Gasha Technical Institute
Started 2nd Aug, 2023
How are orthogonal contrasts selected in case of unequal sample sizes?
I did not find a mathematical formula to find or through which we can determine or choose the correspondences in the case of unequal sample sizes
All replies (2)
When dealing with unequal sample sizes in statistics, you can consider using methods like pooled variance, weighted means, bootstrapping, Bayesian approaches, non-parametric tests, or meta-analysis to handle the disparities effectively. The choice depends on the nature of your data and the specific analysis you want to perform.
The answer depends on whether your intention in a contrast is to treat means as having equal import regardless of group size (n), which is the unweighted means approach, or to weight means relative to their sample size, which of course, is a weighted means approach.
For an unweighted means approach, two contrasts are orthogonal if the sum of coefficient product terms, across groups, equals zero: e.g., c11c21 + c12c22 + ... + c1kc2k = 0 (where cij is the coefficient used for the i-th contrast and j-th group).
For a weighted means approach, two contrasts are orthogonal if: n1c11c21 + n2c12c22 + ... + nkc1kc2k = 0 (where cij is defined as above and nj is the sample size for group j).
In many experimental designs, the usual intention of behind a contrast is to compare means as having equal import regardless of group size. Therefore (using cij and nj as defined above):
SS(contrast i) = (ci1*M1 + ci2M2 + ... + cikMk)^2 / (ci1^2/n1 + ci2^2/n2 + ... + cik^2/nk) (where Mj is the mean for group j)
Here's a link that walks through a worked example: https://www.uvm.edu/~statdhtx/StatPages/Unequal-ns/Unequal_n's_contrasts.html
Finally, B. J. Winer's 1971 text, Statistical principles in experimental design (2nd ed.). also addresses the issue.
Good luck with your work.
Top contributors to discussions in this field
Similar questions and discussions
Sample size calculation for a post hoc pilot study?
- Carla Amado
Does anyone have a recommendation to carry out a post hoc sample size?
The data I used I also used two microscopes same brand, but 1 has a higher resolution, I ensured this was spread throughout my data. I also normalised the control averaged to all my data to mitigate any differences of using diff microscopes & to determine the normal condition data, which is the control group. I know there's a slight difference in variance due to this, which I plan to discuss. But wanted to still conduct the sample size needed.
I have collected some data, but most of it is not significant. I have a low sample size and would like to find a rough sample size needed for the assumption of p>0.05 and perhaps a low SEM for a future study of large-scale quantitative data.
I have used G*power software to find out the effect size d= value with this, I used to determine the (1-beta) power I know that anything less than 0.80 is termed very low if you set it as 80%. My (1-beta) power values are also lower than 0.80, meaning this study has low power.
I now want to determine how to calculate sample size with this information for a larger study. Does anyone have any tips on how to do it or any software I could use OR formulas with the variables I have given?
Thank you :) !!
Is the Conditional Inference Tree a suitable statistical method for analyzing Likert scale-type responses and multiple-choice questions??
- Pelden Nima
Inquiry on Conditional Inference Tree to assess the knowledge and attitude in conservation science
What does significant interaction plot and non-significant statistics mean?
- Duygu Gulseren
I ran a 2x2 ANOVA. My interaction plots show full reversal (i.e., perfectly X-shaped plot) but statistics are non-significant. Am I missing anything?
What package do you use for meta analysis in R?
- Gautam Maddineni
I was recently trying to figure out R vs. Revman for meta-analysis. Revman as a beginner, looked easy and user-friendly. But on the contrary to that, I have been reading R gives you much more flexibility. If I had to use R, which package should I use for metanalysis?
What should be my sample size?
- Sudarshan S.
I am a Research Scholar from INDIA. Doing my research in Human Resource Management.
I am currently working on a research about the Manager's Emotional Intelligence influences the Service employee's performance. Where;
Manager's Emotional Intelligence (MEI) - 1 Dependent Variable - Qualitative Interview and Quantitative Survey
The MEI is measured from:
Qualitative Interviews from Managers and Perception Based Survey from the service employees about MEI. (Data Triangulation)
Service Employee's Performance (SEP) - 7 Independent Variables - Quantitative Survey
The SEP is measured from:
7 Variables of SEP from Customers as a Quantitative Survey.
Could someone help me out?
SPSS repeated measures ANOVA: How to compare individual measurements between treatments?
- Isa Hallman
I am conducting analysis on my data and have mostly already figured it out. However, there is still one problem I haven't been able to master.
Statistical program: SPSS 29.0
Cross-over study design with NINE (9) subjects and TWO (2) treatments:
Subjects were given treatment 1 or 2 on two separate study dates. At the end of the study all subjects had received both treatments.
After administering the treatments, the patients were monitored for blood parameter changes on NINE (9) separate measuring time points.
What I aim to do, is to compare the two different treatments and have used RM analysis to do so. Initially I defined Treatment(2) and Time(9) as Within-subject-factors and have been able to gain an answer to most of my questions.
But what I haven't understood yet is how can I compare individual measured time points (for example treatment 1 blood parameter at 30 mins compared to treatment 2 blood parameter value at 30 min) between the treatments through the RM ANOVA - to my knowledge and understanding, the output does not provide this and I haven't been able to figure out how to get it out of the analysis? Or can I? Or do I have to go about it with a different analysis completely?
Best Regards, Isa
ANOVAs: is post-hoc testing always required?
- Sarah Corthorne
I'm hoping to get some advice for my thesis research. I am running an RCT and due to having a large number of outcome measures (18 in total), I have conducted 18 4 (time: T1-T4) x 2 (group: intervention vs. control) mixed ANOVAs. For those with significant interactions, I am now thinking about the best approach to use for follow-up analyses.
Due to the vast number of comparisons that would be needed for post-hoc testing, there is a high risk of Type 1 error, and the required bonferroni correction would lead to a high risk of Type 2 error. It has therefore been suggested to me by an academic colleague that I could choose to not carry out post-hoc tests and, instead of looking at measures of statistical significance, focus on measures of effect size to interpret my results. This is not an approach I am familiar with and I have not yet been able to find examples of this in the literature.
I wondered whether anyone is aware of research where post-hoc testing has not been carried out in studies of this nature? Would be helpful to hear views on whether this could be an acceptable approach to analysis in this context or whether it would be frowned upon!
Thank you in advance.
A practical and relatively simple method of measuring correlation functions is presented. The method, which is applicable to all orders of correlation functions, is based upon orthogonal expansions. The application of this method to the experimental determination of a second-order crosscorrelation function is discussed in detail and some experiment...
Let S be a simply connected orthogonal polygon in the plane, and let n be fixed, n≥ 1. If every two points of S are visible via staircase n-paths from a common point of S, then S is starshaped via staircase (n+1)-paths. Moreover, the associated staircase (n+1)-kernel is staircase (n+1)-convex. The number two is best possible, and the number n+1 is...