Which t-test (complication)?

#1
Hi there, Im new here but any help would be greatly appreciated :)

I have 48 lettuces which were judged by their weights (grown in separate pots).

Half of these pots used normal soil, the other half a very sandy soil (which significantly reduced lettuce weights).

Half of these pots (spread equally between soil type) also were mixed with charcoal, the other half not. (Charcoal slightly increased lettuce weights).

I don't think ANOVA is appropriate and it gave out not significant results... I want to find the significant improvement from using the charcoal.

My advisor is now unreachable but previously mentioned a paired t-test but I would have thought this is inappropriate considering the different soil mediums right?


Basically I need to come up with a graph with error bars with (normal without charcoal, normal with charcoal, sandy without charcoal, sandy with charcoal) and some significance of these.


Thank you very much for any help,
Regards,
Marcus
 

Karabiner

TS Contributor
#2
I don't think ANOVA is appropriate and it gave out not significant results...
It looks like a two-way ANOVA with the factors "soil" and "charcoal yes/no"
is the most appropriate choice.
I want to find the significant improvement from using the charcoal.
According to ANOVA results, seemingly the effect of charcoal
in your sample cannot be distinguished from mere chance.

With kind regards

K.
 
#4
Thanks for the speedy reply.

I performed the two-way ANOVA and Significance for charcoal was only 0.065.

I really think I should be able to find a significant result by looking at it in another manner though, by looking at my actual results it seems fairly clear. Error bars overlap for normal soil but not for sandy soil.

Do you think given my data an independent or paired t-test might be best suitable? I propose I do this just on all sandy soil and then on normal soil?

Thanks,
Marcus
 
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#5
So if I run a One-way ANOVA on JUST sandy samples with

Dependent List: Weight
Factor: Charcoal (0 means none, 1 means yes and its Nominal data)

I get F=12.037 Sig.=.006 So it is significant in sandy soil then right?

In normal soil I get F=1.930 Sig.=.195
Not significant. This was reflected by the error bars as well.

Anyone see anything wrong with this use of One-Way Anova?
 
#6
It is not wrong to run such an one-way-anova, but it would be slightly more efficient to use a two-way-anova with an interaction term("charcoal*soil"). The result indicates an interaction term. I suggest make an interaction-plot for the four means with error bars for the confidence intervals.

(To me as an biological amateur it seems natural that in the low nutrients sand soil, when adding some nutrients by the charcoal, that the growth will be higher.)

In the normal soil, the effect is not significant, but the F-value=1.93 is larger than the expected value of one (under the null hypothesis), so there could be an effect, it is just that the sample size is not large enough to show it.

Why don't you show us the data, so that everybody can learn something from it?
 
#7
The data I'm running this initial stats on are just for the following pots (grown in an early year).

Soil ____ 10.25_ 13.7_ 13.25_ 12.3_ 9.6_ 34.75

Soil+char 20.05_ 37.4_ 24.5_ 31.2_ 18.35_ 9.2

Sand ____ 2.35_ 2.3_ 3.2_ 3.15_ 2.65_ 4.1

Sand+char 9.35_ 4.55_ 5.2_ 8.9_ 5.7_ 4.1


With two-way ANOVA Soil type of course comes out hugely significant (no surprises there). I'm really most interested in proving the worth of the charcoal in sandy soil though
Charcoal comes out at F=3.823 (Sig.=0.065)
Soil type*charcoal F=0.614 (Sig.=0.443)

It seems to make most sense to me to run one-way ANOVA on just the sandy samples and normal samples alone so you're not finding the normal soils holds back the sandy soils, on sandy alone F=12.037 (Sig.=0.006)
 
#8
For anyone interested or believes I'm making a mistake here:

I am settling with saying:

Error bars don't overlap only for sandy soil.
Two-way ANOVA gives a p-value of 0.065 so there is no statistically significant difference in yield between samples with and without biochar.
However independent t-tests only considering biochar for each soil separately suggest biochar in sandy soil has a significant effect at the 99% level (gives .195 for normal soil)