Kls Int Mdl Riset Stat Inferensial Nov 08

8/21/2019 Kls Int Mdl Riset Stat Inferensial Nov 08

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Zarni Amri Inferential statistics 1

Inferential statistics

Zarni Amri


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Inference (statistical)

The process of drawing

conclusions about a population of

observations from a sample ofobservation


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INFERENCE

population

statisticsX

S

P

infert

parametersample

sp


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Test Statistics

Number of variables

Data scale

numeric, category Sample size

Sampling methods (paired, unpaired;

dependent, independent; related,unrelated)


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SIGNIFICANCY STEPS

Determine null hypothesis

Determine alternative hypothesis

Determine significance levelStatistical calculation

Probability interpretation


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SOURCES OF DIFFERENCE

POPULATION DIFFERENCE

SAMPLING VARIATION

Both components are complementary


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Pop B

Pop ASp1

Sp2

Sp3

X1 S1 P1

X2 S2 P2

X3 S3 P3

Pop Difference

Sampling variation


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NULL HYPOTHESIS

Presumption of innocence

Sampling variation role

No group difference

A = B

RR = 1

OR = 1


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ALTERNATIVE

HYPOTHESIS

Depends on study direction

Two tailed test

A = B

RR = 1

One tailed test

A > BA < B

RR > 1 or RR < 1


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Two tailed test

One tailed test


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SIGNIFICANCE LEVEL

Sampling variation level

Type one error (false +)

Type two error (false -)

Depends on sample size

Depends on seriousness


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Hypotheses Testing

Signific (+) Not Sign. (-)

Signific (+)

(Reject H0)

POWER

(1-)

True positive

Type I error

()

Not Sign. (-)

(Accept H0)

Type II error

()

CON.LEVEL

(1- )

True negative

ACTUAL

TEST


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SIGNIFICANCE TEST

To conclude whether samples

difference is also true for population

PARAMETRIC METHODSNON PARAMETRIC METHODS


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BASIC PRINCIPLE

No perfect test

Only most appropriate test

Based on data and design

Should know all test types


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PARAMETRIC TESTS

Based on parameters

Numerical data

More sensitive tests

Normal distribution

Random sample derivation

No extremes value


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NON PARAMETRIC TESTS

No requirement needed

Categorical data

Numerical but not normally distributedCould be applied to all conditions

Rather less sensitive tests

Second choices


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PARAMETRIC TESTS

Difference of two means

(Big and small samples)

( independent and paired samples )

Analysis of varianceCorrelation & regression

Analysis of covariance


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Choosing statistical test for two variables

Data scale unrelated related correlation and

regression

Nominal X2 (2x2)

Fisher exact test

Mc. Nemar test Logistic Regression

Ordinal Kolmogorov-Smirnov test

Mann-Whitney U-test

- Uji Sign- Uji Wilcoxon

matched-paired

Spearman test

Numerikunpaired t-test paired t-test

- Pearsoncorrelation

- Linear reression- Multiple regression


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Data scale unrelated related

Nominal X2

(rxc)

Cochran Q test

Ordinal Kruskal-Wallis test Friedman test

NumericAnova Anova related

Choosing statistical test for two variables


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Is there any difference between mean age of shift

and non shift worker?

Tests of Normality

.113 88 .008

.186 89 .000

Kerja g ili r

ya

tidak

Usia responden

Statistic df Sig.

Kolmogorov-Smirnova

Li lli efors Significance Correctiona.

Group Statistics

89 35.39 8.08 .86

88 29.42 5.42 .58

Kerja gilir

tidak

ya

Usia responden

N Mean Std. Deviation

Std. Error

Mean

95% CI = mean + 1.96 SE = 35.39 + 1.96 x 8.08/89 =


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Tests of Normality

.186 89 .000

.113 88 .008

Kerja g ilir

tidak

ya

Usia responden

Statistic df Sig.

Kolmogorov-Smirnova

Li lli efors Signi ficance Correctiona.

Test Statisticsa

2121.500

6037.500

-5.274

.000

Mann-Whitney U

Wilcoxon W

Z

Asymp. Sig. (2-tailed)

Usia

responden

Grouping Variable: Kerja gil ira.

Tests of Normality

.146 177 .000Usia responden

Statistic df Sig.

Kolmogorov-Smirnova

Li ll iefors Significance Correctiona.


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Have you ever been this

tired???


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Hypothesis Testing

Univariat

Bivariat

Multi variate


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Bivariat: numeric vs cathegoric

E.g. To compare mean of Blood Pressure (numeric)in two groups: with therapy and without T/

PARAMETRIK

- 2 mean : t-distribution test

- > 2 mean : ANOVA

NON PARAMETRIK- 2 mean : Mann Whitney

- > 2 mean : Kruskal Wallis


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Tests of Normality

.186 89 .000

.113 88 .008

Kerja g ilir

tidak

ya

Usia responden

Statistic df Sig.

Kolmogorov-Smirnova

Li lli efors Signi ficance Correctiona.

Test Statisticsa

2121.500

6037.500-5.274

.000

Mann-Whitney U

Wilcoxon WZ

Asymp. Sig. (2-tailed)

Usia

responden

Grouping Variable: Kerja gili ra.

Group Statistics

89 35.39 8.08 .86

88 29.42 5.42 .58

Kerja gili r

tidak

ya

Usia responden

N Mean Std. Deviation

Std. Error

Mean

numeric vs category


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Example paired t-test

Pre-intervention LDL 177,3 + 31,8 mg/dL

Post-intervention LDL 155,6 + 32,5mg/dL

H1: Intervention LDL

Paired sample (pre-post intervention)

Distribution : KS normal

paired t-test, =0,05, p


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Tests of Normality

.127 30 .200* .971 30 .591

.130 30 .200* .958 30 .372

LDL pre

LDL post

Statistic df Sig. Statistic df Sig.

Kolmogorov-Smirnova

Shapiro-Wilk

This is a l ower bound of the true significance.*.

Lilliefors Significance Correctiona.

Paired Samples Statistics

174.2667 30 31.7750 5.8013

155.6333 30 32.5285 5.9389

LDL pre

LDL post

Pair

1

Mean N Std. Deviation

Std. Error

Mean

numeric vs numericUJI 2 PAIRED MEANS


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190.3636 11 17.4142 5.2506

166.3636 11 21.4209 6.4586

SBP1

SBP2

Pair

1


Std. Error

Mean

Paired Samples Correlations

11 .792 .004SBP1 & SBP2Pair 1

N Correlation Sig.

Paired Samples Test

24.0000 13.0920 3.9474 15.2047 32.7953 6.080 10 .000SBP1 - SBP2Pair 1

Mean Std. Deviation

Std. Error

Mean Lower Upper

95% Confidence

Interval of the

Difference

Paired Differences

t df Sig. (2-tailed)

Test : 2 PAIRED MEANS


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Group Statistics

11 190.36 17.41 5.25

11 166.36 21.42 6.46

GROUPPlacebo

HCT

SBPN Mean Std. Deviation

Std. ErrorMean

Independent Samples Test

.089

.769

2.883 2.883

20 19.200

.009 .009

24.00 24.00

8.32 8.32

6.64 6.59

41.36 41.41

F

Sig.

Levene's Test for

Equali ty of Variances

t

df

Sig. (2-tailed)

Mean Difference

Std. Error Difference

Lower

Upper

95% Confidence Interval

of the Difference

t-test for Equality of

Means

Equal variances

assumed

Equal variances

not assumed

SBP


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.089 .769 2.883 20 .009 24.00 8.32 6.64 41.36

2.883 19.200 .009 24.00 8.32 6.59 41.41

Equal variances

assumed

Equal variancesnot assumed

SBP

F Sig.

Levene's Test for

Equality of Variances

t df Sig. (2-tai led)

Mean

Difference

Std. Error

Difference Lower Upper

95% Confidence

Interval of the

Difference

t-test for Equali ty of Means


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Category >< Category, 2x2 tableKerja gilir * Insomnia/bukan Crosstabulation

34 55 89

38.2% 61.8% 100.0%

19 69 88

21.6% 78.4% 100.0%

53 124 177

29.9% 70.1% 100.0%

Count

% within Kerja gil ir

Count


Count


tidak

ya

Kerja

gilir

Total

tidak ya

Insomnia/bukan

Total

Chi-Square Tests

5.820b 1 .016

5.056 1 .025

5.882 1 .015

.021 .012

5.788 1 .016

177

Pearson Chi -Square

Continuity Correctiona

Likelihood Ratio

Fisher's Exact Test

Linear-by-Linear

Associat ion

N of Valid Cases

Value df

Asymp. Sig.

(2-sided)

Exact Sig.

(2-sided)

Exact Sig .

(1-sided)

Computed onl y for a 2x2 tablea.

0 cells (.0%) have expected count less than 5. The minimum expected count i s

26.35.

b.


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SPSS

Correlations

1.000 .040

. .884

16 16

.040 1.000

.884 .

16 17

Pearson Correlation

Sig. (2-tai led)

N

Pearson Correlation

Sig. (2-tai led)

N

age type A personali ty

age type B personali ty

age type A

personality

age type B

personality


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Descriptive Statistics

42.25 9.35 16

129.06 18.90 16

age type A personality

Rest Blood Pressure

type A personality

Mean Std. Deviation N

Correlations

1.000 .440

. .088

16 16

.440 1.000

.088 .

16 16

Pearson Correlation

Sig. (2-tai led)

N

Pearson Correlation

Sig. (2-tai led)

N

age type A personality

Rest Blood Pressure

type A personality

age type A

personali ty

Rest Blood

Pressure type

A personality


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Correlations

1.000 .035

. .560

279 279.035 1.000

.560 .

279 279

Correlation Coefficient

Sig. (2-tailed)

NCorrelation Coefficient

Sig. (2-tailed)

N

Anaemia status

Age (years)

Spearman's rho

Anaemia

status Age (years)

Correlations

1.000 .003

. .958

279 279

.003 1.000

.958 .

279 279

Pearson Correlation

Sig. (2-tai led)

N

Pearson Correlation

Sig. (2-tai led)

N

Anaemia status

Age (years)

Anaemia

status Age (years)

Pearson >< Mann Whitney reasons

haemoglobin

haemoglobin

haemoglobin


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Numerical vs Categorical

E.g. age between shift-non-shift workers

NORMALLY DISTRIBUTED

- 2 groups : t-distribution test- > 2 groups : ANOVA

NOT NORMALLY DISTRIBUTED

- 2 groups : Mann Whitney- > 2 groups : Kruskal Wallis


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Group Statistics

16 42.25 9.35 2.34

17 37.88 13.40 3.25

16 129.06 18.90 4.72

17 127.41 25.32 6.14

GRUP

A

B

A

B

age

Rest Blood Pressure

type A personal ity

N Mean Std. DeviationStd. Error

Mean


2.775 .106 1.080 31 .289 4.37 4.05 -3.88 12.62

1.091 28.657 .284 4.37 4.00 -3.82 12.56

.745 .395 .211 31 .834 1.65 7.82 -14.29 17.59

.213 29.516 .833 1.65 7.75 -14.18 17.49

Equal variances

assumed

Equal variances

not assumed

Equal variances

assumed

Equal variances

not assumed

age

Rest Blood Pressure

type A personality

F Sig.

Levene's Test for

Equali ty of Variances


Mean

Difference

Std. Error

Difference Lower Upper

95% Confidence

Interval of the

Difference

t-test for Equality of Means

ttest? Reasons?


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190.3636 11 17.4142 5.2506

166.3636 11 21.4209 6.4586

SBP1

SBP2

Pair

1


Std. Error

Mean

Paired Samples Correlations

11 .792 .004SBP1 & SBP2Pair 1 N Correlation Sig.

Paired Samples Test

24.0000 13.0920 3.9474 15.2047 32.7953 6.080 10 .000SBP1 - SBP2Pair 1

Mean Std. DeviationStd. Error

Mean Lower Upper

95% Confidence

Interval of the

Difference

Paired Differences


paired t-test? why ?


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Cathegoric vs Cathegoric

Rows x Column

2 x 2 table

eg. smoking exposure vs lung cancer

CHI-SQUARE

No NOL cell

No cell with expected value


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Z i A i I f ti l t ti ti 39

Category Age * Category of Blood Pressure Crosstabulation

Count

17 2 19

6 8 14

23 10 33

40

Category

Age

Total

140

Category of Blood

Pressure

Total

Chi-Square Tests

8.294b 1 .004

6.233 1 .013

8.577 1 .003

.007 .006

8.042 1 .005

33

Pearson Chi -Square

Continuity Correctiona

Likelihood Ratio

Fisher's Exact Test

Linear-by-Linear

Association

N of Valid Cases

Value df

Asymp. Sig.

(2-sided)

Exact Sig.

(2-sided)

Exact Sig.

(1-sided)

Computed only for a 2x2 tablea.

1 cells (25.0%) have expected count less than 5. The minimum expected count is

4.24.

b.

Chi-square test or fishers exact test Why ?

Kls Int Mdl Riset Stat Inferensial Nov 08

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