KW Test applicable?

I am new to Statistical Analysis, and I am analysising this data based on a conversation with a old associate over the phone. Am I headed in the right direction?

I am comparing two types of devices for volume of blood draw. I am trying to see if Device A is better or equal to Device B.

I have 40 subjects from which I have drawn blood(3 samples per device per subject). Both devices used on the same subjects. SO n=120 for each device.

The data does not come from a Normal distribution curve, therfore I am conducting a KW Test to determine if there is a significant difference in the devices ability to draw blood.

Based on the results P>.05, what can I do to/say about the data?
Here I am saying that there is no significant difference and stop there.

Based on the results P<.05, what can I do to/say about the data?
Here I am saying there is significant difference and comparing the averages of blood drawn to distinguish which is better.

I appreciate any help



TS Contributor

The Kruskal-Wallis test does not compare means - it compares medians, or more generally, it compares distributions.

How far from a normal distribution is the data? Usually when we compare means, especially from large samples such as this, we comfortably assume that the distribution of sample means follows a normal distribution - so I would argue that you could have done either a t-test or z-test here...

Hey John,

Thanks for your input.

When I used the KW Test, I knew I was comparing the medians. I concluded that I couldn't use a t test since the ks Test and Chi-Squared P values would not give me the confidence I needed to assume they were from Normal distributions.

Could I have just assumed Normal distribution and ran with the t Test?



TS Contributor
Be careful how you interpret p-values on tests of normality when you have large sample sizes -> they can get quite small, when in fact the difference between the underlying distribution and normality is not significant, from a practical standpoint.

The best method, IMHO, is to use the Anderson-Darling test along with a normal probability plot.

Having said that, remember that we're not so concerned about the distribution of individual points - that's not what we're drawing inferences on - it's the distribution of sample means.

I would assume normality unless the normal probability plot shows that the departure from normality is extreme.
Hey John,

I have added the data you suggested. I copied and pasted from Statgraphics.
Attached is the Distribution of both devices.

My objective is to show that Device A is as good or better than Device B, but I don't see it happening with this data.

Tell me what you think. We had allot of zeros in the data for Device A, so I am not sure how to evaluate those with respect to the Device B.

Goodness-of-Fit Tests for Blood Volume Device A

Chi-Square Test
Lower Upper Observed Expected
Limit Limit Frequency Frequency Chi-Square
at or below -1.24369 0 15.00 15.00
-1.24369 0.536252 45 15.00 60.00
0.536252 1.8673 20 15.00 1.67
1.8673 3.05917 13 15.00 0.27
3.05917 4.25103 8 15.00 3.27
4.25103 5.58208 10 15.00 1.67
5.58208 7.36202 5 15.00 6.67
above 7.36202 19 15.00 1.07
Chi-Square = 89.6011 with 5 d.f. P-Value = 0.0

Estimated Kolmogorov statistic DPLUS = 0.187474
Estimated Kolmogorov statistic DMINUS = 0.206718
Estimated overall statistic DN = 0.206718
Approximate P-Value = 0.0000703058

EDF Statistic Value Modified Form P-Value
Kolmogorov-Smirnov D 0.206718 2.27846 <0.01*
Anderson-Darling A^2 8.10643 8.15836 0.0000*

Goodness-of-Fit Tests for Device B

Chi-Square Test
Lower Upper Observed Expected
Limit Limit Frequency Frequency Chi-Square
at or below -0.597864 0 15.00 15.00
-0.597864 2.72083 36 15.00 29.40
2.72083 5.20256 20 15.00 1.67
5.20256 7.42479 21 15.00 2.40
7.42479 9.64702 11 15.00 1.07
9.64702 12.1288 7 15.00 4.27
12.1288 15.4474 6 15.00 5.40
above 15.4474 19 15.00 1.07
Chi-Square = 60.2669 with 5 d.f. P-Value = 1.0705E-11

Estimated Kolmogorov statistic DPLUS = 0.163735
Estimated Kolmogorov statistic DMINUS = 0.143522
Estimated overall statistic DN = 0.163735
Approximate P-Value = 0.00321149

EDF Statistic Value Modified Form P-Value
Kolmogorov-Smirnov D 0.163735 1.80469 <0.01*
Anderson-Darling A^2 5.44678 5.48167 0.0000*


TS Contributor
It's difficult to judge one way or another - at first glance, without knowing much about how each device is supposed to behave, it's difficult to draw conclusions.

How are the devices supposed to behave - is there a targeted amount of blood to draw - is it the same target every time?

If you could provide a little more background, it might shed some light on the comparison / evaluation.

Yes, it appears that device B has fewer zeros, and may be better on average or the median, but that doesn't necessarily mean it's good enough in the first place.
Targets are rather subjective, depending on who you ask. The problem is that not everyone has the same biological make-up, Candidate A may have thin skin and bleed like a pig as opposed to Candidate B who has 30 yrs of calluses.

Based on the Distribution plots, Could I run with the t Tests or are the plots too extreme?


TS Contributor

You need to do a dependent-samples t-test. Draw blood from a person using device A, compute the average, then draw from that same person using device B, and compute that average. Now, compute for each person:

delta = average blood drawn by A - average blood drawn by B

Then test whether the average delta is significantly different from 0.
Reading this brought back a nightmarish memory of my research discussion group in grad school where someone was flirting with paired-t-tests and dependant samples and i was argueing that they should find a stat prof to help them get it right. i guess that horse was not thirsty....

good luck,