I want to test if there is any difference in two laboratory methods for determining the carbon content in soil. I would calculate the average and standard deviation of the results with both methods (eg. using a ANOVA), but I am unsure how should I design the experiment. For instance, if I would have n=20, should I:
- make 20 x 2 samples from one soil and run both methods on samples from a single soil?
- make 20 x 2 samples from different soils (with varying carbon content) and run both methods on those samples?
ANOVA stands for Analysis of Variance. It is a statistical method used to analyze the differences between the means of two or more groups or treatments. A one-way ANOVA is used when you have three or more categorical, independent groups, but it can be used for just two groups (but an independent-samples t-test is more commonly used for two groups). A two-way ANOVA is used to estimate how the mean of a quantitative variable changes according to the levels of two categorical variables. The sample size should generally be large enough to meet the assumptions of the ANOVA, such as normality and homogeneity of variances. A common rule of thumb is to have at least 20 observations per group in the ANOVA. n=2 is enough for the results to be valid. If your variables do not meet these requirements, then ANOVA may not be the best choice. if you're using multiple different independent variables, a two-way or MANOVA approach might be more useful.
https://byjus.com/anova-formula/
https://www.scribbr.com/statistics/two-way-anova/
https://www.google.com/url?sa=i&url=https%3A%2F%2Fwww.scribbr.com%2Fstatistics%2Ftwo-way-anova%2F&psig=AOvVaw0attvcIV4FbIQc4K6Ln-sl&ust=1704542376297000&source=images&cd=vfe&ved=0CBMQjRxqFwoTCLCosteZxoMDFQAAAAAdAAAAABAE
Have you considered the potential cause(s) of any difference between methods? That should guide your choice of samples.
Much is known about C methods and their biases. Is this an exercise in designing/conducting an experiment or in obtaining new knowledge?
You test n = 30 samples (to fulfil the CLT) of the same soil sample using the two methods, then perform a two sample t test to compare the mean results of the two methods. You have to use the same soil to be able to compare the outcome from the different methods. No ANOVA required :)
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