Statistics How To

Welcome to Statistics How To!

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Welcome to Statistics How To! was last modified: January 21st, 2018 by Stephanie

98 thoughts on “Welcome to Statistics How To!

  1. marwan salah salman

    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

  2. Andale

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

  3. Rory

    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.

  4. Sekeli Maboshe

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

  5. Andale

    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).

  6. diamond doctor dallas

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

  7. Prasit Rattanasupa

    Dear sir/madam:

    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

  8. Melissa

    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.

  9. Jack Weakley

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

  10. Ayo

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

  11. sarinee

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

  12. Vanshika Datta

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

  13. Francisco

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

  14. Andale

    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 :)

  15. ayodele


    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

  16. Andale

    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.

  17. Chris

    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

  18. Leaders

    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?

  19. Andale

    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.

  20. sarah

    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?

  21. Jeff


    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?


  22. Andale

    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.

  23. Bess

    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!

  24. Paul

    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.

  25. Delores

    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?

  26. Rose Goehring

    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.

  27. Andale

    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).

  28. Sian Williams

    Dear Sir / Madam,

    WJEC ( 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 ( / 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,

  29. Andale

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

  30. Satin Youth

    It’s nearly impossible to find well-informed people for this
    subject, but you sound like you know what you’re talking about!

  31. Chris

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

  32. Armani

    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!

  33. Paul Sherwin

    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.

  34. Andale

    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.

  35. Meticularius

    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.

  36. Jason Sandusky

    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?

  37. Amish Gupta

    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!

  38. Vikram Kumar

    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.

  39. Lerato

    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

  40. Bukhosi

    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

  41. Andale

    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.

  42. Richard Tarschis

    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.

  43. Predictive Analyst

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

  44. Carsten

    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!

  45. Andale

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

  46. EnnDot

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

  47. Andale

    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?

  48. Andale

    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.

  49. Paul Ikele

    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.

  50. Pihu

    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?

  51. Andale

    “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.

  52. cher

    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?

  53. Eyal Shahar

    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.

  54. Andale

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

  55. sam

    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?

  56. sam

    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.

  57. Andale

    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.

  58. sam

    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?

  59. Lena N

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

  60. Decoracion

    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?

  61. Ligar con chicas

    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.

  62. Bryan Malakou

    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

  63. Andale

    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 ;)

  64. Deepshikha Sharma

    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

  65. Deepshikha Sharma

    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?