In this part of the website, we apply the ANOVA methodology of One-way ANOVA and Two-way ANOVA to an extension of the paired samples analysis studied in Paired Sample t-Test. This analysis is called ANOVA with Repeated Measures. Here the rows correspond to subjects or participants in the experiment and the columns represent treatments for each subject. Usually, the treatments represent the same treatment at different time intervals.
Topics
- One within-subjects factor
- Sphericity
- Real Statistics support for one-within factor case
- Two within-subjects factors
- One within-subjects factor and one between-subjects factor
- Two within-subjects factors and one between-subjects factor
- One within-subjects factor and two between-subjects factors
- Analysis using regression
- Friedman test
- Page’s test
- Cochran’s Q Test
References
Howell, D. C. (2010) Statistical methods for psychology (7th ed.). Wadsworth, Cengage Learning.
https://labs.la.utexas.edu/gilden/files/2016/05/Statistics-Text.pdf
Winer, B. J. (1962) Statistical principles in experimental design. McGraw-Hill
https://psycnet.apa.org/record/2008-16855-000
Maxwell, S. E., Delaney, H. D., Kelley, K. (2018) Designing experiments and analyzing data. Routledge.
https://www.routledge.com/Designing-Experiments-and-Analyzing-Data-A-Model-Comparison-Perspective/Maxwell-Delaney-Kelley/p/book/9781138892286
Pls can I use a single factor or double repeated factor ANOVA in Excel to analyse eight
different blood groups in day 1,day 7 day 14, 21, 28, for a particular parameter
Probably, but the specific version depends on the details and the hypothesis (or hypotheses) that you are trying to test.
Charles
i have one query …..in my research study after intervention i have done two post test …..in this which test is good to use repeated measure one way annova or one way annova????
Hi Kiran,
It all depends on what hypothesis you want to test. What kind of data do you have and what hypothesis or hypotheses do you want to test?
Charles
Hey there,
My study is investigating the effect of eye contact and head orientation on the N170 peak.
I have two independent variables (eye contact and head orientation) and one dependent variable (N170 amplitude). All participants contribute to the independent variable. I want to examine the statistical difference between these groups.
head orientation (in degrees)
0 30 60
EC: 22 25 24
NOEC: 25 27
Can I do a test to measure the difference between all these numbers? and then can I just use the EC category and see if head orientation is effected by it? Thank you, Alice
Hi Alice,
I would need more information to answer your question, but the way you display your data, perhaps you are trying to use an ordered chi-square test, but I can’t say for sure.
Charles
I have 10 measured Toluene concentrations from 10 sampling points.
P1-156.4 mg/kg
P2-128.2 mg/kg
P3-1201.45 mg/kg
P4-1125.1 mg/kg
P5-1225.85 mg/kg
P6-879.23 mg/kg
P7-458.8 mg/kg
P8-695.5 mg/kg
P9-205.36 mg/kg
P10-1552.3 mg/kg
The recommended Dutch Intervention Value for Toluene in soils is 130mg/kg
Which statistical test can i use to show whether there is a statistical significance between the measured concentrations and the Dutch Intervention Value?
If the 10 sampling points are independent, then you can conduct a one-sample t test against the value 130 provided the data is reasonably normally distributed (you can use a Shapiro-Wilk test to check this). If the data is not normally distributed, you can use a one-sample Wilcoxon Signed Ranks test. All of these tests are described in the Real Statistics website and supported by the Real Statistics software.
Just looking at the numbers I would be surprised if there wasn’t a significant difference.
Charles
Dear Charles,
ı have three groups of teachers depending on the experience of teaching.
I have 2 scales and they have also some subscales:
1. efficacy scale (student engagement, classroom management and instructional strategies)
2. self-reported proficiency scale (reading, listening, speaking, writing)
ı would like to analyze the relationship betweeen efficacy and proficiency scores in three groups and also analyze whether three groups of teachers differ in their efficacy and proficiency scores (both the subscale scores and totatl scores)
ıf I am not mistaken, ı am going to use repeated meausures design? How am ı going to handle all these analysis?
One repeated measure for efficacy and one for proficiency?
can you help me?
Sorry, but I don’t completely understand the scenario that you are describing. Here are some questions for you:
1. How do you measure efficacy and proficiency? Are these numeric values (e.g. values between 0 and 100)?
2. Why do you think you need to use repeated measures? Is this because each teacher will have two measurements: one for efficacy and one for proficiency?
Assuming that the answers to these questions is yes, then you could use a repeated measures ANOVA with one fixed factor with 3 levels (Teaching Experience) and one repeated measures factor with 2 levels (efficacy and proficiency). Alternatively you can use MANOVA with 3 groups (Teaching Experience) and two dependent variables (efficacy and proficiency).
Charles
Dear Charles,
Thank you for your quick reply.
1. I measure efficacy and proficiency using numeric values.
2. I have 2 questionnaires (efficacy and proficiency). there are subscales of these questionnaires, so the same participants will be tested in different subscales of the questionnaires. this is why I am planning to use one repated measure ANOVA for the subscales of efficacy for three experience groups. ı want to see whether the participants in each experience group differ in their scores for the subscales in efficacy.
I am also planning to use another repated measure ANOVA for the subscales of proficiency for three experience groups. ı want to see whether the participants in each experience group differ in their scores for the subscales in proficiency.
Thank you for your help!
Yes, this does look to be a fit for two separate repeated measures ANOVAs (although MANOVA may be another approach).
Charles
thank you!
Hello,
I was wondering if you could help me think through the appropriate test for an analysis plan. We have subjects from 2 groups (healthy vs. illness) who all received an intervention to four sites during two behavioral conditions (so each subject got all 8 variations of this experimental manipulation 4 sites * 2 behavioral conditions). We measured the response to this intervention in 2 locations (or for one experiment, in 3 locations).
We want to assess if there are differences in this response to intervention based on: (1) group [=2]; (2) intervention type [= 4]; (3) behavioral condition at time of intervention [=2]; and (4) location of response measurement [= 2-3]. For each subject, there are 16-24 measured dependent variables based on these combinations.
For most subjects, there is some missing data (i.e. they got tired before receiving all 8 experimental conditions, which were given in a randomized order). We don’t have a rigorous way of imputing missing data.
Is there a way to do some type of ANOVA that accounts for all of these factors? Or is a mixed effect model necessary?
Thank you for your help!
Fi
Hello there! Your website is very informational and has been a great help to me. Currently, I am trying to perform a statistical analysis on an experiment performed over 5 time points, with three trials per experimental level (in my case it is ampicillin and bacteriophage concentration). In order to perform the repeated measures ANOVA, should I average out the numbers for each time point and perform the ANOVA on that? Or how should I do so? Can this be done on Excel? Thank you!
Jennifer,
Does this mean that you have 15 data elements (5 x 3)? If so you just need to use ANOVA with Repeated Measures without averaging the data.
Charles
Dear Charles,
Thank you for the very informative website, it has been tremendously helpful in my project!
I am looking for the right kind of analysis for my data. I did a pre- and a post-test (questionnaire) in two conditions (two independent samples). I counted the amount of keywords mentioned for each question and would like to compare the numbers. I have up to 14 different keywords I would like to compare.
My table looks like this:
Condition 1 Pre Condition 1 Post Condition 2 Pre Condition 2 Post
Keyword 1
Keyword 2
Keyword 3
…
Am I correct in using a repeated measures ANOVA? Which kind? Do I have to use it for condition 1 first and then separately for condition 2?
Also, is there a feature in the toolkit that draws a graph which compares the two conditions over time?
Any help would be highly appreciated!
Best regards,
Anna
Anna,
Sorry, but I don’t understand the scenario that you are describing. Pre-and post-tests can be performed using repeated measures ANOVA (or sometimes by ANCOVA or MANOVA). If you have two conditions, you may need to use repeated measures ANOVA with both a within subjects factor and a between subjects factor. This is one of the topics on the referenced webpage.
What test to use probably also depends on what hypotheses you want to test.
Usually Excel’s charting capabilities are sufficient.
Charles
Hi Charles,
Thanks for all you work on this website – I regularly use it to solve my problems.
For my current data set, I have scan images for 25 patients. I want to compare 3 different methods of measuring the amount of scar present on each of these scans. (calculated as a persentage, so continuous data).
Each scan has been analysed using each of the 3 methods, so I have 3 sets of data. To compare these methods is the repeated measurements ANOVA appropriate?
If there were 2 methods, I think Bland Altman LOA and bias would be best, but I can not work out what test to use to compare more than 2 methods.
Thanks
Laura,
I am pleased that the website has been useful for you.
If you have a different person measuring each of the 25 patients using three methods, then Repeated Measures ANOVA could be the way to go.
If you have one person measuring all 25 people using three methods, then you would be violating the independence assumption of ANOVA.
Regarding using Bland-Altman with three methods, see the following webpage
https://www.ozgrid.com/forum/forum/help-forums/excel-general/112590-create-bland-altman-type-of-chart-using-three-sets-of-data?t=169138
I have not read it myself, but it may be useful to you.
Charles
Thank you Charles,
I think I may have misunderstood – I thought that in repeated measures ANOVA, in a similar way to the paired T test, the means are not independent?
I have a data set for 50 subjects made up of images. These images can be analysed using 3 different methods to give me the number I need. Am I right to compare these analysis methods using a repeated methods ANOVA?
Louise,
It depends on what hypothesis you want to test. If the each subject analyses all the 3 methods, then repeated measures ANOVA may be the right approach.
Charles
HI Charles,
Thanks for your awesome website! It has helped many people and I refer many of my coworkers to it regularly.
My study is a two bowl preference choice for cats. They are given two food bowls side by side one time per day for 4 days. The cats choose the better tasting food based on how much they consume. Essentially the 4 days is a repeated measure or replication of each of the cats. One every other day the bowl position is switched from left to right to prevent “handedness” in the cats. Meaning if the two foods taste the same, they might only eat from the left or right bowl that they would normally choose first. Normally we would represent the data as an “intake ratio” of one to the other, but can also use the grams of each diet consumed. The industry norm is to use a paired T test, but I want to ensure there are no diet x day interactions. Any suggestions on how to analyze?
Nathan,
Glad you like the website.
You can use ANOVA with Repeated Measures, with the repeated measures factor being Day (with levels 1,2,3,4).
Charles
Hi Charles,
Is it possible to get multiple comparisons for interaction effects on a repeated measures ANOVA on SPSS (it is actually a mixed method ANOVA)? I understand we can compare main effects, but don’t see an option to compare interaction effects. I need point estimates of differences!
Tash,
I don’t use SPSS, but I would certainly think that SPSS would offer this capability. You can do this with Real Statistics.
Charles
Dear Charles
I have a data set which I would like to analyze using an ANOVA two factor within subjects design. I downloaded Real Statistics for Mac along with your example set. I tried to duplicate the analysis you performed on the example data set titled:
Example 1-ANOVA with matched samples – 2 within-subjects factors
I was unable to duplicate your results. I obtained an ANOVA table with “two factor Anova” at the top and Rows labeled: rows, columns,inter ,within, and total. A (Training), A X C (Error), B (Skill), etc were not present. Column labels we’re same as yours except the last column, Which was labeled “sig” instead of F crit. I copied your data to a new worksheet.
After pressing control M, my menu choices were:
1. First menu titled real statistics, Choose analysis of variance
2. Second menu titled Analysis of variance, choose Anova two factors. Two factors repeated measures is not an available choice.
3. Third menu titled two factor Anova.
a) for input range choose all data, Including blank cell at the upper left (12 rows and7 columns)
b) check COM/RO headings included with data
C) alpha 0.05
d) input format Excel
e) Number of rows per sample one
f) output range was several columns to the right of the Data.
Please advise on correct menu choices to duplicate your analysis.
Thanks very much.
Joel
Joel,
The website describes the features in the latest release of the Real Statistics software. The Mac version was released about two years ago, and so some things have changed.
The good news is that i am now working on a new Mac release, which should bring the Mac version up-to-date and also be easier to use.
In the meantime, if you send me an Excel file with your data and results, I will check to see what is happening. You can find my email address at Contact Us.
Charles
Thanks very much Charles. I will send the data file with results.
hello everybody,
my design is quasi-experimental with one independent variable, 2 dependent variables, three groups: experimental 1, experimental 2 and control, and pre-test & post test.
need to run repeated measure ANOVA …. However, I can’t run …. could anyone help me????
Mohammed,
With two dependent variables, perhaps you really want to use MANOVA.
Charles
Hi
I’m hoping you can help, I am trying to analyse some data but am struggling to work out how best to do it.
I have 4 subjects that have 3 measures taken over 4 variables which i then repeated over 4 weeks.
Do I analyse the results in separate weeks or all together
Hi Laura,
It depends on what hypotheses you want to test. In general, you should try to test all together.
Charles
Hi Charles,
Once I performed the repeated measures ANOVA to my data, I got a statistically significant result. What would be the most appropriate post hoc test be to perform on my data? Would it be a Bonferroni test?
Thanks,
Elliot
Hi Charles,
I want to be sure I’m using the appropriate test for a project I am working on and I would appreciate any help you could provide. I THINK Anova with repeated measures is the test I need but I am not sure. My goal is to see if I have impacted lab values within my clinic. I have multiple subjects, each subject has multiple readings for a specific lab value, lets say systolic blood pressure, however, the time period between measurements is not consistent between any of the subjects. I want to compare the blood pressure in the patients before and after I came to the clinic looking at 2 years prior to me coming into the clinic and 2 years after. Thank you for any help!
William,
Based on the the info that you have provided, it sounds like a repeated measures ANOVA fit, except for the fact that the time period between measurements is inconsistent. If you have measurements for 2 years prior and 2 years after then you might be able to use a paired t test.
Charles
Dear Charles
I have one problem.
I need to do Repeated Measurment Anova but in one of my works. But the mail data become out because of missing of my USB flash and now I have only the number of cases, mean and SD of the data in both groups. the levels of measurment are 5 times (0 week and 1-4 weeks after starting the intervention)
Please help me with very thanks
Mohammad,
You will need more data than that. To see what data you need, please look at the examples in the repeated measures ANOVA topic on the webpage
https://real-statistics.com/anova-repeated-measures/
Charles
Hi Charles,
Thanks for the great help! I’m struggling to figure out the correct test to use for my situation. I have 4 audiogram test results from each corresponding to a different date over a five year period. Within each audiogram test is a decibel value for each of the 6 measured frequencies. I’m trying to compare the audiograms to see if they differ in a statistically significant manner. What do you think would be the most appropriate test to use?
Ravi,
I understand that you have 2 factors: a fixed factor representing frequency and a repeated measures factor representing time. You have 4 replications for each combination.
If this characterization is correct, then it seems like you can use a mixed repeated measures ANOVA as described on the following webpage:
https://real-statistics.com/anova-repeated-measures/one-between-subjects-factor-and-one-within-subjects-factor/
Charles
charles,
your ability to field so manyquestions here is really impressive; thank you so much for illuminating all of these anova odds and ends.
…now assuming you’re sufficiently buttered up, i have what might be a doozy for you! haha
i measure cells within animals (i.e. clustered repeated measures) and am trying to check on a genotype difference that’s, obviously, nested (i.e. a fully between subjects factor) and a location difference that’s MOSTLY nested (i.e. i usually only got one location from each animal, but i have data in both locations from a few animals, so mostly between subjects).
the lack of balance is deplorable: some animals gave one cell while others gave forty-something, and the number of animals in each group is uneven as well. (my smallest group has N=3 animals; when i start trying to analyze subsets, it will be even smaller, but that’s a whole ‘nother story…!)
i’m looking primarily for an effect of the interaction.
so (as far as i can tell), the multivariate approach is totally unfit given balance considerations, and i’ve read about approaches like repeated measures ANOVA (but accounting for such unusual sampling and imbalance is questionable in stats programs primarily because i can’t see what they’re doing) or generalized least squares specifying the within group correlation (among repeated cell measurements within a given animal), or mixed effects models treating animal as a random effect, but the plethora of different ways to specify this are crazy!
my main question: does there exist such an ANOVA that can account for such multilevel-unbalanced, semi-crossed, clustered data in a reasonably principled way? if so, what is it?
…and close behind: does more than one exist such that i could get comparable results (e.g. from said ANOVA approach and, say, repeated measures gls or mixed effects models)?
thanks for any input (and please let me know if i’ve been too unclear for you to say one way or another),
b
it might be useful to know: my dependent variable is a continuous measurement from each cell, i.e. it’s not just measuring the # of cells from each animal but the activity of each cell as summed up in one continuously variable metric per cell.
b,
There may be an approach that fits your situation, but none that I have included yet on the website. I plan to add multilevel and more unbalanced models in the future.
Charles
Hey there!
I’m am getting confused when finding the F value. My SSB is 143.44 my SSW is 715.5 and my SSS is 658.3
Any help would be greatly appreciated!
There are 6 participants being measured at 3 different time points
It depends on which ANOVA test you are performing. Probably you want F = SSB/SSW.
Charles
Hi Charles,
Your website is definitely making people’s lives easier!
I have a question and I hope you will be able to give me a hint.
I am experimenting with electrical stimulations on subjects.
Each stimulation has 2 parameters (frequency and pulse), in total I have 12 combinations of frequency/pulse (3 frequencies and 4 pulses).
I have 16 subjects.
Each of the subjects has been stimulated with 36 random stimulations (each combination frequency/pulse has been given to them 3 times).
In order to characterize I thought to use a 3 way repeated measurement ANOVA, do you think is a good idea?
Andrea,
I understand that your fixed factors are Frequency and Pulse and the repeated factor is Time (time 1, time 2 and time 3). You have 16 replications (the subjects). This does seem to fit the profile of a 3-way repeated measures ANOVA. If there is a learning element, then this seems to be an appropriate model. If not, the times are completely interchangeable, and perhaps you can simplify the model by adding (or averaging) the three time measurements to obtain a two factor ANOVA.
Charles
Hi Charles. Thanks again for such a great website!
I have run some experiments comparing 2 groups, control and treatment, monitoring an output for 5 days, thus I believe ANOVA with repeated measures is the right model to analyze my data. I then run an F-test for variance between subjects which turns out statistically significant, so that I do not have common variance. You state that ANOVA is pretty robust to reasonable violations of this assumption, but what it is “reasonable” in this case? What do you suggest to do in this case? I can run more experiments of course, but there is any other way to analyze the data?
You also use the same dataset for two factor multivariate Repeated Measures Analysis with Two Dependent Variables and conclude saying that in this model “All the tests show there is no significant difference between the mean hours of sleep for the three age groups. Interestingly enough this is the opposite conclusion from the univariate test” . My question is how do I choose which one is the most powerful analysis?
Ciao!
Alessandro,
A common variance is an assumption of the ANOVA test, not a conclusion. I significant result from ANOVA is that the means (not the variances) are different. To test the assumption that the variances are equal, you can use Levene’s test. See the following webpage:
Homogeneous Variances
Regarding whether to use the univariate test or MANOVA, some guidelines are given on the following webpage:
Sphericity
This is one of the areas that makes statistics as much art as science. Different tests may yield different conclusions, usually based on different assumptions, which may not be 100% satisfied. Also keep in mind, if one test yields p-value = .049 and the other yields p-value = .051, the formal conclusion will be different, but clearly both tests show a borderline result.
Charles
Hi Charles, thanks for your prompt reply. Yes of course the test of homogeneous variances is an assumption that needs to be tested before to compare means with ANOVA. My question though is, if I run an F-test (with two groups) or a Levene`s test (with more than two), and I do not find equal variances, can I still “trust” the ANOVA results? Or if I cannot do it, what other tests can be run, in the absence of equal variances? Is it simply better to generate more data?
Thanks!
If the variances are not reasonably similar, then you can’t trust the ANOVA results. A rule of thumb is that if the largest variances is more than 3-4 times the smallest variance, then I will be concerned about the accuracy of the ANOVA results. This is only a rule of thumb, sometimes ANOVA can tolerate a larger spread, sometimes it can’t even tolerate this spread. When the assumption fails, you should consider Welch’s ANOVA. If your samples were very small, then generating more data could be helpful in order to better estimate the real (i.e. population) variances. But with reasonable sized samples, generating more data is probably not helpful.
Charles
Hi Charles,
I’m studying the effect on Fv:Fm (photosynthetic efficiency of photosystem II) of a chemical over a period of 5 days.
I have 6 concentrations (including 1 control) and 6 repeats /treatment.
All treatments are continuous over a 5 day period.
Would a repeated measures ANOVA be the correct test?
Thank you in advance for your time
Dan,
This sounds like a fit for repeated measures ANOVA, with the proviso that I am not sure what you mean by “treatments are continuous…”
Charles
hi sir. what test do i use in an experiment wherein there are 3 groups assigned with different doses of a drug with pre- and post-treatment blood glucose levels taken? sample sizes for each group are 6, 6, and 8. thank you in advance!
It sounds like an fit for ANOVA with one fixed factor (dosages) and one repeated measures factor (pre/post). Of course, this depends on what you are trying to test.
Charles
I would like to determine what dose is most effective, sir.
Also, how do I do ANOVA in excel if the sample sizes are not equal?
You don’t need to do anything special for One Factor ANOVA. For Two Factor ANOVA, see the webpage:
Unbalanced Factorial ANOVA
For simple repeated measures ANOVA, by definition, you really can’t have unequal samples. If you do this is simply due to missing data.
Charles
Hi Charles,
I am investigating the number of prey brought home by 26 domestic cats over 4 seasons.
1) Is the repeated-measures ANOVA the correct test to use when comparing the no. of prey brought home between each season?
2) Does Excel 2013 allow you to conduct a repeated-measures ANOVA or is it best to use SPSS?
Thanks for your time,
Elliot
Elliot,
1. If you have the data for the same 26 cats over 4 seasons, then the repeated measures ANOVA looks like a good test to use.
2. As described on the referenced webpage, you can use Excel 2013’s Two Factor ANOVA without Replications to do the One Factor ANOVA with Repeated Measures test, but without accounting for sphericity. You can use the Real Statistics Excel tool to perform the full repeated measures test including sphericity. You can download this tool for free from the website.
Charles
Thank you for your help. Much appreciated.
Dear Charles the example you referenced is repeated with discrete values for the variables of interest, i.e. each variable’s value was taken exclusive of its previous value. But mine is also repeated but with continuous values that are cumulative i.e. the value of the plant heights for the sixth week is cumulative of the previous 5 weeks value, the value for the fifth week is cumulative of the previous 4 weeks and so on
My question:
Should the analysis be on the RATE OF CHANGE OF GROWTH (difference in growth from week to week) or the CUMMULATIVE VALUE OF GROWTH (continuous height values)?
Perhaps, but I don’t know enough about the situation to be able to answer your question definitively.
Charles
Okay, Thanks anyway for your time
I have an experiement of a plant which was randomly assigned to 4 treatment with 9 replication each, the weekly height was taken over six weeks. how do I carry out my anova.
It is done as described on the website. See
https://real-statistics.com/anova-repeated-measures/one-between-subjects-factor-and-one-within-subjects-factor/
There are two factors: one fixed factor for the treatments and one repeated factor for time (weeks).
Charles
Dear Charles,
I have 3 doctors performing the same operation individually . i have the hemoglobin level data for pre and post. How do i compare the results?
Now if i have 1 week after hemoglobin values to go with this like pre, post and 1 week after how do i compare the 3 doctors values?
Please guide me on this.
Sorry, but I don’t understand your questions. Which results do you want to compare?
Charles
Dear Sir Charles,
I have a problem with my data, I have 317 respondents, 3 groups/ treatment (Cow Milk, Blend Milk, Coco Milk), and time period (Baseline, Midline and Endline). I want to see the difference of the time periods to see if there is an effect in weight of children for each group/treatment. My problem is at baseline (before the experiment was conducted) I have 317 respondent measured there weight in kg, at midline some of the respondent had drop out in the experiment. Now I only 158 respondent at midline (middle stage of the experiment) and at endline (final stage) i now only have 111 respondent. Is it valid to use RM ANOVA with unequal sample? or shoul I use list deletion for my data?
I hope you can help me Sir Charles,
Thank you
Marvin
Marvin,
You can us RM ANOVA with unequal samples, but I don’t support this yet.
Right now, the only approach that I support is listwise deletion of samples with missing data.
Charles
Thank you Sir Charles,
One last question sir Charles, can I use mixed model ANOVA with my data?
Marvin,
It depends on what you mean by mixed model ANOVA. If I remember correctly, you have one repeated measures factor (Time) and one fixed factor. In this sense it is a mixed model.
Charles
Dear Dr Charles,
I’m a beginner in statistic and Im not quite sure what design should I used to analyse my data. I hope you can help me figure it out. I took my sample on the upstream and downstream of a river, and I measured the total cell concentration in both samples (without replicates). I repeated this steps monthly for one whole year (12 times). Can I use two-way anova without replication to analyse my data? And if there is significant difference, how can I determined in which month the upstream and downstream are significantly different?
Im really sorry for asking basic questions. I would really appreciate your help.
Sue,
Each month are you taking one sample upstream and one sample downstream? Or more than one sample?
Charles
Each month I take one sample upstream and one sample downstream. I also have another sampling point which is at the outfall, which makes my total sampling point= 3. But for this test, I just want to analyse data from upstream and downstream point. Is it possible to do analysis with only these data?
Fixed factor : Sampling point (2 level: upstream, downstream)
Repeated factor: month (12 level: jan-dec)
Depended variable: total cell concentration
Hi, I’m a little confused as to what to use to analyse my data, and I wonder if you could assist me.
My participants have watched a tv show from three different distances, and I want to see if there is a relationship between engagement and distance. I have 3 means from answers for each participant, but I’m unsure which ANOVA test to run?
Pedro,
If the same participants are watching the tv shows from the three distances then this is ANOVA with repeated measures.
Charles
Dear Charles
I really need some advice about which statistics to use.
I have conducted a study on tumor growth over time in two groups of mice. One group was treated with placebo, one group with a drug. In each group there were 6 mice.
Tumor size (volume) was measured at day 4, 8, 11, 15, 19, 22, 25 and 28.
Do I use a repeated measures ANOVA to finde out, if there is any significant reduction in growth, when mice are treated with the drug.
And can you recommend an online internet-site to d0 these calculations?
Thank you! Ane
Ane,
Assuming that you have assigned the mice to the two groups at random, you can use repeated measures ANOVA of the type explained on the following webpage>
https://real-statistics.com/anova-repeated-measures/one-between-subjects-factor-and-one-within-subjects-factor/
The Real Statistics Resource Pack will do these calculations, which you can download for free. I don’t know of an online site that will do them.
Charles
Thanks for the quick response to my question. It was useful help! Ane
Dear Charles,
My data consists of a. Control (untreated), b. Treatment 1, c. Treatment 2, d. Treatment 3. I measure the bone length at day 0, 4, 7 and 14. I follow the same bones each time I measure the length. The experiment was repeated twice and each experiment had 4 bones per group. I have combined the data of the experiments and included in the sheet.
I basically want to know if the treatment is having any effect as compared to the control and also within the treatment groups (different doses) does it have any effect.
I tried doing One way ANOVA for this and Bonferroni’s Multiple Comparison Test and the result was not significant. When I performed RM ANOVA with Bonferroni’s Multiple Comparison Test, the result is significant.
Please let me know which is the ideal test?
Sowmya
Sowmya,
You have one fixed factor Treatment (with 4 levels). You have repeated measures factor Time (with 4 levels). The dependent variable is bone length. So far this looks like a Repeated Measures ANOVA of the type shown on the following webpage
https://real-statistics.com/anova-repeated-measures/one-between-subjects-factor-and-one-within-subjects-factor/
There are three things that are not clear to me:
1. You mention that you want to understand the effect of different dosages. Do the treatment reflect the different dosages or is Dosage yet another fixed factor? If the latter, this makes the design more complicated.
2. What do you mean that the experiment was repeated twice? Was it repeated on the same bones or different bones?
3. When you say that there are 4 bones per group, are these the same type of bone selected from 4 different individuals or are these 4 bones from the same individual? In the section case another factor, namely Bones, may be necessary.
Charles
Thanks a lot for the prompt response!
To clarify:
1. Yes, treatment reflects different doses. Each group has different dosages (like group 1 – 90mJ, group 2 – 120mJ, group 3 – 180mJ). So does the treatment (different doses) affect the bone length is what I would like to know?
2. I had done one set of experiment on the bones, monitored their lengths individually at different time point. And the same experiment was repeated on another set of bones on another day (another animal). Therefore it’s is n=2. For the purpose of statistics, I averaged the values from set one and set two and then did the statistics to be able to get individual error bar at different time points.
3. Yes, it is 4 bones per group from the same individual.
Is RM ANOVA, a suitable for this experimental design?
Thanks
Sowmya
It does seem like repeated ANOVA is the correct test. The sample is quite small and so I would expect that the power of the test would be quite low.
Charles
Hello,
I have three treatments with six individuals in each treatment. I have collected mass and length data for each individual for a five year period. I would like to see if the treatments have had an impact on growth. I was told that an RM ANOVA was required and I wanted to ask if this is correct.
Thank you!
Katie
Katie,
This is correct provided you can use the mass and length data to create a combined statistic for growth. Otherwise you need to use Repeated Measures MANOVA.
Charles
Dear Charles,
I am doing a quasi experimental research with three therapies. A,B, C. In this there are three groups of 10 each who will be given three treatments such as: group 1-treatment A, group2- treatment A-B, group 3- treatment A-C. There is a control group as well with other routine remedies. What statistical analysis I can use to identify intervention impact.
Note: treatment -A is common for the three groups.
Dear Panniker,
It sounds like a one-way fixed factor ANOVA.
Charles
Dear, Experts!
I have a little problem with my statistical analysis for Master’s work. In my experiment, I am observing changes in composite material radiation attenuation after material repeated use. So, I have 6 samples: three of them are 3mm thick structured with particle sizes 50nm, 500nm and 5um; and three of them are 7mm thick structured similar as first. Radiation attenuation changes are observed on 5 electron energies: 6, 9, 12, 16 and 20MeV. The measurements were performed four times: first time – material mixed with US method and other 3 times after hand mixing – the transmission factor was measured. I wanted to perform N-way ANOVA test in SPSS to understand are there any relations between these factors and is there any impact on transmission factor changes. I used General Linear Model->Repeated Measures. Defined 4 repeated levels – four transmission factor measurement and then, “Between Subject Factor(s) ” are energy, particle size and thickness. But when I get output, there are no calculated F values or significance levels and the following message is displayed: Box’s Test of Equality of Covariance Matrices is not computed because there are fewer than two nonsingular cell covariance matrices.
What is wrong with my SPSS?
Best wishes,
Sandra
Sorry Sandra, but I don’t use SPSS.
Charles
If I am doing multiple trials, do the trials correspond to the rows (subjects) and the various treatments for the columns? Ex: Testing drift on a sensor with multiple pressures over time and repeating 3 times
Zoey,
If in your example, the treatments are multiple pressures over time, then the answer is yes.
Charles
i want to apply statistical tool in which i have 8 treatment groups and five animals in each group and 3 time i have to collect data which statistical tool will fit on my data
If I understand your scenario correctly, you can use mixed ANOVA with one fixed factor (treatment) and one repeated measures factor (time).
Charles
Hi Charles
I have data for pre test post test 1(30minutes) post test 2 (60minutez).I have three scale.
I want to find the mean and difference within the group.how can I finf
You can use the Excel function AVERAGE to find the mean. When you say “difference within the group”, do you mean the difference from the mean? This is x – m where x is a data point and m is the mean.
Charles
Sorry it should be difference within intervention
Hi Dr. Charles,
My name is Hung Bui and doing experiment with chemicals to inhibit the hatching of nematode eggs.
My experiment was conducted with 5 chemicals with 4 reps. Each rep contains 100 eggs soaked in chemical. I collected number of hatched nematodes in each rep/day. I did a repeated measures ANOVA and I wonder this is a good statistical analysis?
Please give me more advice.
Thanks
Dear Charles,
I have two groups of test subjects who both did a certain test 6 times. Group 1 had extra help in the 4 of the tests and the other group had no help at all. The first and last test for group 1 were without help. I cannot figure which ANOVA analysis to apply, none of the examples seem to have different people in 2 groups.
Any help would be greatly appreciated, thanks for your great website 🙂
I don’t completely understand your question. What hypothesis are you trying to test?
You can use ordinary ANOVA, i.e. ANOVA with independent groups (not ANOVA with repeated measures) if you have different people in the two groups, but I am not sure this fits with the problem you are trying to solve.
Charles
The idea is that the first test administered to both groups is a “zero” test without help. The last test is a control test without help. test 2-5 are different between the 2 groups as one has help and one does not.
The hypothesis is: What is the effect of added help on training in these subjects.
The training is caused by them repeating the test 6 times.
As I understand the problem, you have two factors. Factor A contains two levels, representing the two groups of subjects. These groups are independent. Factor B represents the tests given to the two groups. This factor has 6 levels, and the factor contains repeated measures since the same subjects take all 6 tests. Under this interpretation, you would use a two factor mixed model ANOVA.
This is the model described on the webpage
https://real-statistics.com/anova-repeated-measures/one-between-subjects-factor-and-one-within-subjects-factor/
Let me know whether this captures what you are trying to model.
Charles
Ah! That makes sense! Thanks a lot for your detailed site and answer to my question.
While working I discovered a possible mistake in the repeated measures:mixed ANOVA plugin for excel.
The F crit value calculated between subjects; rows has is currently calculated by taking FINV(alpha,df(rows),MS(rows)) I think the correct way would be FINV(alpha,df(rows),error(rows)) .
Hope this helps you.
Luc
Luc,
This mistake was corrected in the latest release of the software (Rel 4.3), and so you just need to upgrade to the newest release.
In any case, thanks very much for informing me of the error. This helps make the software better for everyone.
Charles
Dear Dr. Charles,
I would appreciate if you help me to do stability analysis of multi year data, of plant breeding. I am using crop stat 7.2, i did the analysis but interpretation of the results is difficult, as you know.
with best regards
Manoj
Manoj,
Sorry, but I am not familiar with CropStat. I can help you with the Real Statistics software, but not a tool that I have never used.
Charles
Is it possible to do multiple comparison following repeated measures ANOVA with your tool?
Thanks,
Yi
Yes, multiple comparisons for repeated measures ANOVA is supported. See the webpage https://real-statistics.com/anova-repeated-measures/one-within-subjects-factor/.
Charles
Regarding the comment above left by Brijesh, I am using ANOVA with matched samples – 1 within-subjects factor and 1 between-subjects factor to compare contaminants in fish from three locations over time. I catch varying numbers of fish from these three locations once per year. The fish are sacrificed to yield a mean contaminant concentration for each location for each year. My sample size varies. Am I using the wrong approach to analyze this data set?. Thanks for providing this excellent resource.
Ed,
If the fixed factor is Location and the repeated factor is Contaminant then you are using the correct test (assuming that each fish is measured for the various contaminants).
Charles
I have run the repeated measures anova with contrast (which I believe is the post-hoc function), however this function results in Zeros in the ‘diff’ column and a subsequent mean of zero – therefore the contrast does not yield a result.
Is there something wrong with my method?
Hello Charles,
will “ANOVA with Repeated Measures” work correctly for unequal sample sizes of different groups? Is it possible to incorporated unequal group-size in SPSS also?
Thanks
Brijesh
Brijesh,
For repeated measure designs, generally the same subject is measured multiple times (these are the groups). Thus unequal group size can only mean that some of the data is missing, in which case you need to handle missing data as described elsewhere on the website; see especially .
The situation for ordinary ANOVA is quite different. Here unequal group size normally doesn’t mean missing data but simply that the samples for each of groups may have different sizes.
Charles
So, just to clarify, am I correct in understanding that the most recent version of Real Statistics can carry out mixed-model ANOVAs? And if so, is it capable of does do in combination with Excel 2007?
One more question (as a long-term SPSS user), is there a(n easy) way to get Excel to read my SPSS files?
Thanks for your trouble, Rory
Rory,
You are correct. The latest release of the Real Statistics Resource Pack handles two factor ANOVA with two fixed factors, two random factors or one fixed and one random factor (mixed). These are available for use with Excel 2007, 2010 and 2013.
I don’t know of any way for Excel to read SPSS files, but there is a way around this. If you have a copy of SPSS, it should be able to output data in Excel format. If you don’t have access to SPSS, you can use PSPP, which is a free, open-source (limited) version of SPSS. It can read SPSS files and then output the data in Excel format (using a procedure that works, although it is more complicated than it should be). The procedure for doing this is described at http://lists.gnu.org/archive/html/pspp-users/2011-11/msg00033.html
Charles
Charles, Thank you for your clear and helpful response. After searching high and low for an alternative to SPSS, it seems that I have finally found one. I only occasionally need to run such tests, and with the IBM/SPSS prices now somewhere in the stratosphere, finding your website is a godsend. All the best, Rory
Charles:
The new version of Real Statistics has disabled the option “Two factor Repeated Measures Anova”: when I click that option and press OK button, the macro doesn’t run. All the rest of options seems OK.
William.
William,
Thanks for catching this. The “Two factor Repeated Measures Anova” option should have been removed (it was originally on the main menu only for testing purposes). This capability is assessible, however, from the “Analysis of Variance” data analysis tool using the “Repeated Measures Anova – mixed” tool.
Charles
I have done a repeated measures Anova using this software but I cannot get the interaction between the subjects and groups in the Anova table. I am wondering is it possible to calculate the interaction between both using the software? I would also like to thank you for this excellent resource.
David.
David,
Currently the only form of ANOVA with Repeated Measures that is supported in the software is as described in https://real-statistics.com/anova-repeated-measures/one-within-subjects-factor/. Other forms are described on the website and Excel worksheets that implement these forms are provided in the Workbook Examples file which is available for free download. I plan to add other forms to the Real Statistics software later this year.
Charles
Is the p value provided by excel in the ANOVA single factor (and other ANOVA’s) a 1 or two tailed p value?? SPSS historically only provides the two tail p value with instructions to divide in two if you wanted the 1 tail value.
thanks in advance
matt G
Matt,
Excel’s single factor ANOVA test calculates the p-value based on a one-tailed F-test. The resulting p-value is the same as the output from SPSS, at least based on all the ANOVA examples I have tested in the past. Despite the use of a one-tailed F-test I have often seen this referred to as a two-tailed Anova test.
Charles