Welcome

What is Real Statistics Using Excel?

Real Statistics Using Excel is a practical guide for how to do statistical analysis in Excel plus free statistics software. This software package extends Excel’s built-in statistical capabilities. This will enable you to more easily perform a wide variety of statistical analyses in Excel.

What does Real Statistics Using Excel consist of?

Real Statistics Using Excel is comprised of the following four components:

Real Statistics Resource Pack

An Excel add-in that extends Excel’s standard statistics capabilities. It provides you with advanced worksheet functions and data analysis tools. This will enable you to more easily perform a wide variety of practical statistical analyses. The software supports Excel 2007, 2010, 2013, 2016, 2019, 2021, and 365 for Windows. It also supports Excel 2011, 2016, 2019, 2021, and 365 for the Mac. The current version is Rel 8.9.1 (released 2 October 2023). There is also limited support for Excel 2002 and 2003.

Real Statistics Website (i.e. this site)

  • Lets you download a free copy of the Real Statistics Resource Pack
  • Provides tutorials and descriptions of how to perform a variety of statistical analyses using built-in Excel capabilities. You will also learn how to use the supplemental capabilities provided by the Real Statistics Resource Pack.
  • Presents numerous examples in the form of Excel worksheets which you can download to your computer

For the student and the novice, the Real Statistics website is an excellent tutorial for learning the basic concepts of statistics and how to do statistical analysis. For all users, it provides a step-by-step guide for how to do statistical analysis in the Excel environment and the tools necessary to carry out these analyses.

You can use this website to learn how to perform statistical analyses in Excel even without using the Real Statistics Resource Pack. But we recommend that you download the resource pack so that you can have access to its powerful capabilities.

Real Statistics Examples Workbooks

Consists of fourteen Excel files that contain all the examples shown on the website. These example files can be downloaded for free (click here). Each example focuses on a specific statistical concept and has been designed to demonstrate simple concepts before moving on to more complicated topics. 

Over time, the webpages on the Real Statistics website are being updated so that you will be able to download an Excel file with any of the examples found on that particular webpage.

Real Statistics Community

Each webpage has a Comments section where you can make suggestions, identify errors, ask questions to others in the community, or request their advice.

You can also get updates about new releases and other information via the @Real1Statistics twitter feed.

How do I get started?

Step 1: If you elect to use the Real Statistics Resource Pack, click on the following icon. You will be given the opportunity to download and install for free the Real Statistics Resource Pack. 

free-download-real-statistics

Once you have downloaded and installed the Real Statistics Resource Pack, you will be able to use the supplemental capabilities with your copy of Excel. This is described throughout the rest of the website and is summarized in Using Real Statistics Functions and Real Statistics Data Analysis Tools.

If you choose not to download the resource pack or examples now, you can do so later at any time.

Step 2: Browse through the website to learn how to perform a wide range of statistical analyses in Excel using standard built-in as well as supplemental Real Statistics capabilities. We suggest that you begin by clicking on the Website Introduction (and especially Organization of the Website). These will explain how to navigate the website to get the information you need to run any specific statistical test or learn about any particular topic.

Why do statistical analysis in Excel?

The reasons for choosing Excel are as follows:

  • It is widely available and many people already know how to use it
  • It is not necessary to incur the cost of yet another tool
  • There is no need to learn new methods of manipulating data and drawing graphs
  • It already contains some basic statistics functions and data analysis tools
  • It is much easier to see what is going on since unlike the more popular statistical analysis tools very little is hidden from the user
  • Excel provides the user with a lot of control and flexibility

This makes Excel an ideal tool for learning statistical concepts and performing some basic statistical analyses. Unfortunately, its built-in statistics capabilities are limited. As a result, many prefer to use statistical tools such as R, SPSS, or SAS for carrying out more advanced statistical analyses.

We created the Real Statistics Resource Pack to address these shortcomings. This software package contains various supplemental tools that enable you to carry out a wide range of advanced statistical analyses without leaving the Excel environment. You can download the Real Statistics Resource Pack free of charge from this website.

853 thoughts on “Welcome”

  1. Thanks for wonderful and great work. I must confess I really benefitted from your work.
    Sir, I want to ask is there anyway I can make the realstatistics soft permanent on my excel, I had to re-add everytime the need arise. Thank you as I await your response

    Reply

  2. Hi Charles , i am looking for your support how can use excel program to estimate the margin cost in Lerner Index , it is regarded as the mark up of price over marginal cost and is a measure of the degree of market power. In other words, a ‘smooth’ measure of the magnitude that price exceeds marginal cost, and is calculated as:
    〖Lerner〗_it=(P_it-〖MC〗_it)/P_it
    Where P_itis the price of total assets for bank i at time t, and 〖MC〗_it is the marginal cost of total assets. The resultant Lerner for each country is averaged over the period under analysis for bank i at time t (Berger et al, 2009). 〖MC〗_it is not directly recognizable for a specific organization, hence are estimated using bounds of a total cost function from the organizations data and obtaining the marginal cost from the subsequent translong cost function:
    〖LnCost〗_it=β_0+β_1 LnQ_it+β_2/2 Ln〖Q_it〗^2+∑_(k=1)^3▒γ_kt lnW_(k,it)+∑_(k=1)^3▒∅_kt LnQ_it lnW_(k,it)+∑_(k=1)^3▒〖∑_(j=1)^3▒Ln W_(k,it) 〗 lnW_(j,it)+ ε_it

    Reply

  3. I have found using Excel to be a nightmare for most things. Probably my lack of attention to tutorials. I am going to follow the instructions here and see how I go.
    Thank you.

    Reply

  4. Hi Charles,
    I am analysing diagnostic efficacy of two new tests (named SA and SB) test against an established old test (named WLI). The test results have three positive results: Yes, No and Indeterminate. In calculating the sensitivity, specificity I have excluded the indeterminate results. How can I know whether the indeterminate results affect the diagnostic efficacy of either WLI, SA or SB?

    Reply

  5. Dr Zaiontz, good morning, receive a cordial greeting and thanks for your very good page, please how can I calculate the size of a sample to work with decision trees?.
    There are some page?.

    Dr Zaiontz, buenos días, reciba un cordial saludo y agradecimiento por su muy buena página, por favor como puedo calcular el tamaño de una muestra para trabajar con arboles de decisión?

    Reply

  6. Nice idea.

    Unfortunately when I tried it it, (was going to try a Chronbach Alpha) couldn’t see the Reliability tool in the menu, then it froze.

    On restart, Excel complains it can’t open the RealStatistics file due to an unrecognized extension.

    More disturbingly, it previews in file manager (which it didn’t do before) and opens multiple windows-within-windows on the file.

    Kicking myself for risking Excel in this casual manner. Really cannot afford to lose it right now. (grading deadline time).

    Reply

    • Hello Ed,
      I don’t really understand why this has happened. Tens of thousands of people have used Real Statistics without this sort of problem occurring.
      The file extension for Real Statistics is .xlam, which is quite a recognizable extension. (if you are using Real Statistics with Excel 2002 or 203, then the extension is .xla, which is also quite recognizable extension).
      To use Cronbach’s Alpha you need to choose Internal Consistency Reliability from the Corr tab.
      It is important to use the Installation instructions and not simply double click on the Real Statistics file. The Installation instructions can be found on the webpage from which you downloaded the Real Statistics file.
      Charles

      Reply

  7. I had the idea that your excellent add-in included spectral regression analysis, but do not see it. Have you included it somewhere?

    Reply

  8. Hi Charles,
    Have you considered adding a multilevel modeling capability to the real-statistics add-in?
    Thanks for your great work,
    Andrew

    Reply

  9. Hello Charles,
    I am trying to predict employee retention using logistic regression. I have created several data points for those employees who fulfil the criteria of tenure in the organisation. Now, I want to create a model which will tell the probability of employee staying in the organisation depending upon these data point. What should be my approach?

    Reply

  10. Hello,
    I cannot recall the RealStats.xlam but it’s already in my Add-ins list.
    Solver was installed before.

    I have Excel for Office 365 MSO 32-bit

    Reply

    • Elisabeth,
      What is your question?
      Have your installed Real Statistics and it is not working? If so, what do you see when you enter =VER() in any cell? What do you see when you press the key sequence Ctrl-m ?
      Charles

      Reply

  11. I am ecologist having a number of data in large spreadsheets and I would like to use your “Real Statistics for Excel”. Before I start downloading your softwyre I would like to have your assurance that there are no hidden costs which I will be compelled to pay later. Of course, I am prepared to fully respect your copyright license.

    Loooking forward for your answer.

    Reply

  13. Hi Charles
    I am analysing diagnostic efficacy of a new test against an established old test. The test results (for both control and new test) have only two possible results: yes or no. I have calculated the sensitivity, specificity etc. What is the best graphical method to depict the diagnostic efficacy of new test with respect to old test?

    Reply

    • Hello Prashant,
      You could plot both ROC on the same graph.
      I don[t know whether this is the best approach, but it seems like a reasonable approach to me.
      Charles

      Reply

  14. Hello Charles,

    Have installed the Add-Ins for a requirement to run logistic regression (using Binomial and Probit Regression) on a relatively small set of data of (approx 500 rows). However the model was giving me valid outputs till the time I was using 4 independent variables. All my independent variables are binary in nature. However the instance I included the 5th independent variable I am not getting valid outputs (all set of values are either 0 or are NUM!). Can you help or guide me wherever I am going wrong? Seek your feedback.
    Thanks,
    Raunak

    Reply

  15. Hi Dr. Zaiontz,
    Currently my team are working on a model for Stress Test.
    We are having a problem which is the R squared of our models are small (which is 0.2).
    Is there something wrong with our data?
    What are the properties that can make the R squared small?

    Reply

  16. Doctor Charles, good morning, thank you very much, for the update in the order of the chi-square test, really very useful.

    Doctor Charles, buenos días muchas gracias, por la actualización en el el orden de la prueba chi cuadrado realmente muy útil.

    Reply

  17. Hi Charles,

    Thanks for this helpful website.
    Currently I’m working with some mines data stuff.
    I want to compare mines data (quality of minerals content in the soil) using X-Y-Z coordinate (3 dimensional). We want to know is there any significant effect of X axis, Y axis and Z axis simultaneously to the quality of minerals.

    So there’s 3 factor which correlated each other. Is it better using 3 factor ANOVA or is there any better method?
    By the way my background is not statistics :), please help me to resolve it

    Thanks and regards

    Erik

    Reply

    • Hi Erik,
      With 3 factors, you can calculate pairwise correlations. You can also calculate the correlation between one of these variables and the other two. You can also perform three factor ANOVA.
      In order for me to determine which of these methods, or some other method, is appropriate I would need to have a better understanding of what you want to accomplish and the data you have available.
      Charles

      Reply

      • Dear Charles

        So for instance, we have a volume of silver mines which has: Length (L) 10 m x Width (W) 10 m x Depth (D) 10 m. We clustered the area by 1 m3. So there will be 10 separate volume of soil. On each volume of soil (@ 1 m3) (total 10) we check the silver concentration.

        On the random location let me say (L: 5 m, W:4 m and D: 1 m), it has a concentration of silver 20%. in the other hand, the other location (L: 5 m, W:4 m and D: 10 m), it has a concentration of silver 80%.

        We already have a full images of concentration of the silver in exact location (X-Y-Z) 1 m3 variation in all spots. Now we want to check is there any significant effect of the position (X-Y-Z) to the quality of the minerals. As we know, in the mines there’s always uncertainty of the quality of minerals in different area even it is close each other.

        Thanks Charles, looking forward for your help
        Erik

        Reply

          • Dear Charles

            Ok thanks for your recommendation. Is it possible also to see the significance effect of each position (XYZ) with its interaction to the silver content with 3 factor anova?

            Thanks

            Erik

  18. Hi Charles,

    When I try to preform a binary logistic and profit regression, and include my input range, I get this message “Compile error in hidden module: Address”. Do you know what I should do to address this?

    Thank you!

    Reply

  19. Charles, I’m attempting to compare three variables amongst 20 separate individuals to see if there is a correlation. Can you please help?

    Reply

    • Hello Eric,
      You can calculate the pairwise correlations using the Excel function CORREL.
      If you want to see whether there is a significant difference between the three populations whose samples you have, then you can use ANOVA.
      Charles

      Reply

  20. Hi Charles
    I need your guidance
    I have a Database of Race Horse Results that i would like to analyse.
    I have been trying to self teach myself Statistical Analysis, but i am finding some topics a little complexed.
    I downloaded the Real Statistics add on.
    From my readings and advice from other people in the Racehorse Data Analysis,
    i believe that i must use Multinomial Logit Regression.
    Is this possible on the Real Statistics Package?
    Am i able to email you a small sample of my database? with say 1 dependent Variable Column and 4 Independent Variable Columns and advise if i can use the Real Statistics Add on to carry out Multinomial Logit Regression.
    Can you please send me an email with your email with your email contact details and i can then send you the small database sample,
    I prefer to keep my discussions private at this stage.
    Thanks
    Charles

    Reply

  21. Dear Charles,
    Thank you so much for the site and the Real Statistics. It’s a good software for analysis, and I recommend it for anyone who needs to analyze and do statistical analysis with Excel.
    A few comments/questions if I may:
    1. Data input: will it be possible to select full column, and the system with know how to take the relevant data cells?
    2. Data input: will it be possible that the system processes cells that are empty or blank, and disregard / remove / estimate them?
    3. And to select range composed of not adjacent columns?
    4. How about pooled regression / panel data (i.e. fixed effect, first difference, random effect), cross section of specific year/time?
    Thanks,
    Ron

    Reply

    • Hello Ron,
      Glad that you like the website and software.
      1. I am not sure I know what you are referring to, but for any of the data analysis tools, you can select the first cell and then request that the software highlight all relevant cells in the range.
      2. This depends on the tool. Often the answer is yes, although sometimes I have not yet implemented this capability. The website should make this clear.
      3. Generally no. There is a data analysis tool that does select non-adjacent columns and so you can use the results of this tool for other analyses.
      4. You can perform pooled regression and differencing, along with ARIMA and SARIMA. Random effects are supported for ANOVA. I am currently working on support for panel data; this will be in the next software release.
      Charles

      Reply

  22. Great web site – Excel is still the spoon and fork available for all and available anywhere. Great functions great quick stats! Hopefully in the future it can also include Monte Carlo Simulations in Excel.

    Reply

  24. Charles,
    I use Real-Statistics when I teach undergraduate and graduate statistics courses, and it’s been very helpful. Thank you.

    My students who use Macs have been having trouble with Real-Statistics for a week or more (perhaps after Apple pushed an OS update?), although it worked for them prior to that. Control + M results in a very long wait (with spinning blue disc). Sometimes Real-Statistics dialog boxes eventually show up, but other times Excel crashes instead. Have other people reported this new problem? (Did today’s version 6.1 fix this problem?)

    Thank you,
    Megan Petra

    Reply

  25. Dr Zaiontz, I hope you are very well, receive a cordial greeting. Dr, please how can you estimate the sample size to apply Kappa by Cohen and / or Kappa by Fleiss?

    Dr Zaiontz, espero se encuentre muy bien, reciba un cordial saludo. Dr, por favor como se puede estimar el tamaño de muestra para aplicar Kappa de Cohen y/o Kappa de Fleiss?

    Reply

  26. Dear Charles,
    In the comparing logistic regression chapter , I noticed I could not run water-only model with the logistic-probit tool box. The error message is ” Input range must have at least many data rows as the column. How can I resolve this problem.

    Thank you.
    Chyke

    Reply

    • Hello Basil,
      Make sure that you have inserted the complete range address in the Input Range field. There are a sufficient number of rows to run the logistic regression tool without getting this error message.
      Charles

      Reply

  27. I am looking at Likert scale responses of 1-5 (strongly disagree to strongly agree) on a questionnaire for one individual only. Is Cronbach’s alpha appropriate or, if not, what do you recommend?

    Reply

  28. Sir Charles
    May I ask if agree, strongly agree, disagree and strongly disagree with only four raters can use Kappa Fleiss Reliability Tes possible t.. for a specific statement in an a researcher made instructional materials. say, agreement and disagreement of validators or would only be ok for Inter Rater % agreement.. Thanks

    Reply

    • Hello Maribel,
      You can use Fleiss[ Kappa for agree, strongly agree, disagree and strongly disagree with four raters, but it won[t take the order of the ratings into account. Better to use a different measurement.
      Charles

      Reply

  29. Hi Sir Charles ,

    Can you help me with my data? My basis for acceptance of likelihood is anchored on the Null Hypothesis, Ho, stated as: There is no significant difference between the travel distance of the 1st recapped and the 2nd recapped tires.

    MY DATA
    1st Recapped 2nd Recapped
    DISTANCE TRAVELLED (km) DISTANCE TRAVELLED (km)
    0.7 0.7
    2 2
    4.1 4.1
    6.8 6.8
    8.3 8.3
    9.9 9.9
    45.1 45.1
    105.2 76.9

    RESULTS OF EXCEL FORMULA FOR T-TEST
    DISTANCE TRAVELLED (km) DISTANCE TRAVELLED (km)
    Mean 23.2 20.04444444
    Variance 1150.5275 659.200277777778
    Observations 9 9
    Pearson Correlation 0.9879788
    Hypothesized Mean Difference 0
    df 8
    t Stat 1.003970846
    P(T<=t) one-tail 0.172394753
    t Critical one-tail 1.859548038
    P(T<=t) two-tail 0.344789505
    t Critical two-tail 2.306004135

    Should I reject my hypothesis?

    Thank you hope you could help me in this.

    Reply

  30. Thank’s for all developed the real Statistics Dr. Charles Zaiontz….this free software help a more students in all point of the word….very thank for you help and congrutulation !

    Reply

  32. Hi Charles,

    If I have compared two independent samples then which P-value I should use for reporting my results?

    For example, Below there are p-1-tail and p-two-tail??

    Variable 1 Variable 2
    Mean 196.6666667 110
    Variance 826.6666667 5480
    Observations 6 6
    Hypothesized Mean Difference 0
    df 6
    t Stat 2.673177394
    P(T<=t) one-tail 0.018434997
    t Critical one-tail 1.943180281
    P(T<=t) two-tail 0.036869994
    t Critical two-tail 2.446911851

    Reply

    • This depends on whether or not you want a one-tailed or two-tailed test. If you know that one direction is impossible or very unlikely, you should choose a one-tailed test. Usually you should choose a two-tailed test. See the following webpage for more details:
      Hypothesis Testing
      Charles

      Reply

  33. Dr. Zaiontz, good morning, I would like to know why the Poisson regression does not work, using the tool, Real Statistics. I do not know if I’m making a mistake, but even the example does not work either, with the tool.

    Dr. Zaiontz, buenos días, quisiera saber por que no funciona la regreson de Poisson, utilizando la herramienta, Real Statistics. No se si estoy comentiendo un error, pero incluso el ejemplo tampoco funciona, con la herramienta.

    Reply

  36. Hi Dr. Charles Zaiontz,

    Firstly I would like to thank you for this site and the dedication that you have put to make statistical techniques more accesible. I teach inferential and correlational techniques at a psychology program in Santa Marta, Colombia and the RealStats add-in and this site have proven fundamental.

    Have you thought about developing the RealStats app for android or IOS?

    Thanks!

    Reply

    • Jorge,
      I have thought about doing this, but I have not taken it any further since I would have to develop a lot more infrastructure that was already available from Excel VBA. I am not knowledgeable about android and IOS, but if I didn’t have to build up a lot of these infrastructure capabilities myself, I would do it.
      Charles

      Reply

  37. Hi Dr. Zaiontz. I just came across your add in, Realstats. Thank you. You must be a mathematical genius! Most of this stuff seems like voodoo to me. alpha, beta, gamma, MSE, MASE, SMMAPE, MAE, RMSE? You must be kidding. I still haven’t figured out what these measurements really are. Mostly confidence or fit values, I know.
    Congratulations on your new app. The breath and scope is simply amazing.
    A couple of questions: Let’s say I run a toll booth. I need to know how many employees I need to staff starting tomorrow, and for the next six days. How many days of historical staffing data would you prefer to start with? And, is there a real way to estimate this? If using time series, what seasonality would you use? 365?
    I read about your upcoming book somewhere on here. I don’t see anything about it. So I take it that it is not ready to be published yet. I will support your work by purchasing your book, whenever it is released. Keep up the great work! Kev, Boston

    Reply

    • Hi Kev,
      Glad that you are getting value from the website.
      Re the toll booth questions: There is no definitive answer for how much data your need; usually the more data the better. This is really a queuing theory issue. You need information about the speed at which the employee handles each driver, the volume of traffic (this may vary from peak to non-peak times), the distribution of traffic demand, wait time targets, etc. If traffic has a weekly pattern (e.g. heavier on weekdays or Fridays, etc.) then seasonality is probably weekly; in addition you may have other spikes (e.g. around Thanksgiving or other holidays). Since this is quite a complicated problem, you probably want to use a simulation model.
      The book keeps getting delayed. I had hope to publish it this month, but I have now found myself, unexpectedly, teaching a course on experimental design, and so I don’t have the time to finish proof-reading the book. I now expect the book to be published at the end of this year.
      Thanks for your support and hi to Boston, where I lived for many happy years.
      Charles

      Reply

  38. Trying to install Real Statistics to use with Excel 2016. Get a compile error hidden file. MS says may be trying to add 32 bit to a 64 bit in VBA code. My computer is a 64 bit.
    Just checking to see if you have any ideas.
    Really like the product and I use frequently.

    Reply

  41. Hi Dr Charles,

    I was running Chi Sq Test using Excel. However, I noted that when I switched my two data sets around (i.e. actual range vs expected range AND vice-versa), I get two different p-value outcomes. How should I reconcile this? My categorical data sets consist of one column from 2017 and one column from 2018. There is no exact F(observed) & F(expected) per se.

    Many thanks.

    Reply

  42. Dr. Zaiontz, muchas gracias por esta página, realmente como siempre lo he manifestado es muy útil y didáctica.
    Dr. Zaiontz, thank you very much for this page, really it is very useful and didactic.
    Dr., please what probability do you have to add in the Cox Regression, the statistics and p-value, of Concordance, R squared, maximum likelihood test, and the test of the logrank ?
    Thank you very much for your attention.

    Dr. por favor que probabilidad hay de agregar en la Regresión Cox, los estadísticos y valor p, de Concordancia, R cuadrado, prueba de máxima verosimilitud, y la prueba de el puntaje logrank ?
    Muchas gracias, por su atención.

    Reply

  43. Hi Charles,

    There is a need for a website specializing in Statistics questions and answers in line with Stackoverflow but specific to statistics. I have lots of questions but no where to go. Hope you can solve this. Considering everybody can contribute to an open website, this glut can be removed.

    thanks

    Reply

  44. Hi Charles,
    I have a dataset that I’ve been analyzing using logistic regression. I get different coefficients when I use Excel 2010 versus Excel 2013, so my predicted probabilities are different. Also, in Excel 2010 I get errors (#DIV/0!) for a number of test statistics (Chi-Sq and Hosmer, for example). What could be happening to cause this?

    Reply

    • That is indeed very strange. I don’t know of any reason why this should happen. Are you using Real Statistics to do the analysis or some other approach?
      Charles

      Reply

  45. Dear Charles,
    I have downloaded the pack but unfortunately I cannot find it in excel. I tried ctrl+m but it does not open something. The same with ctrl+ti. Could you please help me to find it?
    when i go to file that the pack is downloaded and click to open it, it does nothing, too.
    Thank you very much for your help

    Reply

  46. Estimado Charles:

    Muchas gracias por tu gran aporte, el complemento para Excel me ha servido enormemente para la investigación que realizo. Un saludo desde Xalapa, Veracruz, México.

    Dear Carlos:

    Thank you very much for your great contribution, the Excel plugin has served me enormously for the research I do. Greetings from Xalapa, Veracruz, Mexico.

    David Torres

    Reply

  47. Hi Charles,

    Thanks for your helpful posts! I’ve been using a one way anova to look for difference between three groups of results (from a geography project focusing on weathering but that doesn’t matter). I’ve computed it and got good F results, but my P value is appearing as “1.33158270396591E-09”, which doesn’t seem to make very much sense? There is a very large difference between the calculated f and the critical f (calc f is 34.5735871812038 whilst crit f is 3.21994229317612), yet I do not know what the meaning of the capital E within my P value is.

    Could you help?

    Reply

    • Wilson,
      Sure. You can demonstrate and use these functions in your class.
      Many instructors and professors are using Real Statistics in their class.
      Charles

      Reply

  49. Hello Charles,
    The tools you propose are very helpful.
    I’ve just downloaded the pack, and I use it for PCA of analytical data.
    Is there somewhere in the pack some tools to go further the calculations and develop graphical representations of the sample distribution according the different axis generated by the PCA analysis ?
    Thanks a lot!
    Christian

    Reply

      • Thank you Charles.
        Just to refresh my memory : the new coordinates of the observations in the (Axis1, Axis2, …, AxisN) space are calculated by multiplying the matrix of their reduced centered responses by the eigenvectors matrix?
        Thanks again

        Reply

          • Hi Charles
            Let’s consider my observations data matrix [ObsLabel(i), Val1(i), …, Valn(i)]. Using the Factor Analysis function of your pack, I’ve got the eigenvectors of the sub-matrix [Valj(i)] for each axis Axis1, Axis2 and Axis3.
            If I want to plot ObsLabal(i) in a {Axis1, Axis2} graph, I have to calculate the coordinates of each point representing one observation in that 2D space.
            I remember this can be done by multiplying the {eigenvectors coefficients vs Axis} matrix by the matrix of the reduced centered values associated to the observations which are: //Valj(i)// = (Valj(i) – mean of Valj(i))/(standarddeviation Valj(i)).
            Is this calculation correct to generate the observations plot in the Axis1-Axis2 space?
            Thanks

  50. Thank you so much for the amount of effort you have put into creating this site and the supporting excel addin. I really struggle with statistics and you have taken so much of the stress out of it. You have made it clear and concise and give those of us that struggle the support we need.

    Thank you again
    Hannah

    Reply

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