# I believe Kruskal-Wallis is the right choice, but where do I go from there?

#### jempweber

##### New Member
Assumption:
Tertiary wing feathers are warmer

Hypotheses:
1) During cold weather feather mites will accumulate on the tertiary wing feather
2) During warm weather feather mites will spread evenly over the entire wing

In winter 2010-11 and summer 2011 I took exact counts of feather mites for each individual wing feather (primaries: p1-p10, secondaries: s1-s6, and tertiaries: t1-t3) of blue tits. And, looking at the data, I can see with the naked eye that in winter most mites are accumulated on the tertiary feathers and during summer they are spread all over the wing. However, so far I've been unable to employ the right statistical test to back those findings. The data is not normally distributed, the variances are not homogenous and the sample size is greater than 20, hence I tried using the Kruskal-Wallis test (Dytham 2011). The results from Minitab 15 are as follows:

Kruskal-Wallis Test: Winter Mite Count versus Winter Remiges

Kruskal-Wallis Test on Winter Mite Count

Winter
Remiges_____N__Median____Ave Rank____Z
Win Prim____48_2.000_____61.7______-2.20
Win Sec_____48_5.500_____78.1_______1.15
Win Tert____48_7.000_____77.7_______1.05
Overall_____144__________72.5

H = 4.83 DF = 2 P = 0.089
H = 4.92 DF = 2 P = 0.085 (adjusted for ties)

Kruskal-Wallis Test: Summer Mite Count versus Summer Remiges

Kruskal-Wallis Test on Summer Mite Count

Summer
Remiges_____N_______Median____Ave Rank____Z
Sum Prim____44______4.5000____90.2_______5.03
Sum Sec_____44______1.0000____63.7______-0.60
Sum Tert____44______0.0000____45.6______-4.43
Overall_____132_______________66.5

H = 30.17 DF = 2 P = 0.000
H = 33.07 DF = 2 P = 0.000 (adjusted for ties)

Although this gives me a P-value for winter (P>0.05) confirming that there is a difference and a P-value for summer (P<0.001) for no difference, which is exactly what I wanted, I believe that there is an overall difference between the three kinds of remiges, but how can I compare primaries and secondaries with tertiaries? Or does this already show what I need?

If there is a way to attach my data (.xls) to this post, please let me know, I'll gladly do so. The upload manager doesn't seem to except my .xls (500(IOErrorEvent type="ioError"bubbles=false cancelable=false eventPhase=2text="Error #2038"))

https://files.me.com/xavierschmit/5vqcw9
Please note: summer and winter data in separate work sheets in same document

Any help would be greatly appreciated as I'm running out of time,

Cheers,
aXe

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#### Karabiner

##### TS Contributor
The table for winter shows some accumulation on the second and the third feather,
although the global test for differences between feathers is not statistically significant
(p > 0,05).

Regarding summer, there is clearly an accumulation on the primary feathers, and the
differences between feathers are statistically significant (p < 0,001).

So, your first hypothesis is not supported and the second hypothesis is clearly refuted.

Regards

K.

#### jempweber

##### New Member
Thanks for that, however if you'd have a look at the data, a normal histogram shows such a high number of mites on the tertiaries in winter that there must be a provable significant difference. Maybe I did chose the wrong test after all or I may have used it wrong.

#### Karabiner

##### TS Contributor
I do not know why your histogram does not properly represent your data. According to
your raw data, in winter there was a total of 684 mites on the third feathers but 751 (!)
on the second (and still 633 on the first). Only for 15 birds the highest number of
mites was on the third feathers, but for 19 birds it was on the second, for 8 it was
on the first. If there was a "significant" accumulation, then it has to be on the
second feathers, not on the third.

Regards

K.

#### jempweber

##### New Member
Blue Tits (Blaumeisen) have 10 primaries (p1-p10), 6 secondaries (s1-s6), and only 3 tertiaries (t1-t3) as represented within the hidden columns of the Excel worksheet. I wonder if that has any significance

#### Karabiner

##### TS Contributor
That is a scientific question in the first place, not a statistical one. I do not know why mites move,
or which role the respective numbers of first/second/third feathers might perhaps play, or which
role the total size of the feathers' surface might play, or what else. Your hypotheses did not mention
such factors.

Regards

K.

#### jempweber

##### New Member
I was wondering if it would not screw up the power of the data if I'd just take the means of the mite numbers, for example divide the number of mites on primaries through 10, secondaries through 6 and tertiaries through 3 and ultimately use that data...

#### jempweber

##### New Member
It turns out that the data is not independent as the mite counts are taken from three different kinds of feathers on the same bird. I was told that maybe Friedman was the correct test to run, however, I don't know how to input my data for a Friedman Test into Minitab 15 because it wants
1) Data into the "Response" box - I presume that is my mean value from each feather type per bird
2) The conventional factor into the "Treatment" box - What does that mean
3) The repeated measure into the "Block" box - That got me completely lost...

Any would be awesome as I need to hand in the work on Thursday...