blog/hypothesis-test-by-hand/

[utterances-bot]

Hypothesis test by hand - Stats and R

Learn the structure of a hypothesis test by hand, illustrated by 4 easy steps using the critical value, p-value and confidence interval methods

https://statsandr.com/blog/hypothesis-test-by-hand/

[drfurtado]

Excellent write up; I am always learning something new from your posts. God bless you!

[AntoineSoetewey]

Excellent write up; I am always learning something new from your posts. God bless you!

Thanks for your kind words!

[vonjd]

For a gentle introduction and some intuition see also: https://blog.ephorie.de/from-coin-tosses-to-p-hacking-make-statistics-significant-again

[AntoineSoetewey]

For a gentle introduction and some intuition see also: https://blog.ephorie.de/from-coin-tosses-to-p-hacking-make-statistics-significant-again

Thanks for your input!

[abuabara]

Incredible post, amazing. I use R for research but I teach introductory statistics mostly using Excel. Your posts are very cool and thought-provoking. Thanks a lot for sharing! ;)

[AntoineSoetewey]

Incredible post, amazing. I use R for research but I teach introductory statistics mostly using Excel. Your posts are very cool and thought-provoking. Thanks a lot for sharing! ;)

Thank you for your feedback! Glad you find them useful.

[sicabi]

Thank you very much for this explanation. Several textbooks and teachers never get to convey these difficult concepts and procedures as clearly as this article.

[AntoineSoetewey]

Thank you very much for this explanation. Several textbooks and teachers never get to convey these difficult concepts and procedures as clearly as this article.

Thanks for your feedback!

[zhou8p]

Great article! I am a data science student from springboard.com, my mentor pointed me to this article, which I found truly helpful.
One question is on the method 2, step3, "1. The critical value is -2.189", do you mean the t-stat computed at step2?

Also, could I summary these 3 methods in a way as below?

• Method 1, is to compare the t-stat with the critical value, which is the line drawn on the distribution graph used to reject the null hypothesis.
• Method 2, is to compare the significance level alpha with the p-value, which is a probability represented by the sum of the area under the curve.
• Method 3, is to compare the target parameters with the confidence interval, which is a range of number.
  And to better memorize them against on the distribution graph, I consider the 3 method as line - area - interval.

[AntoineSoetewey]

Great article! I am a data science student from springboard.com, my mentor pointed me to this article, which I found truly helpful.

Thanks for your feedback!

One question is on the method 2, step3, "1. The critical value is -2.189", do you mean the t-stat computed at step2?

Yes, indeed it is the t-stat and not the critical value. I corrected the typo in the article. Thanks!

Also, could I summary these 3 methods in a way as below?

• Method 1, is to compare the t-stat with the critical value, which is the line drawn on the distribution graph used to reject the null hypothesis.
• Method 2, is to compare the significance level alpha with the p-value, which is a probability represented by the sum of the area under the curve.
• Method 3, is to compare the target parameters with the confidence interval, which is a range of number.

And to better memorize them against on the distribution graph, I consider the 3 method as line - area - interval.

Yes, exactly, that's a very good (and concise) summary!

[ctarafdar]

A very interesting article. As someone who does not use or know much Statistics, this was very helpful. Thank you.I did have a question, and wondering if you could help.

As you have described hypothesis testing is used to draw conclusions about a population attribute (e.g. variation in weight of widgets produced by two machines in a factory) using a subset of widgets (e.g. a sample of say 1,000 widgets produced by both machine). And this makes sense since it will be difficult to measure the weight of each widget produced by the two machines.

But, if we had the weight of each widget produced by both the machines (e.g. 100,000 widgets from machine A and 80,000 widgets from machine B) would we still take a sample and apply the hypothesis tests?

That is to say if I have data for the entire population, would I still take samples and apply the tests or just go ahead and compare the population attributes?

[vonjd]

If you have data for the whole population, you don't need a hypothesis test. But what would "whole population" even mean for parts produced by a machine?

[ctarafdar]

Thank you for the response, Prof. By the way, I just happened to see your blogs - and read the one on Einstein Puzzle. Never knew about constraint programming and MiniZinc.

By whole population I implied al the parts produced by a machine. Similar to example 6 in this post, the example I had in mind was of comparing parts produced by two machines A and B that produce the same part. Machine a produced 100,000 and machine B produced 80,000 parts. The weight of each part produced is available. Each part should weigh 15 gm, but there is a variance. If I want to decide if the variance is same or different, can I apply the hypothesis tests to the entire data (without taking samples).

Can the t-tests be applied to this case?

Apologies I f my question is unclear and not formulated perfectly..

[AntoineSoetewey]

Hello,

Thanks for your question.

As said by Prof. von Jouanne-Diedrich, there is no need to do a hypothesis test if you have the data for the entire population.

You just need to compute the variance for each machine and compare it to see which one is larger (or eventually check if they are very close to each other).

This becomes descriptive statistics, and not inferential statistics anymore.

Just one additional remark: suppose you don't have the whole data, you only have 2 samples and want to compare the 2 variances, you would not use a t-test (because t-tests are used to compare means and not variances).

Hope this makes it even clearer.

Regards,
Antoine

[vonjd]

I cannot say it any clearer and I repeat: "If you have data for the whole population, you don't need a hypothesis test. "

[ctarafdar]

Thank you for your reply. It is now clear to me.

[ctarafdar]

Thank you so much for the clarification. I really liked your blog and right now am reading through the one on Multiple Linear Regression. Keep up the good work. It is so useful for Stat novices like me.

[AntoineSoetewey]

Glad you like it!

[srsdec]

Very informative article. Thanks for sharing this informative write up.

I personally liked the way wherein you have discussed elaborately on the usage of 3 Approaches to be incorporated towards Hypothesis Testing.

With respect to the 3rd method i.e. Confidence intervals, how do you incorporate this method using R tool? Would be grateful if you could enlighten me regarding this.

Looking forward to your response.

[AntoineSoetewey]

Thanks for your feedback @srsdec !

There are two approaches:

1. You can compute it in R using the formula for a confidence interval. Suppose you have a numeric vector x and $\alpha = 0.05$:

lower_bound <- mean(x) - qt(0.975, length(x) - 1) * sd(x) / sqrt(length(x))
upper_bound <- mean(x) + qt(0.975, length(x) - 1) * sd(x) / sqrt(length(x))

c(lower_bound, upper_bound)

2. Using the t.test() function:

t.test(x)$conf.int

Hope this helps.

Regards,
Antoine

[srsdec]

Hi Antoine, Greetings & Trust that you are doing fine...!!! Your prompt response is indeed Appreciated. Indeed this is helpful. Thanks & Regards, Sameer Sippy