Yes it will work very well. ANOVA works with the mean and thus, does not bother whether samples are equal or not. Care must however be taken when coding the data to avoid the presence of outliers.

Yes it will work very well. ANOVA works with the mean and thus, does not bother whether samples are equal or not. Care must however be taken when coding the data to avoid the presence of outliers.

It may depend on the math formulae that you'd be using in Excel to do the calculations. See:

https://www.theanalysisfactor.com/when-unequal-sample-sizes-are-and-are-not-a-problem-in-anova/

and maybe the following for some additional discussion.

https://www.researchgate.net/post/What_does_one_do_while_doing_one_way_ANOVA_with_unequal_sample_size

And, for some more depth:

http://onlinestatbook.com/2/analysis_of_variance/unequal.html

You might consider learning to use R for these types of analyses. It's free, and you can even run it online without installing anything. It's not too difficult to use if you find good examples to follow, but the trouble is that most examples you find around are difficult to grasp for a new user. If you go this route, use car:Anova to use the type-II or type-III sum of squares.

yes, ofcourse you can.

Thanks for the advice.

In such case, perhaps I am laying out my data incorrectly in Excel. I would be grateful for any advice. When I try and run ANOVA in excel with 2 samples of different sizes, I get an error message about non-numeric data (would that be the blank cells?)

@valentine how would you recommend I remedy this?

It seems that your data is/might be a case of two crossed factor anova : first factor : school A ob B, second factor : condition local/non local . Do I understand well your problem ?

If I am correct, treating the data as a one factor anova will resume to a composite test where you are testing the combination of effects of school, condition and their interaction, being unable to separate them.

Hi there,

Jean Maccario It seems that I cannot run 2-factor ANOVA as both types require sample size being the same / cant have empty cells as the error message says 'can't have non-numeric data'.

I can run one-way anova testing using the following categories:

School A Local vs School B local

School A Local vs School A non-local

School A non-local vs School B non-local

School B local vs School B non-local

My personal issue is that, really, I have 2 independent variables (school and nationality, but have been blended into 1) and 1 dependent variable (self-perception attribute score), but do not want to 'throw away' potentially valuable data to reduce the sample size to make the samples even to then do the 2-way.

Any solutions would be welcome...or maybe I have found the solution by following the above.

Any advice would be graciously received,

JIm

Activate the data analysis add-in in excel.

To do this, follow the steps below:

Click on File tab,

hover to "options" and click

In the left pane, click on "add-ins",

Then click "Go" at the bottom centre of the right pane.

you will see various add-ins

check the Analysis tool pack to activate it,

Click ok, relaunch excel

Goto data tab, you will data analysis at the top right corner.

you can perform several analyses from there including one-way or Two-ways ANOVA

1 - in theory anova with 1 or 2 factors do not necessitate equal numbers of observations in every sample/cell of the table - in Excel and some low grade statistical software this is/may be neglected;

2 - splitting your problem is not something I would advice, it is often (if not very often) better to treat it globally ;

Here you may ask three questions (even if they are not all interesting for you)

a) is there a difference between school A and B

b) is there a difference between local and non local

c) is the (possible) difference between school A and B the same for local and non local (also called an interaction between factors) ;

3 - if you don't know how to manage with R give us some data (potentially fake data mimetic of your problem) and someone, including but not necessarily me, will give you a hand.

Why don't you try it in R software ?? It so easy and fast. You first run anova test, if there is significant difference, you perform the Turkey-Kramer post hoc using the package DTK.

Hi Jim. I would avoid using Excel for any semi-serious statistical analysis. To see why, try a Google search on terms such as . Here's one of the hits you should get:

http://biostat.mc.vanderbilt.edu/wiki/pub/Main/TheresaScott/StatsInExcel.TAScott.slides.pdf

If this is a one-time (or infrequent) problem, one relatively easy way you can obtain a two-way ANOVA is via JASP (see the link below). It is a free GUI-based stats package. As it says on the website, "JASP is an open-source project supported by the University of Amsterdam." It runs R-code in the background. (In case someone is wondering, there is no straightforward way to extract the R code in the current version.) It can read several file formats, including CSV. The default setting is Type III sums of squares (i.e., the type often recommended for unbalanced designs), but it also has Type I and Type II sums of squares. I just tried it with a small dataset I used in my notes on unbalanced two-way ANOVA, and it returns the same results I get via SPSS. HTH.

https://jasp-stats.org/

SPSS has a free 2 week trial.... have you tried that?

Here's step by step videos on how to do SPSS from a class I took. (follows Jean Pallant's SPSS survival manual, using SPSS version 23 and 24. Hope this helps.

Chapter 6 - Descriptive Statistics - https://drive.google.com/open?id=0B-jxQv7MUmfZVlhGZXlERUNWSzA

Chapter 7 - Graphs - https://drive.google.com/open?id=0B-jxQv7MUmfZdU05ekJGVnoxMGs

Chapter 8 - Manipulating Data - https://drive.google.com/open?id=0B-jxQv7MUmfZYUNURVlNdjJ5aUk

Chapter 9 - Reliability - https://drive.google.com/open?id=0B-jxQv7MUmfZVHFraC1kTVItTlU

Chapter 11 - Correlation - https://drive.google.com/open?id=0B-jxQv7MUmfZdnNxd0xiYlpwUDQ

Chapter 12 - Partial Correlation - https://drive.google.com/open?id=0B-jxQv7MUmfZc0x3NnFGZHFGWXc

Chapter 13 - Multiple Regression - https://drive.google.com/open?id=0B-jxQv7MUmfZV0QtbEZtQWVkMXc

Chapter 14 - Logistic Regression - https://drive.google.com/open?id=0B-jxQv7MUmfZU240eXJsVjRrR1k

Chapter 15 - Factor Analysis - https://drive.google.com/open?id=0B-jxQv7MUmfZYWFSRVFtRVd0QzQ

Chapter 16 - Non-parametric Statistics Part 1 - https://drive.google.com/open?id=0B-jxQv7MUmfZeVRSSTAyQXhWMzA

Chapter 16- Non-parametric Stats Part 2 - https://drive.google.com/open?id=0B-jxQv7MUmfZR1JkbTZ5dzYzVk0

Chapter 17 - t-test - https://drive.google.com/open?id=0B-jxQv7MUmfZTDBkX2Qya0xsUTA

Chapter 17 - Independent t-test - https://drive.google.com/open?id=0B-jxQv7MUmfZXzlJSlpLYlJnNmM

Chapter 18 - One-way ANOVA - https://drive.google.com/open?id=0B-jxQv7MUmfZRkNTemVtNjM2NVE

Chapter 19 - Two-way between groups ANOVA - https://drive.google.com/open?id=0B-jxQv7MUmfZbVZya0lZREVNYmc

Chapter 20 - Mixed between-within ANOVA –

https://drive.google.com/open?id=0B-jxQv7MUmfZcVBmX0NmQm1rVVU

Chapter 21 - MANOVA –

https://drive.google.com/open?id=0B-jxQv7MUmfZZ19GUmxPUWJSQkU

Chapter 22 - ANCOVA - https://drive.google.com/open?id=0B-jxQv7MUmfZZVlzTDFwU09QUk0

Chapter 4 – SPSS Codebook - https://drive.google.com/open?id=0B-jxQv7MUmfZTE1Qc21pQnpJWms

Jim Schofield , it sounds like the underlying issue is trying to use Excel for this type of analysis. Bruce Weaver mentioned JASP, which is free and relatively easy to use. I tend to like jamovi better. I'll check out each in the case of two-way anova and report back if I have any further observations. Any software will have a bit of a learning curve, but I suspect very quickly (e.g. 5 minutes!) it will be easier than using Excel....

ADDED MATERIAL: Jamovi is really nice for anova, with nice-looking output, effect size statistics, q-q plots of residuals, post-hoc analysis including a plot of marginal means and confidence intervals, choice of type of sum of squares. Easy-peasy.... JASP is very similar in its operation, with some different options. It didn't have the effect size statistics or the marginal means, but it did have some other options like Welch anova for one-way anova and traditional post-hoc tests.

Salvatore S. Mangiafico, thanks for the heads-up re Jamovi. Sometimes I need free software user-friendly software for students who do not have access to packages like SPSS, Stata, etc., so I'll check it out. I like that it appears to allow one to extract/view the underlying R-code.

Cheers,

Bruce

https://www.jamovi.org/

Here's another discussion about JASP vs Jamovi. (I see that Salvatore S. Mangiafico posted to that one too.)

• https://www.researchgate.net/post/Has_anyone_used_JASP_and_Jamovi

Thanks very much for all your advice

You can try GraphRobot (www.graphrobot.com), a free smart web app that can make publication quality plots. It supports ANOVA with unequal sample sizes. It can automatically select the appropriate statistical analysis for your data, and automatically add significance asterisks to the plot if it detects statistical significance in your data.