How To Know Which Statistical Test To Use For Hypothesis Testing

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Elementary Number Theory:
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MIT OpenCourseWare: / @mitocw
Khan Academy: / @khanacademy
PBS Infinite Series: / @pbsinfiniteseries
Lex Fridman: / lexfridman There are plenty of methods for testing a hypothesis using statistics. When you are faced with a bunch of data, how do you know which test to use? Let's break down when to use each test in a simple way. Let's think how scientists think.
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My name is Kody Amour, and I provide online math lectures to the public. My aim is to provide content that attends to a sound, productive conceptual understanding. Basically, I want to make sense, and I want my videos to be coherent with each other. If you think that these videos have helped you, please consider supporting this channel by subscribing, and please consider donating to this cause via Patreon!
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[@quantquill]

We do not use a t-test for a one-sample test for proportion. We use the z distribution. I teach undergraduate and graduate statistics and have reviewed a dozen statistics textbooks and with 99% confidence, claim that we do not use the Student's t-distribution when testing a proportion. From the Stats Stackexchange: "The reason you can use a z-test with proportion data is because the standard deviation of a proportion is a function of the proportion itself. Thus, once you have estimated the proportion in your sample, you don't have an extra source of uncertainty that you have to take into account." Z distribution doesn't ask for sample size to determine the critical value, whereas t distribution does. However, as sample size gets large, z and t converge until t = z. For example, the sample size of 1000 would have no difference between z and t values.

[@AmourLearning]

Thank you for the correction 🙂

[@ombotimbe]

I agree, Professor. I lately took some class on regression analysis at Google and that's exactly what we've been told. You haven't missed a word in your explanation. Thank you!

[@user-cy9zf4oz2i]

The z-test for proportions is DERIVED from the binomial distribution under the assumption of a large sample size. The key idea behind this test is based on the Central Limit Theorem, which states that the distribution of the sample mean of a large enough sample will be approximately normally distributed, regardless of the shape of the underlying population distribution. hence you use z-test with proportion data

[@beachwave5705]

ok tryhard

[@mrbenizzle4087]

@@beachwave5705that’s such a bananas thing to say to a professor making a correction to a statistics video on KZbin 💀

[@aflowerthatbloomsinadversity]

Spent 16 weeks in a graduate level stats class, but learned everything I needed to know in this 20 minute video. Thanks! Super clear.

[@AssGasGottaBlast]

Came here to say the same thing! lol

[@konami584]

yes, agree :)

[@biruktesfaye7472]

Those 16 weeks has laid a huge foundation for u to understand this 20' lecture easily though.

[@Noname11364]

Right? I was thinking in class, there has to be a more concise way to explain this stuff.

[@cjohnson3836]

Given its a year later, you've probably now also learned that none of these tests are relevant any longer.

[@Misterz3r0]

There is nothing wrong with the 1-sample z test. It produces the correct answers as long as you have the population parameters. But because we rarely have the population parameters we don't use it. Its not inherently flawed as implied by the host of the video. It's pretty easy to explain why it isn't used very often, like I just did. Otherwise, great video.

[@Canuck1000]

I was going to say the same thing. In addition, when the sample is greater than 30, both tests are pretty much the same. For the Chi-square, he should have said that each "bin" needs to have more than five observations. Two of them were below five.

[@sssam844]

@@Canuck1000 he seems to be quite incompetent

[@claireli5044]

@@Canuck1000do you know the difference of 2 sample t-test proportion vs chi squared? I feel they are quite interchangeable, like the depression example he mentioned. Can it be used for chi-squared as well?

[@Canuck1000]

@@claireli5044 The issue that is discussed here is the z-test vs t-test (population vs sample). The z-test is valid if we know the information about the entire population, but is very difficult to obtain as Z3r0 said above. It should not be automatically rejected. In the end, if n>30, both tests will give you the same results (if it is a sample still use the t-test though).

[@hyowonkim8168]

@@claireli5044 Hi, isn't the t-test for comparing the means of two or more different continuous variables and the chi-squared test for nominal and/or ordinal variables? If I am not mistaken I don't think they are interchangeable. I would appreciate it if someone can correct my understanding. Thank you.

[@jamiyana4969]

Simply the greatest explanation. I spent hours trying to get the main gist and difference of all these confusing test. This video was the brilliant saver for me. Thank you so much !!!!!

[@aishwaryar1998]

The fact he explained the entire semester statistics portion in 20 minutes clear and precise. Amazing 🔥

[@HamzaAfridi999]

As a medical student with a small portion of statistics I m just confused 🥲

[@girlwithquestions]

This was super helpful in so many levels. Not only did you described the tests in detail without hassle but it helped me understand when to use them. Thanks!!

[@antoniorobinson1727]

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[@mcyap92]

Clear explanation, good example, energetic lectures! Thanks, this is so helpful!

[@koenhouse]

You are one in a million! I finally understand when to use Regression! Thank you & subscribed!

[@jennifervazquez5329]

saved me so much time researching the appropriate technique I should use to test my hypothesis. Glad i watched it

[@fatmazehra3892]

It is amazing! While I listening, I made a mind map and I finally organize my knowledge. Thanks a lot!

[@siddharthvm8262]

Great video! Just wanted to share my 2 cents. We don't use z tests because they require for us to have the population statistics (population mean and standard deviation) to do our analysis whereas in a T-test we just require the sample statistics (sample mean and standard deviation) to go ahead. Since in many cases we are just comparing 2 samples and we might not have the population statistics (especially standard deviation),we use T-tests instead of the z tests. Hope this helps!

[@raideryvs5595]

Just to add a little more, you dont need the population mean to perform a z-test but you need the population standard deviation (which you never really have in practice). If you needed the population mean, then doing a test for the mean would be beyond pointless

[@anuragnegi9636]

@@raideryvs5595 not sure about this. What about a case where a machine is claimed to produce products of size X and we have to look at a sample's Mean and Std to validate that ? Here we have 'claimed' population mean available to us.

[@jermelpurse3018]

I’m not statistician but I’ve been in the statistics classes at least all three or four you might take during your undergraduate year and when you learn about those particular test they also tell you when you should use them. That’s part of learning about the actual test. I think that’s where we’re having a breakdown in the education process now statistics is more college level but even on a more basic level we might learn how to do math but we don’t learn the principles behind the mathematics you should learn the principles behind the statistics tests then you know when to use them

[@KatoOnTheTrack1]

I’m a mechanical engineer. Of course we took the appropriate statistics and probability class but never saw the real significance until my 5th year of being an engineer and working at GE healthcare. Now I apply the DMAIC approach as much as needed.

[@upbornwoman9334]

I am from the university of Jos, Plateau State, Nigeria and l have never learned well during the masters degree statistics classes l took for one year+ but you make it look simple. You are a good communicator and l feel more confident about my statistics knowledge because of you.

[@henetunoel5657]

🇳🇬❤

[@louiechievonmendoza9398]

I commend you! This is the most comprehensive comparison with explanation so far. Thanks

[@LiliaceaeLilium]

That really helped me understand the differences. I've always struggled with that before, so thank you!

[@arj123sub]

Thanks for posting this video. Clarified the difference between the tests

[@tbrazz8482]

This was extremely helpful and clear...thanks so much!

[@hiyaguha]

Kody, Thank you so much. I have spent days trying to figure out ANOVA versus Chi Square versus T tests and so on, and you made it so easy. I am really grateful --and also a little baffled that so many other sources make it so complex.

[@synergi1107]

thank you so much for finding time to really explain this to us

[@MrRemava]

Great! Simple and short resume of a difficult problem. Thanks a lot!

[@bryanlee5464]

wish all teachers are like you can structure so clearly and simply like this!

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[@ladydove5895]

Where have you been all my statistics life? WOW!! Just brilliant...thank you so much.

[@suki1053]

Thank you so much!!!!! This is definitely solved my problems and answered my confused.

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[@zeynepzisan3636]

What a clear explanation with examples. I could understand without statistic background. Thank you

[@annalewis866]

Thank you! Very clear and exactly what I needed!

[@uncutit1995]

Woow woow this is the most clear version of understanding which test, when, where and how to use the statistical test. Thank you

[@ifeanyi_maduka]

This is by far the best approach I've watched on youtube. And I've watched many. So, straight sub and like for sure.

[@laureldennis1727]

Ok, first, I love the way you present the information = terrific!!! 2nd soooo easy to understand; you speak in everyday language. thank you so much for this video, I got it!!

[@akanshasrivastava3001]

Honestly ! I wasn't sure about it. But the content is so simplified,relevant and helpful.

[@Missyheng]

Thank you! This is so helpful for my understanding!! Wish my lecturers would watch this and summed up as such.

[@antoniorobinson1727]

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[@maciejjamrozy]

Clear & Simple - thank you for the summary!

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[@davidoconnor9167]

Wow.. so well explained, Thanks a bunch Kody!

[@LauraGayusi]

Thank you very very much I have an exam tomorrow and you explained it clearly that I understand now I really appreciate your efforts you are a genius thank youuuuuuuuuuuuuuuuuuuuuu

[@PLuna-zb4ol]

Great video, thanks for the clear explanations!

[@MsAndreaskastrup]

Amazing! So much easier and fun to follow along than the other youtube videoes i have seen

[@kevinshao9148]

Great video of lecture of this young man! Thank you so much!

[@abhisheksrivastava3270]

Great video Please clarify what type of test one can use if studies are going on journalism and media comparisons

[@daiversetech8000]

The energy you bring to lectures is contagious. The explanation is extremely clear. Great stuff. Please keep it coming. Thanks

[@sirmarky9991]

Your reaction on the thumbnail is definitely me.

[@erhancinar5954]

Wow. Great introduction. The context is great. But apart from the context, the teaching style is fabulous. Thank you.

[@chandanaanil2249]

LOVED THIS!!! NEVER UNDERSTOOD STATS BETTER

[@filipinaandtheworld698]

I’m on a PhD level program with a statistics course and this is incredibly useful sir. You deserve 22 million subscribers!

[@haidaralolaywi8557]

Same as here

[@antoniorobinson1727]

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[@prithvidhyani1991]

no offense but how is any of the information in this video useful to you while doing a phd in statistics? isn't this taught in high school statistics?

[@joed2444]

@@prithvidhyani1991 Maybe in your high school. Some of us are still learning the basics at the graduate level.

[@prithvidhyani1991]

@@joed2444 ohh I see. I should add then that this video really only tells you things to memorize about these topics. If you dive deeper into the mathematics behind every statistical test, you will not need to remember what test to apply in which situation, it will just make sense. Just my two cents if in case you are interested in studying stats.

[@SiegDaniel]

I learned so much from this. Thanks!

[@mariasahina9657]

Thank you! I'm in graduate school now and your videos still help!

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[@hit4success]

Hello, This lecture has helped me to understand using T and ANOVA Test on categorical variable. Previous my thought was T and ANOVA is used only for MEAN difference.

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[@germb747]

Thank you! You explain this so much better than my professor does.

[@kaylakai]

awesome, clearly defined to understand :) thank you!

[@123du5]

Wow. Incredible content. Thanks a lot!

[@mariamartin6205]

Thanks, this was incredibly helpful!

[@hoaralatoan845]

Thank you so much. My statistics semester packaged in your 20-minute video.

[@marykhairallah5256]

This has been so helpful, Thanks

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Maryam Abdulaziz

[@sanskarkhandelwal]

I learned more in this video than 4 month's of college classes 😂

[@little___artistic]

Thanks for this lecture! You are doing great!

[@hameddadgour]

Great content! Thank you for sharing.

[@hennanoor6346]

omg have an exam on Tuesday and this was a lifesaver!! thank you!!

[@dibagabbary2066]

The best video on this topic. Thanks a lot

[@shshsh857]

Thank you! Very helpful video!!!

[@drj144]

Bro i cannot thank you enough. You explained it very clearly for me. Tq boss

[@joshuandulinga732]

Perfect explanation, Thank you!

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[@VV-xf6fg]

Brilliant! You saved our time. Thank you!

[@captain486]

thanks man, this video helped me a lot doing my graduation research.

[@julianmcneil9769]

I'm another doc student who just learned some new things! Thanks!

[@KnowDAOself]

Great video! Well explained!

[@army-cx7nk]

Interesting and easy to understand.

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[@FruitypantsMcNutz]

OMG you are amazing.. this was so easy to understand thank you!!

[@BillyMathews11590]

Dude I spent $70,000 on a PhD in Boston and could have saved every penny had I seen this before. Thanks your fantastic.

[@cosanostra8341]

Thank you for the explanation!! A quick question please: I measured the hardness of a material 2 times (before and after heat treatment), then I represented it with 2 box plots. Now I want to compare the 2 box with each other. For this I need to know when the boxes are significant. Can I use Chi square method? by the others technics, icant calculate p.value with exel. Thank you again!!

[@xanmos]

You mentioned in 4:40 about t-test for one proportion, which DOES NOT exist because Z-tests for proportions are based on approximation of normal (hence, z) to binomial distribution so it's only z-test for proportion. In times like the sample size is so low in testing a single proportion, then some nonparametric test may be used, like the binomial test.

[@tnmyk_]

Very well explained! THis video is super useful! THank you very much!!!

[@bubblefun4564]

thank u somuch, you have made this so easy for me, i was really struggling. you really simplified it. thanks alot again :)

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[@luisrodrigueziii7316]

My friend, you are AMAZING. Thank you so much for this video.

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[@reginanoureddine3571]

Very very helpful thank you!!

[@Mettaman_420]

Amazing!! Thank you!

[@JamesPavlaine]

there is no equivalent t-test for one sample proportion due to the binomial approximation in these cases so only z -test for one proportion samples

[@solarchannel7943]

Good Thank you.

[@dr024]

Theres no such thing as t-test for proportion. As tests involving single and two proportions, which are technically binomial, may only be estimated by a normal distribution (hence, z test), and not by t-distribution.

[@DigitizedSelf]

I'm amazed that there are not more comments on this.

[@dr024]

@@DigitizedSelf @DigitizedSelf im amazed too that there are 200k+ who viewed this and 5k (who "liked") who are totally no knowledge.

[@rustytulod1449]

t test also follow the same formula with z test.

[@dr024]

@@rustytulod1449 find a book that use t-test for proportion and ull never find one.

[@ujjwalsharma4945]

thankyou... this tutorial was really helpful...

[@annathomas9427]

This is so helpful! Thank you!!!

[@TheColorField]

You use the Z-test when you know something about the population standard deviation. This doesn't happen very often, so the t-test is more common. Saying you should never use it, or that it's "bad" or "dumb" or "unprofessional" is just NOT accurate. It's just more RARELY used. Throwing it out shows a lack of understanding.

[@kamogelokhumalo4792]

WOW thank you very much for that easy to understand explanation

[@amoreggaeton1]

Thank you so much for this, you are awesome at what you do! :) 😍

[@antoniorobinson1727]

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[@muskanvij4811]

Really Helpful! Thanks

[@warmpereer65]

Question: I am conducting a study regarding three types of concrete mix to determine if the three mix techniques are significantly different and to determine the optimum mix among the three. I know I can use one way anova to test the significant difference of means however is there a test that determines which mix is optimal or provide better results?

[@cspineda]

Great explanations!

[@tarekyasseen2019]

thanks man really helpful!

[@roz9140]

Great explanation. Thank you 🙏

[@sorormimm493]

Ugh, hated stats in grad school. Both rounds. Am fascinated by stats now!!

[@mayyagore]

thank you! now its all clear

[@-injection-8060]

Very helpful and clear video.

[@hls_yeah]

When he talked about the 2-independent sample test for mean, 2-independent sample test for proportion, and paired sample test, are those all t-tests just with different null and alternative hypotheses? Or are there different ways to do those tests other than the t statistic?

[@aarushisrivastava5701]

Amazingly explained 👏🙏🏻

[@VikramKumar-yc5rl]

I have 3 independent groups (standard drug, new drug, combination of both) to test a eye drop drug trial. I need to test the significance of new drug for various symptoms( itching, tearing, burning sensation, etc; total 10 symptoms ). I have before and after data for each symptom. Sample size for each group is 13,14 and 15. Which test should I use? To choose test do you I also need to know the normality of data distribution?

[@layaaskari490]

Thank you It was really helpful❤

[@jumaayubumohamedi4813]

I think proportions are for categorical response or variables and not qualitative as said here, qualitative research itself its so much complicated with thematic or content analysis of codes and quotes, regarding Z and t test I think its about sample size that dictates which one to be used, I stand to be corrected if I am wrong

[@dslavbebe]

THANK YOU FOR MAKING THIS.

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[@joannaharnett6334]

SO SO helpful thank you very much

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[@gilangignasraharjo6138]

Thanks man! great lecture

[@SNAKE1375]

Hi Kody. Thanks for this clear explanation of the Anova. However, what's interesting me is only the difference between the control group and the treatment groups. I am not interested in the compaison of treatment groups between them. So what's the use for an Anova? Are T-test between the control group and each treatment groups separately enough? has Anova a role in increasing the statistical power compare to multiple T-tests?

[@davidhencshel5969]

Every time you conduct a t-test there is a chance that you will make a Type I error. This error is usually 5%. By running two t-tests on the same data you will have increased your chance of "making a mistake" to 10%. The formula for determining the new error rate for multiple t-tests is not as simple as multiplying 5% by the number of tests. However, if you are only making a few multiple comparisons, the results are very similar if you do. As such, three t-tests would be 15% (actually, 14.3%) and so on. These are unacceptable errors. An ANOVA controls for these errors so that the Type I error remains at 5% and you can be more confident that any statistically significant result you find is not just running lots of tests.

[@mini8525]

Thank you so much for this!

[@unknownbakimono2733]

Hello, this lecture has helped me much, thank you for that. I have one question if u could kindly answer,, Is there is a test that can draw a correlation using both quantitative and qualitative variables?

[@unknownbakimono2733]

@@AmourLearning thank you for responding eventually : )), may this answer be of help to others in need