This video introduces hypothesis testing using means, while our more recent book editions introduce hypothesis testing using the proportion context, so this video might be a bit confusing. The core ideas are: 1. We form hypotheses (null and alternative), where the null hypothesis represents typically the "no change" or "uninteresting" scenario (a skeptical perspective) 2. We look at data to see if there is convincing evidence favoring the alternative** hypothesis. If so, we will reject the null hypothesis in favor of the alternative hypothesis. 3. If the data doesn't convincingly favor the alternative hypothesis, then we say we "do not reject the null hypothesis". This sort of double negative is okay in statistics. 4. The p-value is a statistic that is useful for quantifying evidence favoring the alternative hypothesis. 5. In general, be a skeptic! If someone suggests an "alternative fact", you should demand strong evidence before you believe them. :) We plan to create an updated version of this video that uses proportions, but the timeline for this new video has not been set.
This introduction is under large sample contexts (n ≥ 30), so using the normal distribution or the t-distribution will give essentially the same result. The next chapter in the book (and corresponding videos) covers using the t-distribution.
> why does the sample size have to be larger than 30? The following video gives an overview: ruclips.net/video/lsCc_pS3O28/видео.html (If you're familiar with the success-failure condition, then this is kind of like the success-failure condition but for means instead of proportions.) > what would be the sample proportion in the sleep scenario? There is no proportion in this problem. This video was created with our books when we used means to introduce inference instead of proportions (something that changed in 2019). We will create a video for this topic focused on proportions at some point, but the timing is still unclear.
@@joseph645201 The answer here is an unsatisfying "it depends on the context", and I'm going to direct you to our book for the details (the book can be downloaded as a PDF for free), because it's going to take a lot of examples to get some feel for this topic. Even at the end of an intro course, I wouldn't expect someone to truly master this topic, but they should be aware of considerations (again, detailed in the book).
It's just to represent that we're talking about the population mean for 2012. Sometimes subscripts are added onto variables in this way to add more clarity about what they are referencing, which becomes especially helpful when there are multiple uses of similar notation, such as the comparison of two population means.
Now 15 comments after yours and mine. 😅 A bunch of views are happening directly on our site, because we embed many of our videos there, so that might reduce the number of comments we get.
The p-value cannot be a measure of both the strength of evidence for the alternative hypothesis and also allow you to derive Type II errors. Either the p-value is used strictly against the cutoff or it is not. Either the video shouldn't discuss power or it should state that the p-value is simply what you use to decide whether the finding is significant or not. What's presented here smacks of NHST and doesn't stick to a specific underlying theory of testing. With continuous data all of the p-values are equally likely if the null hypothesis is true. The only reason the p can have any influence is the prior logical setup that you're going to consider low ones as indicating the null is false. Once you've decided it's false it doesn't mean anything. And therefore, it's not a measure of evidence. This logical problem can be avoided but it requires some rewording in the presentation. The current one implies things like the condition under which the probability is calculated (null = TRUE) is equal to the probability that the condition is true. There's a relationship here but the statement isn't strictly true. Also, I'm not sure presenting hypothesis testing with CIs has any useful purpose whatsoever. A 95% CI correctly tells you where the true value is 95% of the time. So you can say it's in this interval and not outside it relying on your known accuracy frequency. You can use the fact that this is true for hypothesis testing but that's not really what it's for and makes it seem less useful than what it really is. Most importantly, the 95% CIs 95% property is *not* attached to significance testing, thus making it sound more powerful than it is.
This video introduces hypothesis testing using means, while our more recent book editions introduce hypothesis testing using the proportion context, so this video might be a bit confusing. The core ideas are:
1. We form hypotheses (null and alternative), where the null hypothesis represents typically the "no change" or "uninteresting" scenario (a skeptical perspective)
2. We look at data to see if there is convincing evidence favoring the alternative** hypothesis. If so, we will reject the null hypothesis in favor of the alternative hypothesis.
3. If the data doesn't convincingly favor the alternative hypothesis, then we say we "do not reject the null hypothesis". This sort of double negative is okay in statistics.
4. The p-value is a statistic that is useful for quantifying evidence favoring the alternative hypothesis.
5. In general, be a skeptic! If someone suggests an "alternative fact", you should demand strong evidence before you believe them. :)
We plan to create an updated version of this video that uses proportions, but the timeline for this new video has not been set.
Thank you for posting. This is a great video.
Had to drop the speed to 0.9x. Quick speaker for a topic that requires digesting.
We use Z score if we know the standard deviation of population. But we actually only know the Std of sample, so we should use t score instead.
This introduction is under large sample contexts (n ≥ 30), so using the normal distribution or the t-distribution will give essentially the same result. The next chapter in the book (and corresponding videos) covers using the t-distribution.
why does the sample size have to be larger than 30? what would be the sample proportion in the sleep scenario?
> why does the sample size have to be larger than 30?
The following video gives an overview:
ruclips.net/video/lsCc_pS3O28/видео.html
(If you're familiar with the success-failure condition, then this is kind of like the success-failure condition but for means instead of proportions.)
> what would be the sample proportion in the sleep scenario?
There is no proportion in this problem. This video was created with our books when we used means to introduce inference instead of proportions (something that changed in 2019). We will create a video for this topic focused on proportions at some point, but the timing is still unclear.
@@OpenIntroOrg Great that clears things up thank you! But why is 30 the rule of thumb? When does it need to be larger or smaller?
@@joseph645201 The answer here is an unsatisfying "it depends on the context", and I'm going to direct you to our book for the details (the book can be downloaded as a PDF for free), because it's going to take a lot of examples to get some feel for this topic. Even at the end of an intro course, I wouldn't expect someone to truly master this topic, but they should be aware of considerations (again, detailed in the book).
where did the 12 in μ12 come from?
It's just to represent that we're talking about the population mean for 2012. Sometimes subscripts are added onto variables in this way to add more clarity about what they are referencing, which becomes especially helpful when there are multiple uses of similar notation, such as the comparison of two population means.
Attention please, at Two-tail test example, sample size n is not 72, the correct size is n=122.
damn 40k views and only 13 comments
Now 15 comments after yours and mine. 😅
A bunch of views are happening directly on our site, because we embed many of our videos there, so that might reduce the number of comments we get.
The p-value cannot be a measure of both the strength of evidence for the alternative hypothesis and also allow you to derive Type II errors. Either the p-value is used strictly against the cutoff or it is not. Either the video shouldn't discuss power or it should state that the p-value is simply what you use to decide whether the finding is significant or not. What's presented here smacks of NHST and doesn't stick to a specific underlying theory of testing.
With continuous data all of the p-values are equally likely if the null hypothesis is true. The only reason the p can have any influence is the prior logical setup that you're going to consider low ones as indicating the null is false. Once you've decided it's false it doesn't mean anything. And therefore, it's not a measure of evidence. This logical problem can be avoided but it requires some rewording in the presentation. The current one implies things like the condition under which the probability is calculated (null = TRUE) is equal to the probability that the condition is true. There's a relationship here but the statement isn't strictly true.
Also, I'm not sure presenting hypothesis testing with CIs has any useful purpose whatsoever. A 95% CI correctly tells you where the true value is 95% of the time. So you can say it's in this interval and not outside it relying on your known accuracy frequency. You can use the fact that this is true for hypothesis testing but that's not really what it's for and makes it seem less useful than what it really is. Most importantly, the 95% CIs 95% property is *not* attached to significance testing, thus making it sound more powerful than it is.