FIRST, REMEMBERParametric tests has greater power to detect a

genuine effect if one exists than a non-parametric test.

But this is true only if assumptions are met.

EXPLORE YOUR DATA FOR BIASES

Analyze

Descriptive Statistics

Explore

If p < .05 for any group ( sign. different distribution of scores), then it’s recommended to conduct a non-parametric test for all groups being compared.

GENERAL PR OC EDURE S OF NON-PARAM ET RIC TE ST S

Analyze

Non-parametric tests

Independent Samples or Related Samples

WHAT TEST DO I USE?For a basic independent t-test:

• Mann-Whitney test or Wilcoxon’s Rank-sum test

For a basic paired samples t-test:• Wilcoxon signed-rank test

• also called Wilcoxon matched-pair signed ranked

For several independent groups (ANOVA):• Kruskal-Wallis test (rank-sum design)

For several dependent (related) groups (ANOVA):• Friedman’s ANOVA (signed-rank design)

THEORY OF RANK-SUMAll non-parametric tests overcome the shape of the distribution of scores by ranking the scores in your data. Score 3 5 6 6 7 8 9 10 17 24 27 28 29 30 32

35 35 35 36 39 Potential Rank

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Actual Rank

1 2 3.5 3.5 5 6 7 7 9 10 11 12 13 14 15 17 17 17 19 20

Group A A A A A A A A A E E E E A E E E E E E

Sum of ranks for alcohol (A) = 59 sum of ranks for ecstasy (E) = 151

THEORY FOR SIGNED-RANK Star

tMonth 1

Month 2

Start(Rank

s)

Month 1

Month 2(Ranks)

Person 1

63.75

65.38 81.34 1 2 3

Person 2

62.98

66.24 69.31 1 2 3

Person 3

65.98

67.70 77.89 1 2 3

Person 4

107.27

102.72

91.33 3 2 1

Person 5

66.58

69.45 72.87 1 2 3

Person 6

120.46

119.96

114.26 3 2 1

Person 7

62.01

66.09 68.01 1 2 3

Person 8

71.87

73.62 55.43 2 3 1

Person 9

83.01

75.81 71.63 3 2 1

Person 10

76.62

67.66 68.60 3 1 2

Ri 19 20 21

DEMONSTRATE TEST OFTWO RELATED CONDITIONS

The non-parametric equivalent of the paired-samples t-test

Using quail sex study: Matthews et al. (2007).sav

Switch to SPSS and continue…..

WHAT IS THIS STUFF?

z-scorep-value

DESCRIBING YOUR CONCLUSIONIn common terms, conditioning (as a learning mechanism) provides some adaptive benefit in that it makes it more likely that you will pass on your genes.

In more scientific terms; of the 78 eggs laid by the test females, 39 eggs were fertilized. Genetic analysis indicated that 28 of these (72%) were fertilized by the signalled males, and 11 were fertilized by the control males. Ten of the 14 females in the experiment produced more eggs fertilized by the signalled male than by the control male, T = 13.5, p < .05). These effects were independent of the order in which the 2 males copulated with the female.

In addition, the present findings show that when 2 males copulated with the same female in succession, the male that received a Pavlovian CS signalling copulatory opportunity fertilized more of the female’s eggs. Thus, Pavlovian conditioning increased reproductive fitness in the context of sperm competition

WHAT AB O UT EFFECT S IZ E?

r = z-score ÷ √ N

r = -2.23 ÷ √ 14

r = -2.23 ÷ 3.74 = .59

.59 is a large effect.

SEVERAL IN DEPEND EN T GRO UPS

The Kruskal Wallis test

Based on ranked data, like the Mann-Whitney test

Rank scores from lowest to highest, ignoring the to which the score belongs, then assign the lowest a rank of 1.

DATA TABLE EXAMPLENo Soya 1 Soya

Meal4 Soya Meals

7 Soya Meals

Sperm Rank

Sperm

Rank

Sperm

Rank Sperm

Rank

0.35 4 0.33 3 0.40 6 0.31 10.58 9 0.36 5 0.60 10 0.32 20.88 17 0.63 11 0.96 19 0.56 70.92 18 0.64 12 1.20 21 0.57 81.22 22 0.77 14 1.31 24 0.71 131.51 30 1.53 32 1.35 27 0.81 15~~~~ ~~

~~~~ ~~

~~~~~

~~~~

~~~ ~~~

Total Ri

Average

92746.35

88344.15

88344.15

54727.35

CON DUCTING AN EXPL OR ATO RY AN ALYSIS

The Kruskal-Wallis test tells us that, overall, groups come from different populations, but not specifically where they differ between the different groups.

You could do pairwise comparisons, testing each group separately, but it would inflate the Type I error at .05.

The alternative is to use a stepped procedure• By ordering the groups based on the sum from lowest to highest.

The data editor has two columns, one coding variable & one dependent variable

File Soya.sav,

EXAMPL E OF ENTRY FOR EXPL O RING DATA

Dependent variable

Coding variable

Q - Q PL O TS, CLEAR DEVIATIO N IN AL L GRO UPS

Each group has less than n = 30, all have non normal distribution, so use non-parametric test

SPSS PROCEDURES

Analyze

Non-parametric testsIndependent Samples

DON’T FORGET EFFECT SIZE

r = z-score ÷ √ N

r = -2.476 ÷√ 80

r = -2.476 ÷ 8.94

r = -0.28 small to medium reverse effect size

ANY QUESTIONS?

Fewer questions are positively correlated to quicker end of class time.