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Poweranalys: bestämmelse av urvalsstorlek genom linjära mixade modeller och ANOVA
Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
2018 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Power analysis : sample size determination through linear mixed models and mixed-design ANOVA (English)
Abstract [en]

In research where experiments on humans and animals is performed, it is in advance important to determine how many observations that is needed in a study to detect any effects in groups and to save time and costs. This could be examined by power analysis, in order to determine a sample size which is enough to detect any effects in a study, a so called “power”. Power is the probability to reject the null hypothesis when the null hypothesis is false.

Mälardalen University and the Caroline Institute have in cooperation, formed a study (The Climate Friendly and Ecological Food on Microbiota) based on individual’s dietary intake. Every single individual have been assigned to a specific diet during 8 weeks, with the purpose to examine whether emissions of carbon dioxide, CO2, differs reliant to the specific diet each individuals follows. There are two groups, one treatment and one control group. Individuals assigned to the treatment group are supposed to follow a climatarian diet while the individuals in the control group follows a conventional diet. Each individual have been followed up during 8 weeks in total, with three different measurements occasions, 4 weeks apart. The different measurements are Baseline assessment, Midline assessment and End assessment.

In the CLEAR-study there are a total of 18 individuals, with 9 individuals in each group. The amount of individuals are not enough to reach any statistical significance in a test and therefore the sample size shall be examined through power analysis. In terms of, data, every individual have three different measurements occasions that needs to be modeled through mixed-design ANOVA and linear mixed models. These two methods takes into account, each individual’s different measurements. The models which describes data are applied in the computations of sample sizes and power. All the analysis are done in the programming language R with means and standard deviations from the study and the models as a base.

Sample sizes and power have been computed for two different linear mixed models and one ANOVA model. The linear mixed models required less individuals than ANOVA in terms of a desired power of 80 percent. 24 individuals in total were required by the linear mixed model that had the factors group, time, id and the covariate sex. 42 individuals were required by ANOVA that includes the variables id, group and time.

Abstract [sv]

Inom forskning där försök, dels utförs på människor och djur, vill man försäkra sig om en lämplig urvalsstorlek för att spara tid och kostnad samtidigt som en önskad statistisk styrka uppnås.

Mälardalens högskola och Karolinska institutet har gjort en pilotstudie (CLEAR) som undersöker människors koldioxidutsläpp i förhållande till kosthållning. Varje individ i studien har fått riktlinjer om att antingen följa en klimatvänlig- eller en konventionell kosthållning i totalt 8 veckor. Individerna följs upp med 4 veckors mellanrum, vilket har resulterat i tre mättillfällen, inklusive en baslinjemätning. I CLEAR-studien finns variabler om individernas kön, ålder, kosthållning samt intag av makro- och mikronäringsämnen. Nio individer i respektive grupp finns, där grupperna är klimat- och kontrollgruppen.

Totala antalet individer i pilotstudien är för få för att erhålla statistisk signifikans vid statistiska tester och därför bör urvalsstorleken undersökas genom att göra styrkeberäkningar. Styrkan som beräknas är sannolikheten att förkasta nollhypotesen när den är falsk. För att kunna beräkna urvalsstorlekar måste modeller skapas utifrån strukturen på data, vilket kommer att göras med metoderna mixed-design ANOVA och linjära mixade modeller. Metoderna tar hänsyn till att varje individ har fler än en mätning. Modellerna som beskriver data tillämpas i beräkningarna av styrka. Urvalsstorlekarna och styrkan som beräknats är simuleringsbaserad och har analyserats i programspråket R med modellerna och värden från pilotstudien som grund.

Styrka och urvalsstorlekar har beräknats för två linjära mixade modeller och en ANOVA. De linjära mixade modellerna kräver färre individer än ANOVA för en önskad styrka på 80 procent. Av de linjära mixade modellerna som krävde minst individer behövdes totalt 24 individer medan mixed design-ANOVA krävde 42 individer totalt.  

Place, publisher, year, edition, pages
2018. , p. 38
Keywords [en]
Statistics, Power analysis, ANOVA, Mixed models
Keywords [sv]
Statistik, Poweranalys, ANOVA, Variansanalys, Mixade modeller
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-149026ISRN: LIU-IDA/STAT-G--18/003--SEOAI: oai:DiVA.org:liu-149026DiVA, id: diva2:1223571
External cooperation
Mälardalens högskola; Karolinska Institutet
Subject / course
Statistics
Supervisors
Examiners
Available from: 2018-06-28 Created: 2018-06-25 Last updated: 2018-06-28Bibliographically approved

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