Non-parametric Tests

e.g., Chi-Square

When to use various statistics

ParametricParametric Interval or ratio dataInterval or ratio data

Name parametric tests Name parametric tests we covered Tuesdaywe covered Tuesday

Non-parametricNon-parametric Ordinal and nominal Ordinal and nominal

datadata

To compare two groups on Mean Scores use t-test.

For more than 2 groups use Analysis of Variance (ANOVA)

Can’t get a mean from nominal or ordinal data.

Chi Square tests the difference in Frequency Distributions of two or more groups.

Chi-Square X2

Chi Square tests the difference in Chi Square tests the difference in frequency distributions of two or more frequency distributions of two or more groups. groups.

Test of Significance Test of Significance of two nominal variables or of two nominal variables or of a nominal variable & an ordinal variableof a nominal variable & an ordinal variable Used with a cross tabulation table Used with a cross tabulation table

Chi-Square

ected

ectedobserved

exp

)exp(2

Chi-Square =

Logic of Chi-Square Analysis

If the observed values are different enough If the observed values are different enough from the expected values, you reject the null from the expected values, you reject the null hypothesishypothesis

If the observed values and the expected values If the observed values and the expected values are similar, you fail to reject the null hypothesisare similar, you fail to reject the null hypothesis

Example: Work & Pregnancy The impact of working on pregnancyThe impact of working on pregnancy

Ha: Working during pregnancy increases the risk of miscarriage

H0: Working during pregnancy has NO impact on the risk of miscarriage

Example: Work & Pregnancy

Suppose in general population 5 in 100 Suppose in general population 5 in 100 pregnancy results in miscarriagepregnancy results in miscarriage

Probability(Probability(pp) = .05 or 5%) = .05 or 5%

Example: Work & Pregnancy

1000Total

950(95%)

No

50(5%)

Yes

Total (n=1000)

Mis

carr

iage

Example: Work & Pregnancy

500

No Work (n=500)

100

950 (95%)

50 (5%)

Total (n=1000)

500Total

No

Yes

Work (n=500)

Mis

carr

iage

H0: Working during pregnancy has NO impact on the risk of miscarriage

?

Example: Work & Pregnancy

500

475 (95%)

25 (5%)

No Work (n=500)

100

950 (95%)

50 (5%)

Total (n=1000)

500Total

475 (95%)No

25 (5%)Yes Miscarriage

Work (n=500)

Mis

carr

iage

If NULL hypothesis TRUE, both work & no work groups would have same probability of miscarriage. EXPECTED values:

Example: Work & Pregnancy

500

490 (98%)

10 (2%)

No Work (n=500)

100

950 (95%)

50 (5%)

Total (n=1000)

500Total

460 (92%)No

40 (8%)Yes Miscarriage

Work (n=500)

Mis

carr

iage

The actual values in your data = OBSERVED VALUES

Frequency of Sleep BehaviorBy Classroom Seating Location

p=.001

Front Center Back0

20

40

60

80

100Percent

Never Occasionally Often

p = .001

Frequency of Class ParticipationBy Classroom Seating Location

p=.002

Front Center Back0

10

20

30

40

50

60

70

80Percent

Never Occasionally Always

Tourist Expenditure:

Mainlander vs. Japanese

40%

10%

40%

50%

20%

40%

0%

10%

20%

30%

40%

50%

$100 or

less

$101 -

$500

$500+

Mainland

J apanese

Chi-Square x2 = 7.34, df = 2, p<.001

ExcelNot at all Some A lot

Males 12 10 8Females 6 6 18

0

2

4

6

8

10

12

14

16

18

Not at all Some A lot

Do You Like Vegetables?

Males

Females

Finished Chart

02468

1012141618

# of Subjects

Not at all Some A lot

Chi-Square = 6.85, p<.05

Do You Like Vegetables?

Males

Females

The Stats for ChartGender * Do you like veggies? Crosstabulation

12 10 8 30

40.0% 33.3% 26.7% 100.0%

66.7% 62.5% 30.8% 50.0%

20.0% 16.7% 13.3% 50.0%

6 6 18 30

20.0% 20.0% 60.0% 100.0%

33.3% 37.5% 69.2% 50.0%

10.0% 10.0% 30.0% 50.0%

18 16 26 60

30.0% 26.7% 43.3% 100.0%

100.0% 100.0% 100.0% 100.0%

30.0% 26.7% 43.3% 100.0%

Count

% within Gender

% within Do youlike veggies?

% of Total

Count

% within Gender

% within Do youlike veggies?

% of Total

Count

% within Gender

% within Do youlike veggies?

% of Total

Male

Female

Gender

Total

Not at all Some A lot

Do you like veggies?

Total

Chi-Square Tests

6.846a 2 .033

6.997 2 .030

5.863 1 .015

60

Pearson Chi-Square

Likelihood Ratio

Linear-by-LinearAssociation

N of Valid Cases

Value dfAsymp. Sig.

(2-sided)

0 cells (.0%) have expected count less than 5. Theminimum expected count is 8.00.

a.

Use SPSS Crosstabs (for nominal and ordinal data)

Click…. AnalyzeClick…. Analyze Descriptive statisticsDescriptive statistics CrosstabsCrosstabs Highlight variables for rowHighlight variables for row Highlight variable for columnHighlight variable for column Click statistics, click chi-square or Click statistics, click chi-square or

correlationcorrelation Etc.Etc.

Both chi square (non-parametric test) and t-test (parametric test)…

Examines if observed difference between Examines if observed difference between groups in your data is true differencegroups in your data is true difference

True difference = difference that exists in True difference = difference that exists in the populationthe population

HH00 says there is no difference in the says there is no difference in the population population

Which values are compared?

Chi-Square

t-test

Frequencies in each cell

Mean and Standard Deviation of each group

If H0 is true…Chi-Square

t-test

The values in the frequency table will look like Expected Values

The distribution of both groups will look like Population Distribution

Chi- square: If H0 is true…Males = Females (No difference)

70%

30%

Female TotalMale

70%70%NO

30%30%YES

t-test: If H0 is true …Total

Female

Male

Mean

# of cases

Test score

t-test: If H0 is NOT true …Total

Female

Male

# of cases

Test score

Mean Mean Mean

t-test: If H0 is NOT true …Total

Female

Male

# of cases

Test scoreMean Mean