# Violation of normality assumption for One Way Anova - Non parametric test?

#### BOAZ

##### New Member
Hoping somebody can help with this?

Recently we conducted a small study with ten participants. Each participant completed the same two tests, 'Test A' and 'Test B', during one session. Five particpants (Group AB) performed test A first, while the remainder performed test B first (Group BA). The goals were:

1) To see if the two tests were equivalent
2) To establish whether the order of the tests had any effect on the relative scores on each test.

Goal 1
The combined data failed the Levenes test for homogeneity of variance (P = .028), and Test B data failed the Shapiro Wilk test for normaility (P = .008). A Wilcoxin Signed Ranks test revealed no significant difference between tests A & B (Z = -.634, P = .536)

Goal 2
Achieving goal two is a problem. We have used a One Way ANOVA to establish that group (i.e. AB or BA) was not a significant factor for either test (P =.496, and P =.436). However, while the data for both tests A and B passed Levene's tests, only group AB scores on test A passed a Shapiro Wilk test. We are unsure of which non parametric test to use as the Kruskal-Wallis ANOVA by ranks is only suitable for 3+ groups. It may be the case that we do not really know how to set this up properley in SPSS!

Any help would be much appreciated!

#### d21e7x11

##### New Member
Hi BOAZ,

Few notes/questions:
- I believe in 1) you meant the goal is to test if the tests A and B are different. Correct?
- each participant completed both tests - were this accounted for in the analysis you've described?
- since each participant had both tests, you may want to consider doind analysis of diferences (outcome) and the type of difference i.e. (A-B) or (B-A) as a factor. In other words, you can do one-way ANOVA on the differences testing if i) the difference is 0; ii) there is no difference between AB and BA.

Thanks d,