lecture 9a (significancy test for categorical data)

Significancy test for Significancy test for categorical and Interval Datacategorical and Interval Data

Learning Objective Learning Objective

• Be able to understand the significance test for categorical and interval data

Hypothesis TestingHypothesis Testing

PARAMETRIC• Compare Mean:

z, t and Anova test

• Association:Correlation

Regression

NONPARAMETRIC• Compare Mean

Mann Whitney, Wilcoxon

• Association:Spearman Correlation

Normally Distributed data Not Normally distributed

HypothesisHypothesis

• Research HypothesisTemporary conclusion based on theory and/or previous study

• Statistical HypothesisHypothesis that going to be testedConsist Null Hypothesis and Alternative Hypothesis

Hypothesis Testing StepsHypothesis Testing Steps

• Define the null and alternative hypothesis

• Collect relevant data• Calculate the value of the test-statistics

specific to Ho• Interpretation the result

Define the null (Ho) and alternative Define the null (Ho) and alternative hypothesis (Ha) hypothesis (Ha)

• Ho assumes no effect or no different or no association

• Ha which hold if the null hypothesis is not

true. It relates more directly to the theory we wish to investigate

Ho and Ha…cont.Ho and Ha…cont.

• If we wish to identify whether the rate of smoking differ by sex

Ho. The smoking rate are the same in men and women in the populationmen = women

Ha. The smoking rate are different in men and women in the populationmen # women

Ho and Ha…cont.Ho and Ha…cont.

• If we wish to identify whether the rate of smoking differ by sex

Ho. The smoking rate are the same or lower among men than among women in the populationmen ≤ women

Ha. The smoking rate are higher among men than among women in the populationmen > women

P valueP value• TERMINOLOGY:

The probability of obtaining the same result or event more extreme, if the null hypothesis is true

• USING THE P VALUE:p ≤ 0,05, there is sufficient evidence to reject the null hypothesisor there is a small chance of the result occurring if the null hypothesis were true and then we say the result are significant

p > 0,05, there is insufficient evidence to reject the null hypothesis and we say that the result are not significant

Error in hypothesis testingError in hypothesis testing

Reject Ho Do not reject Ho

Ho is true Type I error()

No error

Ho is false No error Type II error()

Which test to use?Which test to use?

Depend on:• The design of study

(one sample, two dependent samples, two independent samples)

• The type of variable (categorical, continuous)

• The distribution of data being studied (normal, t, F, Chi square, binomial)

TOPICS • Single proportion analysis• Two proportion analysis

Single ProportionSingle Proportion

Case 1: (DGK Data) Should we conclude that the proportion of

anemia among pregnant mothers is different from 40%

Hypothesis testing used is Binomial Test

IndicationTo compare a proportion of one sample with a test value

POPULATION = p (anemia)

SAMPELp

Could we conclude that is differ from 0,40?

Ho. = 0,40Ha. # 0,40

Compare a sample proportion (p) with a test value (0,40)

Hypothesis: Ho: = 0,40 Ha: # 0,40

Decision rule: Reject Ho, if p Accept Ho, if p >

Binomial Test

Normal 172 ,7 ,4 ,000a

Anemia 59 ,3231 1,0

Group 1Group 2Total

Status Hb. sbl. intervensiCategory N

ObservedProp. Test Prop.

Asymp. Sig.(1-tailed)

Based on Z Approximation.a.

Ho Rejected; which signify that proportion of anemia among pregnant women significantly differ from 40%

Two ProportionsTwo Proportions

Case 2: (DGK Data) Should we conclude that the proportion of

anemia among pregnant mothers in Gianyar and Klungkung are different

Hypothesis testing used is Chi-square

GIANYAR

KARANGASEM

P1 P2

POPULASI

SAMPEL

COMPARE SAMPLE

PROPORTION USING X2 TEST

Hypothesis: Ho: 1 = 2 Ha: 1 # 2

Decision rule: Reject Ho, if p Do not reject Ho, if p >

Kabupaten

Anemia Non anemia

Total

Gianyar a b a+b

Karangasem c d c+d

Total a+c b+d n

Calculate the value of the test statistic

i

ii

EEO

X2

2 5,0

Kabupaten * Status Hb. sbl. intervensi Crosstabulation

33 102 13524,4% 75,6% 100,0%

26 70 9627,1% 72,9% 100,0%

59 172 23125,5% 74,5% 100,0%

Count% within KabupatenCount% within KabupatenCount% within Kabupaten

Gianyar

Karangasem

Kabupaten

Total

Anemia Normal

Status Hb. sbl.intervensi

Total

Chi-Square Tests

,205b 1 ,650,090 1 ,764,205 1 ,651

,650 ,381

,205 1 ,651

231

Pearson Chi-SquareContinuity Correctiona

Likelihood RatioFisher's Exact TestLinear-by-LinearAssociationN of Valid Cases

Value dfAsymp. Sig.

(2-sided)Exact Sig.(2-sided)

Exact Sig.(1-sided)

Computed only for a 2x2 tablea.

0 cells (,0%) have expected count less than 5. The minimum expected count is24,52.

b.

TOPICS • A Single sample• Two independent samples• Two dependent samples• More the two samples

A Single GroupA Single Group

Case 3: (DGK Data) Should we conclude that the mean of

Hemoglobin Pretest is different from 12 g/dl

Hypothesis test used is One sample t-test

POPULATION (Hb)

SAMPELmean

Could we conclude that (Hb) is different from 12?Ho. (Hb) = 12Ha. (Hb) # 12

Compare a sample mean with a test value (12)

Hypothesis: Ho: = 12 Ha: # 12


nSDXt

/


Ho rejected, which suggest mean Hb-pre differ significantly from 12 g/dl

One-Sample Statistics

231 11,682 1,0768 ,0708Hb. sbl intervensiN Mean Std. Deviation

Std. ErrorMean

One-Sample Test

-4,491 230 ,000 -,3182 -,458 -,179Hb. sbl intervensit df Sig. (2-tailed)

MeanDifference Lower Upper

95% ConfidenceInterval of the

Difference

Test Value = 12

Two Independent Samples/ GroupsTwo Independent Samples/ Groups

Case 4: (DGK Data) Should we conclude that the Hbpre

between Gianyar and Karangasem are equal.

Hypothesis testing used is Independent samples T-Test

GIANYARμ1

KARANGASEMμ2

mean1 mean2

POPULATION

SAMPLECOMPARE

SAMPLE MEAN USING T- TEST

Hypothesis: Ho: 1 = 2 Ha: 1 # 2


21

21

1nn

Sp

xxt

21

21

1nn

S

xxt

Equal variance Unequal variance

Ho does not rejected, which suggest that mean Hb-pre Gianyar is not significantly differ from that of Karangasem

Group Statistics

135 11,729 1,0941 ,094296 11,616 1,0541 ,1076

KabupatenGianyarKarangasem

Hb. sbl intervensiN Mean Std. Deviation

Std. ErrorMean

Independent Samples Test

,055 ,815 ,788 229 ,432 ,1133 ,1439 -,1702 ,3968

,793 209,256 ,429 ,1133 ,1430 -,1685 ,3952

Equal variancesassumedEqual variancesnot assumed

Hb. sbl intervensiF Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper


Difference

t-test for Equality of Means

Two Dependent GroupsTwo Dependent Groups

Case 4: (DGK Data) Should we conclude that the Hbpre equal

to the Hbpost.

Hypothesis testing used is Paired samples T-Test

Hb-pre Hb-postcompare

Hypothesis: Ho: d = 0 Ha: d # 0



nSddt

Ho rejected; mean Hb-pre significantly differ from mean Hb-post

Paired Samples Statistics

11,682 231 1,0768 ,070812,358 231 1,1808 ,0777

Hb. sbl intervensiHb. stl intervensi

Pair1

Mean N Std. DeviationStd. Error

Mean

Paired Samples Test

-,6766 ,8396 ,0552 -,7855 -,5678 -12,248 230 ,000Hb. sbl intervensi -Hb. stl intervensi

Pair1

Mean Std. DeviationStd. Error

Mean Lower Upper


Difference

Paired Differences

t df Sig. (2-tailed)

More Then Two GroupsMore Then Two Groups

Case 6: (DGK Data) Should we concluded that the Hbpost

between gestation ages (Trimester) are equal.

Hypothesis testing used is One-way Anova

Hypothesis: Ho: 1 = 2= 3

Ha: not all equal


Ho rejected,which signify at least mean Hb from one trimester differ significantly from the other trimester

Descriptives

Hb. stl intervensi

14 12,450 1,0450 ,2793 11,847 13,053 10,3 14,1177 12,475 1,1452 ,0861 12,305 12,645 9,7 14,940 11,810 1,2518 ,1979 11,410 12,210 9,5 14,2

231 12,358 1,1808 ,0777 12,205 12,512 9,5 14,9

Trimester ITrimester IITrimester IIITotal

N Mean Std. Deviation Std. Error Lower Bound Upper Bound

95% Confidence Interval forMean

Minimum Maximum

ANOVA

Hb. stl intervensi

14,559 2 7,280 5,422 ,005306,122 228 1,343320,681 230

Between GroupsWithin GroupsTotal

Sum ofSquares df Mean Square F Sig.

Post Hoc Tests

Multiple Comparisons

Dependent Variable: Hb. stl intervensiLSD

-,0251 ,3217 ,938 -,659 ,609,6400 ,3598 ,077 -,069 1,349,0251 ,3217 ,938 -,609 ,659,6651* ,2029 ,001 ,265 1,065

-,6400 ,3598 ,077 -1,349 ,069-,6651* ,2029 ,001 -1,065 -,265

(J) Kelp. umur kehamilanTrimester IITrimester IIITrimester ITrimester IIITrimester ITrimester II

(I) Kelp. umur kehamilanTrimester I

Trimester II

Trimester III

MeanDifference

(I-J) Std. Error Sig. Lower Bound Upper Bound95% Confidence Interval

The mean difference is significant at the .05 level.*.

Mean Hb post women at 1st trimester is not different with the 2nd trimester; but… Mean Hb-post women at 2nd semester different from the 3rd trimester

lecture 9a (significancy test for categorical data)

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