5. non parametric analysis

KNOWLEDGE FOR THE BENEFIT OF HUMANITYKNOWLEDGE FOR THE BENEFIT OF HUMANITY

BIOSTATISTICS (HFS3283)

NON-PARAMETRIC STATISTICS

Dr.Dr. MohdMohd RazifRazif ShahrilShahril

School of Nutrition & Dietetics School of Nutrition & Dietetics

Faculty of Health SciencesFaculty of Health Sciences

UniversitiUniversiti Sultan Sultan ZainalZainal AbidinAbidin

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S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N

Topic Learning Outcomes At the end of this lecture, students should be able to;

• identify types of non-parametric statistics and their use

• explain assumptions to be met when using non-

parametric statistics

• perform non-parametric statistics using SPSS

• explain how to interpret the SPSS outputs of non-

parametric statistics

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Parametric vs. Non-parametric Tests

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• Parametric tests assume the data is of sufficient “quality” – the results can be misleading if assumptions are

wrong

– “Quality” is defined in terms of certain properties of the data

• Non-parametric tests can be used when the data is not of sufficient quality to satisfy the assumptions of parametric test – Parametric tests are preferred when the assumptions

are met because they are more sensitive.


Recap! Assumptions of t-test

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1. Normally distributed1. Normally distributed 1. Normally distributed1. Normally distributed 2. Interval or ratio scale 2. Interval or ratio scale

datadata 2. Interval or ratio scale 2. Interval or ratio scale

datadata

3. No extreme scores or 3. No extreme scores or outliersoutliers

3. No extreme scores or 3. No extreme scores or outliersoutliers

4. Equal variance in the two 4. Equal variance in the two samples (samples (for independent for independent

samples t testsamples t test) )

4. Equal variance in the two 4. Equal variance in the two samples (samples (for independent for independent

samples t testsamples t test) )

Parametric testParametric test Parametric testParametric test


Recap! Assumptions 1 - Normality

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In severe skew the most extreme histogram interval usually has the highest frequency



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In moderate skew the most extreme histogram interval does not have the highest frequency



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Recap! Assumptions 3 – No extreme values

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It is sometimes legitimate to exclude extreme scores from the sample or alter them to make them less extreme. You may then use parametric tests.


Recap! Assumptions 4 – Equal variance

(independent t-test only)

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Variance 25.2 Variance 4.1

• If the variance of one group is 3 or more times bigger than the other, then perform a non-parametric test


Recap! Assumptions 4 – Equal variance

(independent t-test only)

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• Sometimes, the variance in the two independent groups is unequal, but the larger variance is less than 3 times bigger than the smaller variance – In this case you can perform a t test with a correction

for unequal variance (Levene’s Test)


Parametric vs. Non-parametric Tests (cont.)

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Mann Whitney Test

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• Non-parametric tests for comparing two groups

or conditions

• Used when you have two conditions, each

performed by a separate group of subjects.

• Each subject produces one score. Tests whether

there is a statistically significant difference

between the two groups.


Mann Whitney Test

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Assumptions

1. Dependent variable should be measured at the ordinal or continuous level (i.e., interval or ratio).

2. Independent variable should consist of two categorical, independent groups.

3. Independence of observations, which means that there is no relationship between the observations in each group or between the groups themselves.

4. Not normally distributed and distributions in each group have the same variability


Example for Mann Whitney Test

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• Does it make any difference to students'

comprehension of statistics whether the lectures

are in English or in Malay?

– Group 1: statistics lectures in English.

– Group 2: statistics lectures in Malay.

• DV: lecturer intelligibility ratings by students (0 =

"unintelligible", 100 = "highly intelligible").

• Ratings - so Mann-Whitney is appropriate.

Mann-Whitney using SPSS - procedure:

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Mann-Whitney using SPSS - procedure:

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7 7

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Mann-Whitney using SPSS - output:

OUTPUT INTERPRETATION There is no significant difference on Intelligibility if the course is taught in English or Malay, (U = 25.00, p = 0.286)

Ranks

8 10.38 83.00

9 7.78 70.00

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Language

English

Malay

Total

Intelligibility

N Mean Rank Sum of Ranks


WilcoxonTest

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• Non-parametric tests for comparing two related

or paired groups or conditions

• Used when you have two conditions, both

performed by the same subjects.

• Each subject produces two scores, one for each

condition. Tests whether there is a statistically

significant difference between the two

conditions.


WilcoxonTest

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Assumptions

1. Dependent variable should be measured at

the ordinal or continuous level (i.e., interval or

ratio).

2. Independent variable should consist of two

categorical, related or matched groups.

3. Not normally distributed and distributions in

each group have the same variability


Example for WilcoxonTest

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• Does background music affect the mood of

studying?

• Eight student: each tested twice.

– Condition A: background music.

– Condition B: silence.

• DV: Students’ mood rating (0 = "extremely

miserable", 100 = "euphoric").

• Ratings, so use Wilcoxon test.

Wilcoxon using SPSS - procedure:

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Wilcoxon using SPSS - procedure:

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Wilcoxon using SPSS - output:

OUTPUT INTERPRETATION There is no significant difference on Students’ Mood between background Music or Silence when studying, (Z = -1.357, p = 0.175)


Kruskal Wallis Test

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• Non-parametric tests for comparing more than

two groups or conditions

• Used when you have three or more conditions,

each performed by a separate group of subjects.

• Each subject produces one score. Tests whether

there is a statistically significant difference

between the three or more groups.

• Post hoc analysis would require that one

conduct multiple pairwise comparisons using a

procedure like the Mann Whitney U.


Kruskal Wallis Test

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Assumptions;

1. Dependent variable should be measured at the ordinal or continuous level (i.e., interval or ratio).

2. Independent variable should consist of two or more categorical, independent groups.

3. Independence of observations, which means that there is no relationship between the observations in each group or between the groups themselves.

4. Not normally distributed and distributions in each group have the same variability


Example on Kruskal Wallis Test

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• Is there any difference on back pain rating by the

patients between Drug A, B and C?

– Group 1: Drug A.

– Group 2: Drug B

– Group 3: Drug C

• DV: Back pain score by the patients (1 = “lowest

level of pain", 10 = “greatest level of pain").

• Ratings - so Kruskal Wallis is appropriate.

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Kruskal Wallis using SPSS - procedure:

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2 2

3 3

4 4

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Kruskal Wallis using SPSS - procedure:

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Kruskal Wallis using SPSS - Output:

OUTPUT INTERPRETATION There was a statistically significant difference in pain score between the different drug treatments,(χ2(2) = 8.520, p = 0.014)

Thank YouThank You

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5. non parametric analysis

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