# Unequal, independent repeated measures analysis

I have an agricultural ditch that was converted to a different geometry in 2002. I have one year of measured cross-section data on the ditch before construction. I have 3 years of measured cross-section data after construction (multiple columns arranged by year).

For each year, data were measured every 100 feet along the ditch, but neither the starting point nor length of ditch surveyed are the same in each year. For example, year 0 might have 18 measurements, year 1 20 measurements, year 2 19 measurements. Likewise, measurements taken at station 2+00 in year 1 did not occur at the same location as measurements taken at 2+00 in year 2 or 3. Therefore, I have an unequal set of samples that must be treated independently. Data for each year are both parametric and nonparametric.

I want to know if there is a significant difference in the measurements taken within each year (i.e., what is the within site variation) and I want to know if the cross-sections are changing significantly between years (i.e., is the ditch getting wider or deeper). I also want to know between which years are the significant changes occurring (multiple comparisons?).

I have tried One Way Repeated Measures ANOVA with post hoc multiple comparisons in Systat and in Sigma Plot. Both programs treat the data as dependent samples (i.e., if I shuffle the data within a given year, I get a different statistical result). Any suggestions for how to handle this type of data and analysis?

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## 2 Answers

It sounds like you want one-way ANOVA with multiple comparisons. Not with repeated measures, that is. But make sure you read up on it to understand what you're doing.

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Thanks for the response. I'll investigate a little further. I hope your answer is correct so I don't have to purchase any more stats packages! –  Jessica Dec 5 '12 at 16:08

I disagree with your assessment: It sounds like repeated measures design with missing data. I wonder if the Skillings-Mack test (a nonparametric analog to repeated measures ANOVA, like the Friedman test but supporting inference for missing data) would be appropriate?

There are packages in R (http://cran.r-project.org/web/packages/Skillings.Mack/index.html) and Stata (net describe st0167, from(http://www.stata-journal.com/software/sj9-2))

Skillings JH, Mack GA. (1981) On the Use of a Friedman-Type Statistic in Balanced and Unbalanced Block Designs. Technometrics. 23(2):171–177.

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