Chapter5.2-Inferential Statistics.pdf

Truong Thi Hoa, Ph D 1 1 Preparing data for analysis 2 Descriptive statistics 3 Inferential statistics 4 Testing the measurements 5 Testing research model and hypotheses 2 Inferential statistics take[.]

Truong Thi Hoa, Ph.D 1

1 Preparing data for analysis

2 Descriptive statistics

3. Inferential statistics

4 Testing the measurements

5 Testing research model and hypotheses

Inferential statistics: take data from samples and make

generalization about a population

Two main areas

ØParameter estimation

ØHypothesis testing

Hypothesis testing

§ State your research hypothesis as a null hypothesis (Ho) and

alternate hypothesis (Ha or H1)

§ Set the significance level (α)

§ Perform an appropriate statistical test

§ Define the critical value (z-statistics or t-statistics)

§ Draw the conclusion

Hypothesis testing

Null hypothesis (H 0 )

-No statistical relationship or significance between variables

-Assumed to be true until there is evidence to suggest otherwise

Alternative hypothesis (H 1 )

-The initial hypothesis that predicts a relationship between variables

(the research analysis)

î í

ì

¹

=0 1

0:

:

q q

Reject H0P-value >𝛼: Fail to reject H0

Hypothesis testing with SPSS

Ordinal and nominal variable

Ø testing if there exist associations between variables

Testing relationship of nominal-nominal variables and nominal-ordinal

variable (Chi-square test)

Testing relationship of ordinal-ordinal variable (gamma, Sommers’d,

Hypothesis testing with SPSS

Ordinal and nominal variable

Ø testing if there exist associations between variables

Ho: there is no associations between variables

H1 (Ha): There is an association between two variables

Working with SPSS

nominal-ordinal variables

Analyze → Descriptive Statistics → Crosstabs

For example: open file thongke.sav

Ha: There is an association between gender and educational levels

Working with SPSS (nominal-ordinal variables)

P-value > α (0.05) Fail to reject H0èDo not have the evidence to

conclude there is an association between gender and educational level

Test the following hypothesis

Two ordinal variables

Ø testing if there exist associations between tow ordinal variables

Ho: there is no associations between variables

H1 (Ha): There is an association between two variables

Ø Using Goodman và Kruskal’s gamma, Sommers’d, Kendall’s tau-d

ØIf p-value (sig) < 𝛼 → Reject H0; the evidence favors H1

Testing relationship of two ordinal variables

Analyze → Descriptive Statistics → Crosstabs

Ha: There is an association between educational level groups and age group

Testing relationship of two ordinal variables

P-value < α (0.05) Reject H0èhave the evidence supports that there is an association between educational level group and age group

Ø one sample t-test

ØIf p-value (sig) < 𝛼 → Reject H0; the evidence favors H1

Numerical variables

Testing mean difference: one sample

Analyze -> Compare Means -> One-Sample T Test

Example:

H0: Tri trung binh cua tuoi=28; H1: Trị trung bình của tuoi ≠ 28

Numerical variables

Testing mean difference: one sample

P-value < α (0.05) Reject H0

→Accept Ha

Numerical variables

Testing mean differences of two independent groups

Ø Hypotheses

H0: µ1 = µ2 (the means of two groups are equal)

H1: µ1 ≠ µ2 (the means of two groups are not equal)

Øindependence t-test

Levene’s test for equality of variance

H0: σ12 - σ22 = 0 (the variances of group 1 and 2 are equal)

H1: σ12 - σ22 ≠ 0 (the variances of group 1 and 2 are not equal)

ØIf p-value (sig) < 𝛼 → Reject H0; the evidence favors H1

Testing mean differences of two independent groups

Analyze -> Compare Means -> Independent-Sample T Test

Numerical variables

Testing mean differences of two independent groups

Analyze -> Compare Means -> Independent-Sample T Test

Numerical variables

Testing mean differences of paired data

Data from the same individuals, objects (exp: two time points)

Ø Hypotheses

H0: µa = µb ("the paired means are equal")

H1: µa ≠ µb ("the paired means are not equal")

Ø Paired-sample t-test

ØIf p-value (sig) < 𝛼 → Reject H0; the evidence favors H1

Numerical variables

Testing mean difference: Paired data

Analyze -> Compare Means -> Paired-sample T Test

Using testpaired.sav

Numerical variables

Testing mean difference: Paired data

significantly positive correlation

Numerical variables

ØTesting mean differences between several groups

Ø Hypotheses

H0: µ1 = µ2 = µ3 = = µk (The means of all k groups are equal)

H1: At least one µi different (At least one of the means is not equal to the

others")

Ø ANOVA test

ØIf p-value (sig) < 𝛼 → Reject H0; the evidence favors H1

ØPost-hoc test

ANOVA test

Analyze -> Compare Means -> One-way ANOVA

Using thongke.sav

ANOVA test

Fail to reject H0 -> No further tests

Hoàng Trọng và Chu Nguyễn Mộng Ngọc (2008) Phân tích dữ liệu nghiên cứu với

SPSS NXB Hồng Đức.

Nguyễn Đình Thọ (2009) Phương pháp nghiên cứu khoa học trong kinh doanh—Thiết

kế và thực hiện NXB Lao động Xã hội.