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I have data from 3 groups of algae biomass ($A$, $B$, $C$) which contain unequal sample sizes ($n_A=15$, $n_B=13$, $n_C=12$) and I would like compare if these groups are from the same population.

One-way ANOVA would definitely be the way to go, however upon conducting normality tests on my data, heteroskedascity seems to the main issue. My raw data, without any transformation, produced a ratio of variances ($F_{\max} = 19.1$) which is very much higher than the critical value ($F_{\rm crit} = 4.16$) and therefore I cannot perform one-way ANOVA.

I also tried transformation to normalise my data. Even after trials of various transformations (log, square root, square), the lowest $F_{\max}$ produced after transformation with a $\log_{10}$ transformation was $7.16$, which was still higher compared to $F_{\rm crit}$.

Can anyone here advise me on where to go from here? I can't think of other methods of transformation to normalise by data. Are there any alternatives to a one-way ANOVA?

P.S.: my raw data are below:

A: 0.178 0.195 0.225 0.294 0.315 0.341 0.36 0.363 0.371 0.398 0.407 0.409 0.432 0.494 0.719

B: 0.11 0.111 0.204 0.416 0.417 0.441 0.492 0.965 1.113 1.19 1.233 1.505 1.897

C: 0.106 0.114 0.143 0.435 0.448 0.51 0.576 0.588 0.608 0.64 0.658 0.788 0.958

A: 0.178 0.195 0.225 0.294 0.315 0.341 0.36  0.363 0.371 0.398 0.407 0.409 0.432 
   0.494 0.719
B: 0.11  0.111 0.204 0.416 0.417 0.441 0.492 0.965 1.113 1.19  1.233 1.505 1.897
C: 0.106 0.114 0.143 0.435 0.448 0.51  0.576 0.588 0.608 0.64  0.658 0.788 0.958

I have data from 3 groups of algae biomass ($A$, $B$, $C$) which contain unequal sample sizes ($n_A=15$, $n_B=13$, $n_C=12$) and I would like compare if these groups are from the same population.

One-way ANOVA would definitely be the way to go, however upon conducting normality tests on my data, heteroskedascity seems to the main issue. My raw data, without any transformation, produced a ratio of variances ($F_{\max} = 19.1$) which is very much higher than the critical value ($F_{\rm crit} = 4.16$) and therefore I cannot perform one-way ANOVA.

I also tried transformation to normalise my data. Even after trials of various transformations (log, square root, square), the lowest $F_{\max}$ produced after transformation with a $\log_{10}$ transformation was $7.16$, which was still higher compared to $F_{\rm crit}$.

Can anyone here advise me on where to go from here? I can't think of other methods of transformation to normalise by data. Are there any alternatives to a one-way ANOVA?

P.S.: my raw data are below:

A: 0.178 0.195 0.225 0.294 0.315 0.341 0.36 0.363 0.371 0.398 0.407 0.409 0.432 0.494 0.719

B: 0.11 0.111 0.204 0.416 0.417 0.441 0.492 0.965 1.113 1.19 1.233 1.505 1.897

C: 0.106 0.114 0.143 0.435 0.448 0.51 0.576 0.588 0.608 0.64 0.658 0.788 0.958

I have data from 3 groups of algae biomass ($A$, $B$, $C$) which contain unequal sample sizes ($n_A=15$, $n_B=13$, $n_C=12$) and I would like compare if these groups are from the same population.

One-way ANOVA would definitely be the way to go, however upon conducting normality tests on my data, heteroskedascity seems to the main issue. My raw data, without any transformation, produced a ratio of variances ($F_{\max} = 19.1$) which is very much higher than the critical value ($F_{\rm crit} = 4.16$) and therefore I cannot perform one-way ANOVA.

I also tried transformation to normalise my data. Even after trials of various transformations (log, square root, square), the lowest $F_{\max}$ produced after transformation with a $\log_{10}$ transformation was $7.16$, which was still higher compared to $F_{\rm crit}$.

Can anyone here advise me on where to go from here? I can't think of other methods of transformation to normalise by data. Are there any alternatives to a one-way ANOVA?

P.S.: my raw data are below:

A: 0.178 0.195 0.225 0.294 0.315 0.341 0.36  0.363 0.371 0.398 0.407 0.409 0.432 
   0.494 0.719
B: 0.11  0.111 0.204 0.416 0.417 0.441 0.492 0.965 1.113 1.19  1.233 1.505 1.897
C: 0.106 0.114 0.143 0.435 0.448 0.51  0.576 0.588 0.608 0.64  0.658 0.788 0.958
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gung - Reinstate Monica
gung - Reinstate Monica
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Alternatives to one-way ANOVA (transformed data but stillfor heteroskedastic in variances)data

I have data from 3 groups of algae biomass (A$A$, B$B$, C$C$) which containscontain unequal sample sizes (nA=15$n_A=15$, nB=13$n_B=13$, nC=12$n_C=12$) and I would like compare if these groups are from the same population.

One-way ANOVA would definitely be the way to go, however upon conducting normality tests on my data, heteroskedascity seems to the main issue. My raw ratadata, without any transformation, produced a ratio of variances (Fmax$F_{\max} = 19.1$)= 19.1 which is very much higher than the critical value (Fcrit$F_{\rm crit} = 4.16$) of 4.16 and theretherefore I cannot perform one-way ANOVA.

I also tried datatried transformation to normalise my data.Even Even after trials of various transformations (log, square root,square square), the lowest Fmax$F_{\max}$ produced after transformation with a log10$\log_{10}$ transformation was 7.16$7.16$, which was still higher compared to Fcrit$F_{\rm crit}$.

Can any expertsanyone here adviceadvise me on howwhere to go about from here? I can't think of other methods of transformation to normalise by data?. Are there any alternatives to a one-way ANOVA? p/s

P.S.: my raw data is foundare below here.

Thanks in advance.

Cheers,

Rick:

A: 0.178 0.195 0.225 0.294 0.315 0.341 0.36 0.363 0.371 0.398 0.407 0.409 0.432 0.494 0.719

B: 0.11 0.111 0.204 0.416 0.417 0.441 0.492 0.965 1.113 1.19 1.233 1.505 1.897

C: 0.106 0.114 0.143 0.435 0.448 0.51 0.576 0.588 0.608 0.64 0.658 0.788 0.958

Alternatives to one-way ANOVA (transformed data but still heteroskedastic in variances)

I have data from 3 groups of algae biomass (A, B, C) which contains unequal sample sizes (nA=15, nB=13, nC=12) and I would like compare if these groups are from the same population.

One-way ANOVA would definitely be the way to go, however upon conducting normality tests on my data, heteroskedascity seems to the main issue. My raw rata, without any transformation, produced a ratio of variances (Fmax)= 19.1 which is very much higher than the critical value (Fcrit) of 4.16 and there I cannot perform one-way ANOVA.

I also tried data transformation to normalise my data.Even after trials of various transformations (log, square root,square), the lowest Fmax produced after transformation with a log10 transformation was 7.16, which was still higher compared to Fcrit.

Can any experts here advice me on how to go about from here? I can't think of other methods of transformation to normalise by data? Are there any alternatives to a one-way ANOVA? p/s: my raw data is found below here.

Thanks in advance.

Cheers,

Rick

A: 0.178 0.195 0.225 0.294 0.315 0.341 0.36 0.363 0.371 0.398 0.407 0.409 0.432 0.494 0.719

B: 0.11 0.111 0.204 0.416 0.417 0.441 0.492 0.965 1.113 1.19 1.233 1.505 1.897

C: 0.106 0.114 0.143 0.435 0.448 0.51 0.576 0.588 0.608 0.64 0.658 0.788 0.958

Alternatives to one-way ANOVA for heteroskedastic data

I have data from 3 groups of algae biomass ($A$, $B$, $C$) which contain unequal sample sizes ($n_A=15$, $n_B=13$, $n_C=12$) and I would like compare if these groups are from the same population.

One-way ANOVA would definitely be the way to go, however upon conducting normality tests on my data, heteroskedascity seems to the main issue. My raw data, without any transformation, produced a ratio of variances ($F_{\max} = 19.1$) which is very much higher than the critical value ($F_{\rm crit} = 4.16$) and therefore I cannot perform one-way ANOVA.

I also tried transformation to normalise my data. Even after trials of various transformations (log, square root, square), the lowest $F_{\max}$ produced after transformation with a $\log_{10}$ transformation was $7.16$, which was still higher compared to $F_{\rm crit}$.

Can anyone here advise me on where to go from here? I can't think of other methods of transformation to normalise by data. Are there any alternatives to a one-way ANOVA?

P.S.: my raw data are below:

A: 0.178 0.195 0.225 0.294 0.315 0.341 0.36 0.363 0.371 0.398 0.407 0.409 0.432 0.494 0.719

B: 0.11 0.111 0.204 0.416 0.417 0.441 0.492 0.965 1.113 1.19 1.233 1.505 1.897

C: 0.106 0.114 0.143 0.435 0.448 0.51 0.576 0.588 0.608 0.64 0.658 0.788 0.958

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Rick L.
Rick L.
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Alternatives to one-way ANOVA (transformed data but still heteroskedastic in variances)

I have data from 3 groups of algae biomass (A, B, C) which contains unequal sample sizes (nA=15, nB=13, nC=12) and I would like compare if these groups are from the same population.

One-way ANOVA would definitely be the way to go, however upon conducting normality tests on my data, heteroskedascity seems to the main issue. My raw rata, without any transformation, produced a ratio of variances (Fmax)= 19.1 which is very much higher than the critical value (Fcrit) of 4.16 and there I cannot perform one-way ANOVA.

I also tried data transformation to normalise my data.Even after trials of various transformations (log, square root,square), the lowest Fmax produced after transformation with a log10 transformation was 7.16, which was still higher compared to Fcrit.

Can any experts here advice me on how to go about from here? I can't think of other methods of transformation to normalise by data? Are there any alternatives to a one-way ANOVA? p/s: my raw data is found below here.

Thanks in advance.

Cheers,

Rick

A: 0.178 0.195 0.225 0.294 0.315 0.341 0.36 0.363 0.371 0.398 0.407 0.409 0.432 0.494 0.719

B: 0.11 0.111 0.204 0.416 0.417 0.441 0.492 0.965 1.113 1.19 1.233 1.505 1.897

C: 0.106 0.114 0.143 0.435 0.448 0.51 0.576 0.588 0.608 0.64 0.658 0.788 0.958