Statistics 101: Binomially Distributed Factory Accident Data

[@BrandonFoltz]

Hello! No PL2 yet. It is very common sense easy-type stuff that I will come back to later. Thanks! - B

[@augustineowusu2934]

I just want to say thank you for these great videos. So far, I have watched all your PL playlists from PL02 to PL05 up to this video and Statistics has never made so much sense, as applicable in professional life. This depth of understanding makes me want to know more to become an expert in this field. Thanks to you, I think i have a new hobby in applying concepts from a once considered boring subject.

[@thewilfreds]

How come this video has only 15k views? Man you did an awesome work explaining binomial distribution here. Thumbs up!!!

[@InfoTunnel]

Fantastic explaination and nice example. May I know areas where you have applied this binomial distribution ? Thanks

[@tejasvitarun9832]

Awesome example and concepts understanding. Im really thankful to you. Brandon. You made my confidence level go higher like distributions . Im really a fan of your videos

[@MMFawzy]

Hi Brandon, I believe the example illustrated stands for Possion Distribution and not Binomial which will result in using a different probability distribution equation

[@wfalcao69]

I agree with you. Poisson

[@rabeialkhattab6584]

Hi Brandon, I thought the accident data were collected over a span of 5 years period, hence the probability would be something like p=1/(5*12). Could you please clarify? Thanks, Rabei

[@annominous9567]

They were collected over a span of 5 years, but what you're trying to figure out is, "what is the probability of any of the 250 accidents occurring in a given month?" And there are exactly 12 months in a year. So if you randomly select one accident from your sample of 250, there is a 1 in 12 chance that that randomly select accident occurred in January, and a 1 in 12 chance that it occurred in February, a 1 in 12 chance that it occurred in March, etc., etc., etc., REGARDLESS of which year the accident occurred in (every year has the same number of months). So, for each month, success of the binomial test is defined as, "the accident occurred in this month," and failure is defined as, "the accident did NOT occur in this month," and is not affected at all by the year in which the accident occurred. Therefore, the probability that any accident occurred in a given month is 1/12, and the probability that any given accident did NOT occur in that month is 11/12. Not sure if anyone's even coming back to these comments but, if so, I hope this helps.

[@DJVWoodworking]

I'm coming back to the comments. :) I think there may be some problem with the wording of the original dataset that confuses people. If there was a random sample of 250 over a 5 year period and an average of 30 accidents within the month of August then that means of the 250 accidents approximately 150 of the total sample would need to have occurred in a month of August. Now, if they were random samples each year of 250 accidents, and from that 1250 accidents there was an average of 30 accidents in the month of march that would make sense... but over a 5 year period of 250 accidents 30 on average in the month of August would be pretty extraordinary.

[@MdAbdullahAlMuyid_nowho]

Think of it in this way: in the last 5 years, exactly 250 accidents happened. And like you have calculated, 150 happened in August. Yes, it can be real easy to spot it. But, then again, how would you prove it statistically? This video may be dedicated to answering that question only. Plus, had we not took this much easier scenario as an example, the graph and the result might have seemed too complicated to be learnt for many of us. :)

[@vulnerablerummy]

i still don't understand this. based on Ann's and Abdullah's argument, the 250 accidents are collected over 5 years. Then let me ask you this, does the population mean (average accidents per month) of 20.8333 belongs to the population of 12 months (1 year) or 60 months (5 year)? if you still choose 5 years, then shouldn't the total accidents after 5 years become 60 x 20.833 = 1249.98??

[@stalinamirtharaj1353]

@@vulnerablerummy data were collected over 5 years and averaged the no of accidents for each month so the analysis is basically for every month in a year. Hope this helps!!

[@viggosten]

Hey Brandon and thanks again for your great videos! They really help. I have a question regarding the expected number of accidents per month. In the beginning you state that you have 250 accidents over 5 years. Shouldn't it be: n = 250 p = 1/(5*12) rather than 1/12? Or am i missing something here? Thanks!

[@lowqchannel]

im wondering the same thing

[@parthgupta4145]

I thought the accident data were collected over a span of 5 years period, hence the probability would be something like p=1/(5*12). Could you please clarify?

[@pl4ever9]

if you use 1/(5*12), it's the probability of an accident occurs in 1 specific month of the whole 5 year package (60 months), meaning you have to differentiate August 2010, then August 2011, August 2012, August 2013 and August 2014 for example. For this reason, you are not calculating the probability of having a number of accidents in August generally, disregard of the year like the problem requires. Moreover, all the statistics here is in the 5-year period, so the mean of 20 accidents is for 5 year. For example, according to our mean, we may expect that in May 2010, 2011, 2012, 2013 and 2014, the TOTAL number of accident is 20, for ALL 5 may in 5 years. Hope it helps!

[@CuongNguyen-xz3yo]

Let's me illustrate the example 250 is the number of accident in a year 30 in the number of accident in 8th month (August) If I take an accident, and ask "is this in this month?". This month can assume be any month, in this case, we're trying to evaluate the August so the question is "Is this in the August" Let's assume that an accident is distributed equally among the month. So the Success Rate (in August) is 1/12, the Failure Rate (not in August is 11/12) We will try n = 250 trial, and ask "is this in August?" As the calculation, mean = 20.8. So we expect in August it is likely to have 21 or 20 cases (You can say it in other months as well) The x = 30 in August >= Mean + 2 std -> seem to be unusual and then we need to investigate further what makes it higher? Some may confuse with the data collected in 5 years and then average bla bla.. But let's make it simple by looking at the "nature of binomial" distribution The above explanation, I think it is the best to illustrate the case Wanna hear you thought

[@apoorvshrivastava3544]

sir what is random chance varation means

[@kprabu123]

250 random samples would be distributed across Jan - Dec for this analysis and it doesn't matter if the duration of the samples taken were from 5 years or 10 years. Inorder to just analyze the count in Aug, the focus is only on the month of occurrence and not the year. Regarding p=1/12 - it is defined as - the probability of the accident occurring in Aug, which is 1/12th q = 11/12, the probability of the accident occurring in any month other than Aug Assumption is that there is equal probability that the accident can happen any month. As Aug is the success criteria - p will be 1/12 and q will be 11/12

[@vulnerablerummy]

how does its duration not matter? you literally use the duration to calculate the probability, whether it is 1/12 as mentioned or is it actually 1/60.

[@eaintchithmue7273]

According my understanding, the reason of being 1/12 is 1) able to calculate binomial distribution formula and to build bino distribution graph we need to get the value of a) Probability of being accident in each month & b) probability of not being accident in each month. 2) That's why, we don't look 5 years (60 months ) of duration to calculate this and we focus on 1 year (12 months ) firstly. And the probability of being accident in 12 months is 1 or 100% then we find probability of accident in each month and this happens 1/12. 3) Then, we calculate (1- 1/12) to get probability of not success (not accident) by substract from 1 , after that , we can create binomial distribution graph by using excel with 250 random experiments or trials. ( I am still first year student from asian country and if my reply makes you confusing, sorry for that)

[@kicksterama]

Thanks! You're awesome!

[@MrvladivostokMr]

Hi Brandon, I've tried to calculate the probability of 18 - 38 accidents in any given month. The result is 77.3%. What does it mean ?

[@thingocduytran7430]

I like this video. thank you so much.

[@romanvasiura6705]

Thank you!

[@jongcheulkim7284]

Thank you.

[@islamabbas5718]

Thank you so much, really helpful

[@silverlyder]

Thanks

[@ronmohler8170]

In reality this would be completely useless without calculating opportunities for accidents each month like Todd Conklin says but I like the example for learning the math.

[@Kaysar777]

Awesome! Thanks. :D

[@jototland2159]

Ok, so you have 2.8% chance of 30 or more accidents in a given month. But there are 12 months in a year. If the chance of "success" in a given month is 2.8, the chance of "success" in any month of the year is 1-(1-.028)^12=29%. Do you still think you need an explanation for the data in august?

[@CuongNguyen-xz3yo]

Let's me illustrate the example 250 is the number of accident in a year 30 in the number of accident in 8th month (August) If I take an accident, and ask "is this in this month?". This month can assume be any month, in this case, we're trying to evaluate the August so the question is "Is this in the August" Let's assume that an accident is distributed equally among the month. So the Success Rate (in August) is 1/12, the Failure Rate (not in August is 11/12) We will try n = 250 trial, and ask "is this in August?" As the calculation, mean = 20.8. So we expect in August it is likely to have 21 or 20 cases (You can say it in other months as well) The x = 30 in August >= Mean + 2 std -> seem to be unusual and then we need to investigate further what makes it higher? Some may confuse with the data collected in 5 years and then average bla bla.. But let's make it simple by looking at the "nature of binomial" distribution The above explanation, I think it is the best to illustrate the case Wanna hear you thought