intervals work. Finally, these 100 columns drive a graphic that shows all 100 confidence intervals relative to the specified mean Mu and also visually indicates (via the spikes at the bottom) which intervals fail to cover the mean. In any case, you have to simulate an infinite number of samples to get the result you want. Not the answer you're looking for?Browse other questions tagged normal-distribution confidence-interval binomial excel random-generation or ask your own question. What are some good ways to figure out one's interests in mathematics, before applying to PhD programs?

What sort of geological features or weather patterns would create a region with the same temperature year-round? I'm looking for a possibility to calculate and visualize confidence ellipses (not sure if thats the correct term for this). So in principle one has to fit a multivariate normal distribution to a 2D histogram of data points I guess. In that case you should cluster them first, then fit a gaussian to each cluster and finally plot the confidence intervals. I slightly modified one of the examples above that plots the error or confidence region contours. It was giving the wrong contours because it was applying the scoreatpercentile method to the joint dataset (blue + red points) when it should be applied separately to each dataset.

I don't know much how about it, but as a starting point, I would check the sherpa application for python.

Not the answer you're looking for?Browse other questions tagged python matplotlib scipy or ask your own question. But I'm interested in calculating the confidence intervals for Phat, any thoughts on how I could I go about it? I think the reason for it being here is to attract Matlab specialists, programmers and enthusiasts. By looking at the distribution of probabilities amongst subsamples you should get a pretty good idea of what the variance is.

The disadvantage of this method is that it may not be possible actually calculate an interval with a desired given probability. Not the answer you're looking for?Browse other questions tagged matlab statistics markov-chains confidence-interval or ask your own question. Confidence is not built by being able to do everything. Confidence is built by being able to do some things well. If you could go back into your past and get rid of wrongdoings done to you: people who teased you, hated you, did you wrong, you would come out at this end of your life a different person. Decide today to do something you feel you can’t do because you think you haven’t got what it takes. We cannot possibly achieve resolutions without first throwing away the very stumbling blocks that stand in our way of attaining them. You had no control over what happened to you in your past, but the reins are all in your hands now.

Practise probably won’t make you perfect, but it will get you close enough to succeed (and you’ll learn something new in the interim). Once you get rid of bad thoughts about the people in your past (or present) who’ve caused you to feel less confident about yourself, you can start to achieve your dreams whether they’re building confidence, boosting your body confidence or just restoring faith in yourself. If you look at your life as a half empty glass, know that there are many people in the world at this moment who don’t have glasses.

In order to work with what you have, you have to first identify and appreciate what you have. This quote is very encouraging to let someone stop worrying about the past, especially when they can’t change it like you mentioned. This blog uses Comment Love Premium which kindly allows you to put your keywords with your name. You can get Anne's inspirational memoir by clicking on the page called, 'Anne's Memoir' above. You folks have done a better job of explaining difficult concepts than most instructors or textbooks I've encountered. I couldn’t even find agreement on whether the truncation disqualifies it as normal in the strict sense. Is Excel simply incapable of generating random normally distributed data with the level of accuracy needed to make this example work?

If you do $n$ CI's, the number that cover the true mean will follow a binomial distribution $(n,p)$, with $p=0.95$.

I don't yet know what the format of the input data is, I guess a nx2 array where n is the number of points. I hope I got this right: Assuming a multivariate normal distribution, one can simply take the eigenvalues and the eigenvectors to calculate the ellipses. It's not exactly the same because I assume we don't know the number of clusters in advance.

At least, in their Scipy 2011 talk, authors mention that you can determine and obtain confidence regions with it (you may need to have a model for your data though). The advantage is that it should give you good feeling for how the series behaves, and that it may capture some information that could be lost in other methods due to the assumptions that other methods (for example bootstrapping) are based on. It seems that subscribers, readers, and passers-by equally welcome little, digestible bits of confidence and success quotes at intervals. You’ll convert value easier and much quicker if you work with the blessings you already have.

Bearing them in your mind as secrets you hold close to you is NOT the way to get rid of a memory.

Take time off to take that journey which will take you only half way to where you want to be. There are more ways than one and you’ve certainly used up your present way of doing things.

Confidence is built by being able to do some things well”… This will be my favorite quote for the week!

You know how I love quotations, and having published a book of inspirational quotes I know all too well how time consuming it can be to find just the right life lessons.

Feel free to join the discussion by leaving comments, and stay updated by subscribing to the RSS feed.

I only know that RandBetween produces a uniform distribution so it’s useless for these purposes.

Also, I tried a Normal Quantile Plot Test for Normality that I found online on the 128.1k data point example and I did find a very slight amount of leptokurtosis for anyone who knows what to make of that.

Note that I also tried Excel’s data analysis->random number generation tool and got virtually identical results as the Excel formula I included above. Here were the results: at the 90% CL only 60 out of 100 had at least 18 intervals with the pop.

Below is a comparison of the original 100 iterations I recorded compared to the binomial distribution per Excel.

In the calculation function countFcn, I first accumulate the counts of co-occurrences from each sequence (using a less-known syntax of sparse function but we could have also used accumarray), then I divide by the row sums (the bsxfun call). You will have never seen these confidence quotes (or success quotes) on any other blog, or anywhere else on the web but here on How to Build Confidence.

Look at them, claim them, and use them to enrich your life and the lives of those around you. If you don’t do this you will allow the people in your past who negatively affected your confidence to win. If you’ve enjoyed Confidence quotes 3 and know someone who can use a boost today, please share it with them. I liked the idea of picking out parts of previous articles and putting them all in one place.

If I regenerate the prices repeatedly using F9, it only meets the 19 or greater threshold around 70% of the time with some iterations producing 20 out 20 intervals that contain the mean to as low as only 16 out of 20. Your intervals are much narrower, which leads me to suspect you are calculating something wrong. As far as choosing a value of 12, the logic came from trying out various std devs that would result in a data set that was fairly consistently bound between 25 and 100 give or take.

Please note, though--in response to your title--that indeed these CIs are provably correct. I can now demonstrate that out of 20 confidence intervals, the highest probability belongs to scenarios where exactly 2 do not contain the population mean at the 90% confidence level. I was actually talking to my husband just last week about how we all tend to put way too much stuff on our calendar! However, I do have a concern that actually row entries to Phat are not univariate normal distributions because they cannot vary individually.

The key to feeling accomplished is not to have done so many actions in a week but to have done them well… Thank you for the reminder!

That's not likely to be of interest to anyone else unless some specific statistical question emerges.

I want to plot some confidence interval graphs in MATLAB but I don't have any idea at all how to do it. Not the answer you're looking for?Browse other questions tagged matlab plot confidence-interval or ask your own question.

My questions are, iv_l and iv_u are the upper and lower confidence intervals or prediction intervals?? Prediction interval is the confidence interval for an observation and includes the estimate of the error.

Not the answer you're looking for?Browse other questions tagged python statistics statsmodels or ask your own question. Is there any truth to interpreting definition of a second as corresponding to oscillations?

Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.

Given a 95% confidence level, how do I demonstrate 95% of the intervals actually contain the population mean? Let me say first off that I'm consistently impressed with the quality of responses on this site. My basic goal is to prove that confidence intervals actually work, and by work I mean that that a certain percentage of them, say 95%, actually include the population mean (assuming that we know the population mean in the first place).

A) I’ve generated a data set in Excel consisting of 20 samples with 64 observations each (i.e.

C) Below is the best Excel formula I found that can generate something approaching a normal distribution. As you might have already guessed, here’s the issue: theoretically if 95% of these intervals contained the population mean, then only 1 interval out of 20 would have failed to include it. In case someone happens to see this thread, here are screen shots of the 2 main excel spreadsheets; one version with just the values, the other version with just the formulas.

Compared to your population standard deviation of 12, the width of your confidence intervals looks too narrow in many cases. Use meaningful names for ranges and variables rather than cell references wherever possible. To illustrate, let me share a spreadsheet I created long ago for exactly this purpose: to show, via simulation, how confidence intervals work. Finally, these 100 columns drive a graphic that shows all 100 confidence intervals relative to the specified mean Mu and also visually indicates (via the spikes at the bottom) which intervals fail to cover the mean. In any case, you have to simulate an infinite number of samples to get the result you want. Not the answer you're looking for?Browse other questions tagged normal-distribution confidence-interval binomial excel random-generation or ask your own question. What are some good ways to figure out one's interests in mathematics, before applying to PhD programs?

What sort of geological features or weather patterns would create a region with the same temperature year-round? I'm looking for a possibility to calculate and visualize confidence ellipses (not sure if thats the correct term for this). So in principle one has to fit a multivariate normal distribution to a 2D histogram of data points I guess. In that case you should cluster them first, then fit a gaussian to each cluster and finally plot the confidence intervals. I slightly modified one of the examples above that plots the error or confidence region contours. It was giving the wrong contours because it was applying the scoreatpercentile method to the joint dataset (blue + red points) when it should be applied separately to each dataset.

I don't know much how about it, but as a starting point, I would check the sherpa application for python.

Not the answer you're looking for?Browse other questions tagged python matplotlib scipy or ask your own question. But I'm interested in calculating the confidence intervals for Phat, any thoughts on how I could I go about it? I think the reason for it being here is to attract Matlab specialists, programmers and enthusiasts. By looking at the distribution of probabilities amongst subsamples you should get a pretty good idea of what the variance is.

The disadvantage of this method is that it may not be possible actually calculate an interval with a desired given probability. Not the answer you're looking for?Browse other questions tagged matlab statistics markov-chains confidence-interval or ask your own question. Confidence is not built by being able to do everything. Confidence is built by being able to do some things well. If you could go back into your past and get rid of wrongdoings done to you: people who teased you, hated you, did you wrong, you would come out at this end of your life a different person. Decide today to do something you feel you can’t do because you think you haven’t got what it takes. We cannot possibly achieve resolutions without first throwing away the very stumbling blocks that stand in our way of attaining them. You had no control over what happened to you in your past, but the reins are all in your hands now.

Practise probably won’t make you perfect, but it will get you close enough to succeed (and you’ll learn something new in the interim). Once you get rid of bad thoughts about the people in your past (or present) who’ve caused you to feel less confident about yourself, you can start to achieve your dreams whether they’re building confidence, boosting your body confidence or just restoring faith in yourself. If you look at your life as a half empty glass, know that there are many people in the world at this moment who don’t have glasses.

In order to work with what you have, you have to first identify and appreciate what you have. This quote is very encouraging to let someone stop worrying about the past, especially when they can’t change it like you mentioned. This blog uses Comment Love Premium which kindly allows you to put your keywords with your name. You can get Anne's inspirational memoir by clicking on the page called, 'Anne's Memoir' above. You folks have done a better job of explaining difficult concepts than most instructors or textbooks I've encountered. I couldn’t even find agreement on whether the truncation disqualifies it as normal in the strict sense. Is Excel simply incapable of generating random normally distributed data with the level of accuracy needed to make this example work?

If you do $n$ CI's, the number that cover the true mean will follow a binomial distribution $(n,p)$, with $p=0.95$.

I don't yet know what the format of the input data is, I guess a nx2 array where n is the number of points. I hope I got this right: Assuming a multivariate normal distribution, one can simply take the eigenvalues and the eigenvectors to calculate the ellipses. It's not exactly the same because I assume we don't know the number of clusters in advance.

At least, in their Scipy 2011 talk, authors mention that you can determine and obtain confidence regions with it (you may need to have a model for your data though). The advantage is that it should give you good feeling for how the series behaves, and that it may capture some information that could be lost in other methods due to the assumptions that other methods (for example bootstrapping) are based on. It seems that subscribers, readers, and passers-by equally welcome little, digestible bits of confidence and success quotes at intervals. You’ll convert value easier and much quicker if you work with the blessings you already have.

Bearing them in your mind as secrets you hold close to you is NOT the way to get rid of a memory.

Take time off to take that journey which will take you only half way to where you want to be. There are more ways than one and you’ve certainly used up your present way of doing things.

Confidence is built by being able to do some things well”… This will be my favorite quote for the week!

You know how I love quotations, and having published a book of inspirational quotes I know all too well how time consuming it can be to find just the right life lessons.

Feel free to join the discussion by leaving comments, and stay updated by subscribing to the RSS feed.

I only know that RandBetween produces a uniform distribution so it’s useless for these purposes.

Also, I tried a Normal Quantile Plot Test for Normality that I found online on the 128.1k data point example and I did find a very slight amount of leptokurtosis for anyone who knows what to make of that.

Note that I also tried Excel’s data analysis->random number generation tool and got virtually identical results as the Excel formula I included above. Here were the results: at the 90% CL only 60 out of 100 had at least 18 intervals with the pop.

Below is a comparison of the original 100 iterations I recorded compared to the binomial distribution per Excel.

In the calculation function countFcn, I first accumulate the counts of co-occurrences from each sequence (using a less-known syntax of sparse function but we could have also used accumarray), then I divide by the row sums (the bsxfun call). You will have never seen these confidence quotes (or success quotes) on any other blog, or anywhere else on the web but here on How to Build Confidence.

Look at them, claim them, and use them to enrich your life and the lives of those around you. If you don’t do this you will allow the people in your past who negatively affected your confidence to win. If you’ve enjoyed Confidence quotes 3 and know someone who can use a boost today, please share it with them. I liked the idea of picking out parts of previous articles and putting them all in one place.

If I regenerate the prices repeatedly using F9, it only meets the 19 or greater threshold around 70% of the time with some iterations producing 20 out 20 intervals that contain the mean to as low as only 16 out of 20. Your intervals are much narrower, which leads me to suspect you are calculating something wrong. As far as choosing a value of 12, the logic came from trying out various std devs that would result in a data set that was fairly consistently bound between 25 and 100 give or take.

Please note, though--in response to your title--that indeed these CIs are provably correct. I can now demonstrate that out of 20 confidence intervals, the highest probability belongs to scenarios where exactly 2 do not contain the population mean at the 90% confidence level. I was actually talking to my husband just last week about how we all tend to put way too much stuff on our calendar! However, I do have a concern that actually row entries to Phat are not univariate normal distributions because they cannot vary individually.

The key to feeling accomplished is not to have done so many actions in a week but to have done them well… Thank you for the reminder!

That's not likely to be of interest to anyone else unless some specific statistical question emerges.

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