Looking for elementary statistics help? You’ve come to the right place. Statistics How To has more than 1,000 articles and hundreds of videos for elementary statistics, probability, AP statistics and advanced statistics topics. **Looking for a specific topic?** Type it into the search box at the top of the page.

INSTALL OUR ANDROID APP for fast help. It’s Free!

Check out our Practically Cheating Statistics Handbook, which gives you hundreds of easy-to-follow answers in a PDF format.

Subscribe to our Statistics How To channel on Youtube!

Watch the welcome video:

About Us (click here).

Privacy Policy (click here).

If you prefer an online interactive environment to learn R and statistics, this *free R Tutorial by Datacamp* is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try *this Statistics with R track*.

*Facebook page*and I'll do my best to help!

Hi,

Is elementary statistics the same as a basic college Introductory Statistics course? I’m actually using this to help with studying for Finals.

Thanks!

Yes, it’s exactly the same :)

what is a 5 number summary

The five number summary explained

Stephanie, I am not a math-major. 2nd, it has been 35 yrs or so since I have taken and high school or college math/algebra. No Calculus or Trig taken at all in past. My college path now requires a basic introduction to STATS and for some reason I took it online with my instructor being in California and me being in central US. Book is online as well. My problem is the book doesn’t give enough explicit detail on how to complete a statement. I will go as far as to state the book doesn’t even give a bottom line definition for a mean or what the parts are of the statement presenting a normal distribution. Here I am and in chapter 7 and next week is final time. Just by hook or crook I recalled what the “alpha” symbol is/was but did not recall how to compute anything about it. Can you help? Thank you! …..Steve

Does this help? What is an alpha level?

Hello,

I came across your website and I find it interesting and understanding to be able to solve statistical problems. I have a question here on baye’s theorem.

1- A manufacturing company employes three analytical plan for the design and development of a particular product. For cost reason, all three are made at varying time. Intact, plan 1, 2, 3 are used 30%, 20%, & 50% of the product respectively. The perfect rate for the three plans are 0.01, 0.03, 0.02 respectively. If a random product was observed and found to be defective, which plan, was must likely used and thus, responsible.

2-Police plan to enforce speed limit by using radar trap at four different locations within city limit. The radar trap at each of the locations are 40%, 30%, 20%, and 30% of the time respectively. If a person who is speeding on his way to work has probability of 0.2, 0.1, 0.5, and 0.2 respectively, of passing this locations, what is the probability that he will receive a speeding ticket?

Can anyone give me the answer?

What is sampling? Give a definition and then go on to describe situations that necessitate sampling to be conducted

reply to my email: shalox7@gmail.com

Hi Stephanie,

I’m considering buying your handbook. So far it looks helpful, however I couldn’t find the stats/List Editor under APPS. Will you have more calculator help in the handbook?

Hello, Hanna,

I’m updating the TI89 manual with instructions on how to get the app. It’s a TI program and you can download it here:

The e-version of the handbook comes with a TI89 guide.

Best of luck with your course!

Stephanie

A table in the back of the book references this broken link. It troubles me that tables are not included in the download. Broken links like that that will make the book less valuable in time as links are moved and abandoned. Further, it means I can’t use the book absent the internet. This content should be included in the download.

The book itself is not what I had hoped for. However, the price (one night at the honky tonk drinking beer) is worth the risk and I’m hoping there’s some useful content.

A book that would be valuable to me would be one that decodes the myriads of notation found in math and statistics. For example, the integral sign means “find the area under a curve” for the limits given at the top and bottom of the sign. Pretty simple concept, but believe it or not I went through introductory calculus twice before I realized (it was never specifically told to me) that integration was finding an area.

When you start talking about Hamiltonians and Hermetians things get totally out of hand.

Thanks, Todd. I will get to work fixing the broken link. In the meantime, it’s redirecting to the correct page. I can see how a book on the notation would be useful but whew…what a huge endeavor that would be! I have added a couple hundred articles to this site on definitions and I have tried to define statistics terms in plain English. I hope you find the site content to be a helpful addition to the book. Regards, S.

Hi your permutation calculator is not working as it does not generate the distribution when you enter data set. Please see to it. Fran 20 Apr, 2015

Please remove my previous comment no 27.

Thanks for letting me know! We’re working on a fix right now.

I have registered but can’t access forum to post?

What error message are you getting?

Hi Stephanie,

Thanks so much for this site!! It’s helping drastically with an online stats course I’m doing!! Keep up the good work and thanks again!!

Heidi

Glad it’s helping! Good luck with your class :)

How do you find the new mean and standard deviation if your data was off by 1. Such as weight. If your mean is 180.29 and your standard deviation is 10.36 with 100 people, but no data set

Hi Stephanie thanks a bunch for this website it is of great assistance with my online course I am currently pursuing.

:).

Please continue with more Exercises

Hi

I’m currently undertaking a forecast comparison on two aircraft manufacturers and would like to know what tests would be ideal to use if i wish to compare the two together? Chi square, T test or paired T test? Look forward to hearing from you.

Mo

It depends on what kinds of variables you have. This table may help.

Hi

Sorry which table, all I’d like to do is compare the two aircraft manufacturers forecasts in terms of economic, passenger air travel demand and freight market.

Mo

I purchased the downloads for practical cheating for 19.93 via PayPal but do not have the site to download the items. Where can I get my downloads?

Hi, Nick,

You should have the email with the downloads. If not, please let me know!

Stephanie

Lots of information on statistics can be found on this website. Good work!

I see the videos. All i can say is Love you

Helping my daughter with science fair project. We are using spirometry data from my clinic to see which gender smoking ages the lungs the most. My daughter thinks smoking ages a woman’s lungs the most. However, wouldn’t the null hypothesis be there is no gender difference in lung age?

To come up with how much smoking has aged the lungs we subtract the spirometric lung age from biological age. We get this table listed below. We kinda sorta after cutting and pasting. The first roll is the females and the second roll is males.

Female Years Lung Aged Male Years Lung Aged

37 33

30 1

25 29

26 0

23 0

28 12

26 25

37 40

38 0

20 36

27 21

27 12

46 42

41 19

20 37

33 1

8 21

23 2

36 16

26 18

12 19

13 21

4 5

41 13

25 13

60 39

Doing the F test as I followed you on YouTube I get this…

F-Test Two-Sample for Variances

Male Years Lung Aged Female Years Lung Aged

Mean 18.26923077 28.15384615

Variance 188.3646154 148.2953846

Observations 26 26

df 25 25

F 1.270198772

P(F F I can’t reject the null? I guess I need to basically say, there is no significant differences in aged lungs from smoking between the two groups.

Thanks for your help.

Quinton

Hello

When I ran a t test it looks like I can reject the null. How can I determine which to use, t or F testing?

t-Test: Two-Sample Assuming Unequal Variances

Female Years Lung Aged Male Years Lung Aged

Mean 28.15384615 18.26923077

Variance 148.2953846 188.3646154

Observations 26 26

Hypothesized Mean Difference 0

df 49

t Stat 2.746949591

P(T<=t) one-tail 0.004196

t Critical one-tail 1.676550893

P(T<=t) two-tail 0.008392

t Critical two-tail 2.009575237

Thanks again.

Quinton

Quinton,

It sounds like you have two samples, and you think one ages more quickly than the other. Therefore, your null would be:

H0: no difference

H1: there IS a difference

The F test looks for a difference in variances. The results from the f test here would be “there is no significant differences in the VARIANCES in aged lungs from smoking between the two groups”.

I think you probably want to run a t test for a difference in MEANS. T Test for Independent Samples

If you really did intend to run a test for variances, then compare the f-value from the test to your f critical value. Your test results state the F critical value is F 1.270198772, but I don’t know what your test F value is. If the f-value is higher, you can generally reject the null (that the variances are equal).

You would use a t to test for differences between means and the f to test for a difference in variances.

Thank you very much for this site! Extremely helpful. I was reading the page “Sample Variance in Statistics: What is it?” and it helped a great deal to get my head around how variance actually fits in. There was one curious point where is covers the mean of 150 minus the variance of 99. Shouldn’t this be 51? It says 151 on the page.

Hi, Sally. Thanks for catching that typo. It should be 51 (now fixed!).

This is really helpful.

Thanks a lot Friend ☺

Hi Stephanie,

I am a Canadian who is desperate need of help for some of my stats assignments. If you could explain this question to me and the steps in finding the answer that would be a big help come test time.

Question

The mean amount purchased by each customer at Churchill’s Grocery Store is $25 with a standard deviation of $9. The population is positively skewed. For a sample of 41 customers, answer the following questions:

a: What is the likelihood the sample mean is at least $29? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.

b: What is the likelihood the sample mean is greater than $23 but less than $29? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.)

c: Within what limits will 98% of the sample means occur? (Round the final answers to 2 decimal places.)

All three questions are asking for sample mean

Thanks for you help

Brandon

Check out the normal distributions word problems page. That should walk you through the steps for questions like these.

Im having trouble with this one problem. It states find the critical value and give me an n=60 and, a=.05. I’ve looked at the youtube videos and I know how to get a critical value but I cannot figure out this problem. Every critical value I have found does not give me one of the choices. +-.255,+-.253,.255, 0r -.255

Can you post the full question? I need some more info to fully answer your question. n=60 and a=0.05…is this for a t-critical value?

You’re an extremely practical site; couldn’t make it without ya!

I am in a research course and we have reached the statistics portion of the class with minimal instruction on how to do it. I am attempting to discover if there is a correlation maybe? between the responses I receive and the gender or location of a respoder. I have put the information into an excel file and then discovered that I have absolutely no idea what I’m supposed to do with it. The responses have been coded as have the location and gender, I just don’t know how to get the information I need I guess. Is there any information you could give me as to what method I should use to gather this information from my file? Anything would be appreciated. I could analyze based on your videos I’m sure, but first I need some idea of what kind of statistics method I should use for the data analysis.

You need to choose a nonparametric test. You’ve got several options. Try the logistic or Kendall’s Tau.

Dear friend

Thanks alot for these worthy information , i am ophthalmologist and doing research and doing statistical analysis and p value but iam not sure about it, can send figure to you to be sure the p value is correct

thanks alot

clinical assisstant professor dr. marwan salah salman

If you’d like to post some info about what your p-value calculations are, I’d be happy to check it.

In a research which one is the one being tested : the null hypothesis or the hypothesis?

You are testing the alternate.

Grocery shopping question

Hi Gang, could someone please point me in the right direction. I need to set up an excel spreadsheet that will show me the number of possible grocery combinations. There are 200 grocery items from 7 categories (meats, vegetables, etc.), each item has a unique monetary value, you can only use each item only once per combination, and you only have $500 to spend.

Furthermore, there are 7 grocery categories which must be filled with a specific number of items ( 2 meats, 3 vegetables, 1 desert, 1 bread, 1 juice, etc).

How can I get all the possible results!!?? Please help.

When selecting the level of significance alpha, what factors do i have to consinder that can affecte the choice of level of significance?

I’d say mostly what confidence level you are willing to accept. A 1% alpha level (99% CL) is going to be way more precise than a 10% alpha level (90% CL).

It’s very simple to find out any matter on net as compared to textbooks, as I found this

post at this site.

Dear sir/madam:

Greetings.

The local educational agency had notify the teachers to calculate the average T score of the their scores before and after learning. May I ask your utmost advice if it is possible to evaluate the Z score and T score using the steps below. But I can not typing formula on this. Can I sent it by my e_mail.

Your kind thought is highly sought.

Thank you very much.

Sincerely yours,

Mr. Prasit Rattanasupa

Prasit,

I do offer statistics consulting services, but if it’s a quick question I may be able to help without charge. My email is andalepublishing@gmail.com.

Regards,

Stephanie

Appreciate it for all your efforts that you have put in this.

Very interesting info.

Hello, I watched a video of yours on how to plot a histogram on the Ti-89. I am still unsure how to do it, as I have two sets of data, the mid-point (for the x values) and the frequencies (for the y values). I’m not sure how to enter it in the ‘Plot 1’ Section, as it only allows me to enter the first column of information and not the second. Any help would be appreciated. Thank you.

Hi, Melissa, I need a little more info in order to help you troubleshoot.

Please check out the steps here:

http://www.statisticshowto.com/how-to-create-a-frequency-chart-or-histogram-on-the-ti-89-titanium/

And let me know exactly where you get stuck. When you say that it only allows you to enter the first column of information and not the second, do you get an error message? Or are you unable to tab across using the arrow key?

I placed an order for your book download, and I want to cancel that order. I didn’t download the book

Order canceled. Let me know if I can be of further help. Regards, Stephanie

This is quite an interesting lesson. Please what is the sample size of population size of 300? How do I go about the calculation?

very interesting you tube presentation, grateful if you could help in steps in traditional and p-value of hypothesis testing

Will you please tell me how to become an actuary after doing bsc maths honours and what does he do.

would like to receive latest updates & from this site

Good Nigth!

How can to find standard score z from probability in normal standard?

Thanks!

Francisco

The probability is the area under the curve. You can look that area up in the center of a z-table to get the standard score. See http://www.statisticshowto.com/probability-and-statistics/normal-distributions/#NDWP

How do I purchased a hard-or-soft-bound printed copy? I like to make notes in the margins!

Hello, Earles, if you buy the ebook here I’ll ship you a paperback copy of the PC book. Just make sure to include your address in a note if you pay by paypal :)

Hello

Please, what is the dependent and independent variable for this research topic “knowledge and determinants of substance use and abuse among people living with special needs in ibadan.

Hope to hear from you soon. Thank you for reply in advance

The independent variable is constant (i.e. it doesn’t change) so I would say the people living with special needs is the independent variable. So substance abuse would be the dependent.

Hi, I’m applying for a post as an Assistant Statistician in Northern Ireland. Part of that application involves being tested on “basic statistical and social research concepts”. It’s been 6 years since I graduated with a Psychology degree ans (sadly) most of my statistics knowledge has evaporated. Is there a resource on this site that might prove helpful?

Thanks in advance

Chris.

Hi. I intend to do my undergrad research on Occupational Safety and Health among farm workers, focusing on factors affecting safety and health practices on the farm. Could you give me some pointers on the study design, variables, and data analysis methods?

Hi, Chris, have you checked out my YouTube channel? The short (3-5 minute) videos should act as a refresher for statistics. Regards, S.

https://www.youtube.com/channel/UCs3IhN8VOA_5WxpAgbSmFkg

Hi, Leaders, I’m afraid OSHA and farm workers is outside of my area of expertise, so I wouldn’t know where to begin with a study design or variables. Data analysis methods are pretty standard across the board, but it would depend on what your goals are — i.e. identifying specific factors, finding means, comparing means etc. What exactly is your research hypothesis? I would start there.

Hi, would you pleas add section about types of comparison in clinical trials life non inferiority study design,what is the def. of the non inferiority margin and how it is determined?

Stephanie,

Thx for taking the time to create this site and the wonderful and very informative videos as they have helped me immensely.

I had a quick question on moving averages. Say I have a data set of 120 days and I would like to see the average of emails sent per user. I assume a moving average would be the way to go to help smooth out any peaks/valleys that a shorter time might indicate.

Would sampling a certain amount of days provide some “smoothing”, or is it best to run the search for the average on the entire dataset?

Thx,

Jeff

Jeff,

If you suspect there’s a trend going on, a moving average of a certain amount of days will reveal it. That said, it doesn’t sound like you are looking for a trend, or suspect there’s a trend, so I’m not sure what use a MA will do for you. I would run a regular old average on the whole set.

Regards,

S.

I am a first-year university student that is struggling with statistics and I just wanted to let you know that your website has been a lifesaver!

Thank you!

Glad it helps! Good luck with your class :)

I am a graduate student at university. I want to analyze the training effect on firm performance,

To analyze this particular question, I want to use propensity score matching method.

But I don’t know how I should analyze my research question with propensity score matching method.

I would appreciate any recommendation or feedback. Thank you in advance.

I’m not exactly sure why you would want to use PSM for your study, but I’ll assume you know a lot more about it than you’ve written here. See the Propensity Score Matching article for some tips.

I’m stupid with this statistics. Here is the problem. Past records indicate that the probability of online retail orders that turn out to be fraudulent is 0.08. suppose that, on a given day, 20 online retail orders are placed. Assume that the number of online retail orders that turn out to be fraudulent is distributed as a binomial random variable. (a) what are the mean and standard deviation of the number of online retail orders that turn out to be fraudulent? (b) what is the probability that one online retail order will turn out to be fraudulent? (c)what is the probability that one online retail order will turn out to be fraudulent?

(d) What is the probability that two or more online retail orders will turn out to be fraudulent?

Delores,

Can you give me an idea of what you know / where you get stuck?

I am wondering how many combinations of 7 letters can make 5 letter and 6 letter words. A letter may or may not be repeated in the sequence of 7 letters, but only those 7 letters “exist”.

How do you calculate this? I do not know statistics.

Have you tried the combinations calculator? You’ll want to put in 7 for “r” then 5 for “n”. Repeat for “n” as 6. Try the generator at the bottom of the page also. Most of the words will be nonsensical (just random letter combinations).

Dear Sir / Madam,

WJEC (www.wjec.co.uk) is an awarding organisation that provides assessment, training and educational resources in Wales and England.

The resources provided by WJEC to support teachers and students often include material from a wide variety of sources. The use of this original material increases the validity and relevance of the resources making them more interesting and attractive.

WJEC are currently developing a guide to support the teaching of Geology and would like to gain copyright permission to include the ‘Small standard deviation’ and ‘Large standard deviation’ images found on your site.

The Guidance for Teaching will be freely available on our website (www.wjec.co.uk / http://www.eduqas.co.uk) and appropriate acknowledgement will of course be made.

WJEC is a charity and, as such, its role and resources are very different from a commercial publishing company. If you are likely to make a charge for your material, we would be grateful if you would take into account our status as a charity and the use of the material in the context of an educational service.

I hope we have provided sufficient information and that copyright approval will be granted. If you do not control the rights of the above work but are aware of the copyright holder, then we would appreciate receiving any information that can direct us to the source.

Thank you and I look forward to your response,

Sian

Yes, that’s not a problem at all. Please link back to this site. Thanks, and good luck with your project!

It’s nearly impossible to find well-informed people for this

subject, but you sound like you know what you’re talking about!

Thanks

Can you recommend a good book to learn from before signing up for a class ? Trying to get a head start

Just wanted to drop a line and say thanks! Came across this site from a google search working on a take-home stats midterm (PhD student). Then came across it again later while working on another problem. Both times it was the MOST helpful site. Awesome site! Much appreciated!

HI, in the article, “Sampling With Replacement / Sampling Without Replacement”, there is an error. Under sampling without replacement, the outcome “John,John” is listed as a possibility. Since sampling is without replacement and there is only one instance of “John” in the hat. it is impossible for “John” to be drawn more than once.

Thanks for the correction, Paul :)

Chris, you could start with the basic statistics section on this site. It’s free ;)

As far as a book: If it was me, I would purchase the textbook for my class in advance and work from that.

I’m a 69 year old Grandfather who left behind the study of statistics in 1986. I appreciate your work here. It has reopened my mind to what I left behind, and brought new (and I think better) meaning. A younger friend is having difficulty and I have recommended your work here to her.

I’m glad you found the site useful, and thank you for the recommendation!

I am in a Java writing class and I am trying to figure out the Java code to do the combination generator like you have on your site. Is it possible for you to send me a copy of that code?

Sorry, Jason. The code was written by a programmer who no longer works for us.

i have doubts in rank correlations

Have you read this article?

could explain me rank correlation when ranks repeated or equal.

See Spearman Rank Correlation for Tied Ranks

Thank you so much!

Your site is the best that I’ve ever came across in every aspect of what a student aspires.

The language is so easy, not many jargons were used and if used, consisted of a hyperlink. The explanation is accurate and brief. The site had all the topics that I needed to study for my subject (Econometrics).

Keep it up!

thank you

Dear Sir

I am the scholar and working in the field of Hydrology and often have to work for statistical calculation. May I know do you have Matlab code to calculate the common statistical parameters. If then can you please share it with me.

What parameters did you need to calculate?

Can you please help me come up with a bin range so I can draw my histogram using excel. The data is 23571,23988,25871,22608,23953,24855,28511,26730

Lerato, I would say you have too few data points to draw a histogram. If you *must* make one, see How to Choose Bin Sizes.

Hi guys, I’m practicing stats before we do much in the class and I am faced with this problem.

An African news website wants to increase its reach with African graduates living abroad. During March 2016 it undertakes a Facebook campaign targeting those marked on Facebook as born in “any African country”, connected to a university network, aged 25-34 and living in the UK, Australia, Canada or the USA. In the year to February, there was an average of 14,000 unique visitors to the website per day from these four countries, with a variance of 1,587,600. In the month of March the daily average was 14,425. The management wants to know with 99% confidence whether the campaign worked or not.

i) State the null alternative hypotheses, explaining your choice.

ii)Calculate the P-value

iii)Represent your results on a graph that marks clearly the rejection and non rejection regions. What do you concludes.

iv) Construct a 90% confidence interval around the March sample mean. Comment on the, relative to your conclusion in part (iii)

There are more questions but I feel getting a response to these will give me a general flow of statistics and I didn’t want burden anyone with my work.

If you also have any resources that can help me understand the topic please do send them eg specific videos on the site or others so I can get the picture.

Thanks a lot

I purchase the book, The descriptive statistics is blank?

Hello, Natasha,

There is a chapter heading for descriptive statistics (which is blank apart from the chapter title) followed by about a dozen articles on descriptive statistics (starting with How to Spot Fake Statistics). And ending with How To Draw a Cum Freq Table. If you use the hyperlinks in the Contents section to go to the various descriptive statistics articles, you should be able to navigate through them. If you are still having problems with blank pages please let me know.

Hi I have a question I would like to ask, thanks in advance:

A test wanted to investigate whether a change in the manufacturing of light bulbs changed the life span of the light bulb. Before the change the mean life span was 1000 h. After the manufacturing process a random sample was taken of 50 light bulbs of the production, the life span was measured on these and gave the mean of 1050 h and the standard deviation on 100 h. Find out through significance level of 1% whether the light bulbs mean life span changed after the change.

Hello

I enjoyed the ANOVA / MANOVA article, was very informative – the pros/cons part helped me out this time

Cheers,

Chill

This is a great site to learn from. Thanks Bro

I like the look of the Statistical Handbook and I am thinking about buying it – it looks great with the

– detailed walk-throuth-solutions

– easy understandable language

– amount of exercises

I was actually looking for this: For training and inspirational purpose, I am looking for a complete compilation of Statistical Case Studies/ Exercises. It should include:

– Minimum 30 Case Studies/ Exercises

– Detailed Walk-Through-Solutions

– Datasets

– Display of model choices and calculations

– The correspondent R code

– Budget: € 70 / $ 80

Contents should approximate to M.Sc. level:

– Hypothesis tests,

– Confidence intervals,

– Power of Test,

– Type I & II Errors,

– Sample Size,

– Chi-square,

– ANOVA,

– Regression Analysis…

… but except from the content of R code and datasets, maybe this Statistical Handbook can do it? What do you think? – thank you so much!

Carsten

Carsten,

There are no Case Studies/ Exercises in the book. It’s aimed at undergrads. Sorry!

I purchased the book. I have the TI-84 Plus CE. Is there an available add-on for using this calculator?

Hello, EnnDot,

There’s no add-on for the ti-84. It’s very similar…most of the instructions are the same. I am working on ti-84 for the site, when it’s ready, would you like me to notify you?

Hello

I have a question about using Standard Deviation for data sets with low Co-efficient of variation. Below is the link that I posted on another website:

https://stackoverflow.com/questions/44925690/standard-deviation-and-coefficient-of-variation

Any help is appreciated.

Thanks

Awesome post.

Seeing as CV=(SD/Mean)*100 , it should be no surprise that if you have a very low coefficient of variation you also have a very small standard deviation. So you might be surprised at outliers if you use the “sigma” rule. I am not sure what outlier test you mean by this…but any rule (see the six different ways to find outliers here) is going to label a point an outlier if it’s 17.3 standard deviations from the mean.

Pls I m a research student finalising to present my proposal defence and in the research methodology I intend to use the following statical tools for my data analysis. 1. Cronbanch’s Alpha 2. Statistical Package for Social Sciences (SPSS 19) 3. ANOVA 4. T. Test pls kindly assist with the introduction and use of the tools. Regards.

Hi Andale,

your site is extremely helpful to beginners like me. I was checking your page on nonparametric tests. I had a couple of doubts.

1. Although you have written which non-parametric test is an alternative to which parametric test, I am not clear where exactly to use the chi-square test. Can the chi-square test be conducted in place of any of these other non-parametric tests?

2. I have carried out some chi-square tests for categorical variables and in some cases results are showing as 0.0. What does it mean?

“Can the chi-square test be conducted in place of any of these other non-parametric tests?” No. Chi-square is only for categorical data. If you have 1 IV with 2 levels, you could use Fisher’s exact instead. “In some cases results are showing as 0.0”. Chi-square of 0 means your observed values = expected values.

Hi, Finite population corrector (FPC) is applied if sample size/ population is big. If FPC already used to calculate sample size,do we still apply FPC to calculate the confidence interval?

If you know you want to apply it the CI, why not use the FPC formula for a confidence interval for a mean?

Visiting the website again after several attempts to post a comment on collider. I see now. You select which academic comments to post and which not…. Interesting.

I post all comments unless they are caught by the spam filter. What error are you getting when you post a comment?

1) Binomial Distribution

Experiment: Flip 5 fair coins at the same time and count the total number of head.

Mean = 2.5

Variance = 1.25

Repeat 100 times, record the results.

Head = 1

Tail = 0

Question: Describe the shapes of the distribution (pmf) in the experiments of Binomial and Geometric. Explain for each graph, why the graph has this shape and pmf?

2)Geometric Distribution

Experiment: Flip 3 coins at the same time. Record the total number of tosses until you get all heads or tails.

Mean = 4

Variance = 12

Repeat 100 times, record the results.

# of tosses until all heads or tails

(Record 15 if the number > 15.)

Question : Why the Geometric distributions have these shapes and pmf?

Is this homework? What have you tried so far? Did you check the pages for binomial distribution and geometric distribution?

Is an report.

I have try researching, but none of the experiment is about flipping multiple coins leading to the shape of a binomial and geometric distribution.

Yes i have read the pages but i think it did not explain the shape of the binomial and geometric distribution.

The shapes happen because you’re taking discrete counts. They are both step-functions (they aren’t continuous like the normal).

P.S. flipping coins is just a simple way to make these distributions. You could choose anything that has a heads/tail yes/no solution. For example, put a yellow ball and a green ball into a hat then randomly pick one.

Thanks for the explanation.

i will like to ask one last question

In the Geometric distribution trials, on average we need to throw 4 times to get the desired result. If now I want you to guess how many times it takes to get all heads or all tails, in order to optimize your chance to win, which number will you guess? Why?

I think I want to become a statistician now because of your description. It describes me exactly, so thank you!

Yay! We need more statisticians in the world :)

In the Geometric distribution trials, on average we need to throw 4 times to get the desired result. If now I want you to guess how many times it takes to get all heads or all tails, in order to optimize your chance to win, which number will you guess? Why?

I have try researching, but none of the experiment is about flipping multiple coins leading to the shape of a binomial and geometric distribution.

Yes i have read the pages but i think it did not explain the shape of the binomial and geometric distribution.

Thanx for a wonderful site. I am an older surgeon in Johannesburg South Africa often confused by the statistics in modern medical journal articles. I decided to relearn stats from scratch and your website is a godsend!

Kind regards

Bryan

Glad the site helped you, Bryan :)

You can find an example here of the shape of a geometric. Similarly, there’s an image of a binomial here. AThere are infinite possibilities for shapes of distribution, so the shape depends on your specific inputs.

I wouldn’t guess a number. I’m not a gambler lol. It’s a random chance (each throw of a coin is independent and is a 50% chance of being heads or tails) and could be anywhere from zero to infinity. It might take one person 4 throws to get 4 consecutive heads. Or you might spend the whole day failing to get it. So, yeah…I’m not guessing ;)

Thank you for this wonderful blog, it really deserves to be among the best statistical teaching blog.

Hello, your blog is really helpful.Could you suggest a test between a set of quantitative and qualitative data. i’ve to find out correlation of trace elements with gender of the samples. which test doyou think i should use?

Thanks in advance

It really depends on what you mean by “correlation” and what kind of data you have. If you really mean correlation, as in one goes up and the other goes down, polychoric correlation is a possibility.

Thanks a lot for your reply. By correlation i wanted to see if the concentrations of an element such as Strontium depends on the gender of the person or not. Is it possible to do polychoric correlation in excel?