# KW Test applicable?

#### jscholen

##### New Member
Background:
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

Jeff

#### JohnM

##### TS Contributor
Jeff,

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...

John

#### jscholen

##### New Member
Hey John,

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?

Jeff

#### JohnM

##### 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.

#### jscholen

##### New Member
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*

#### JohnM

##### 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.

#### jscholen

##### New Member
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?

#### JohnM

##### TS Contributor
Aha!

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.

#### jscholen

##### New Member
I'll try this...

I'll let you know what I come up with.

#### jerryb

##### New Member
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,
jerry