penelitian skripsi, tesis, disertasi - Analisis Statistik Dua Variabel: Satu Interval, Satu Ordinal

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Analisis Statistik Dua Variabel: Satu Interval, Satu Ordinal

Pada pemilihan analisis statistik jenis ini sebenarnya banyak sekali pemekaran yang harus saya sebutkan dalam postingan kali ini. Semoga usaha saya untuk membuat rangkuman ini tidak menjadikan saudara semua tambah bingung. Karena jenis ini memang tidak bisa seramping dari analisis dua variabel sebelumnya (Kedua-duanya interval, 2. Kedua-duanya nominal, 3. Kedua-duanya ordinal).

Semula saya rencanakan menjadi dua bagian, tapi karena kuatir malah membingungkan, maka saya jadikan menjadi satu artikel. Secara garis besar jenis analisis dua variabel yang terdiri dari satu variabel interval dan satu lagi berupa variabel ordinal adalah sebagai berikut.

A. ordinal variable is two-point variabel

Any two-point variable meets the criteria for an intervally-scaled variable. You will be branched to the interval variable branch.

1. Made Distinction Between a Dependent and an Independent Variabel

a. The relationship as linear

Statistical Test	Regression coefficient (b or beta) Beta is a standardized version of b.
Statistical Measure	F test (F equals t-squared)
SPSS	reggression
SAS	GLM, REG

b. The relationship as not linear

Statistical Test	Coefficients from curvilinear regression (b or beta) (Beta is the standardized version of b. The type of curvilinear regression referred to here is also known as polynomial regression.)
Statistical Measure	F test (F equals t-squared)
SPSS	reggression, ONEWAY
SAS	GLM

2. No Distinction Between a Dependent and an Independent Variable

a. Means on the two variables are equal

Statistical Test	(none)
Statistical Measure	t-test for paired observations The t test for paired observations is appropriate for parallel measures from matched cases as well as for repeated measures on a single set of cases.
SPSS	T-TEST
SAS	-

b. Means on the two variables are not equal

1) The relationship as linear = What the measure?

· Agreement, Should there be a penalty if the variables do not have the same distributions?

Ya	Statistical Test	Robinson's A, or the intraclass correlation coefficient (The intraclass correlation coefficient is a biased estimator.)
	Statistical Measure	F test
	SPSS
	SAS
Tidak	Statistical Test	Krippendorff's coefficient of agreement
	Statistical Measure	(None)
	SPSS
	SAS

· Covariation, How many of the variables are dichotomous?

- Tidak ada perbedaan (None)

Statistical Test	Pearson's product moment r
Statistical Measure	Do Fisher's r to Z transformation and refer the critical ratio of Z to a table of the unit normal curve.
SPSS	PEARSON CORR, CROSSTABS
SAS	CORR

- Satu variabel (Is the dichotomous variable a collapsing of a continuous variable and do you want to estimate what the correlation would be if it were continuous?)

Ya	Statistical Test	Biserial r (This measure depends on a strict assumption of the normality of the continuous variables that have been dichotomized. Furthermore, the sampling error is large when dichotomies are extreme.)
	Statistical Measure	Refer critical ratio for biserial r to a table of the unit normal curve
	SPSS
	SAS
Tidak	Statistical Test	Pearson's product moment r (equals point biserial r) Pearson's r in this case is mathematically equivalent ro a point biserial r; the tests are almost equivalent.
	Statistical Measure	Refer critical ratio for point biserial r to a table of the unit normal curve
	SPSS
	SAS

- Kedua Variabel (Are the variables collapsings of continuous variables and do you want to estimate what the correlation would be if they were continuous?)

Ya	Statistical Test	Tetrachoric r (This measure depends on a strict assumption of the normality of the continuous variables that have been dichotomized. Furthermore, the sampling error is large when dichotomies are extreme.)
	Statistical Measure	Refer critical ratio for tetrachoric r to a table of the unit normal curve
	SPSS
	SAS
Tidak	Statistical Test	Pearson's product moment r (equals phi) - (Pearson's r in this case is mathematically equivalent ro a point biserial r; the tests are almost equivalent.)
	Statistical Measure	Refer critical ratio for phi to a table of the unit normal curve
	SPSS (Critical ratio for phi)	SPSS: CROSSTABS
	SAS (Critical ratio for phi)	SAS: FREQ

2) The relationship as not linear

Sorry, there is no known analysis for this case.

B. ordinal variable is not two-point variable

1. Treat the ordinal variable with normally distributed variable

Statistical Test	Jaspen's coefficient of multiserial correlation (This is a biased estimator. Jaspen's coefficient is the product moment correlation between the interval variable and a transformation of the ordinal variable. The magnitude of this statistic is sensitive to the assumption of normality.)
Statistical Measure	Do Fisher's r to Z transformation and refer the critical ratio of Z to a table of the unit normal curve
SPSS	-
SAS	-

2. Treat the ordinal variable without normally distributed variabel

Statistical Test	Mayer and Robinson's M
Statistical Measure	Do Fisher's r to Z transformation and refer critical ratio of Z to a table of the unit normal curve
SPSS	-
SAS	-

Sumber:

Draper, N. R., and Smith, H. Applied Regression Analysis. New York: Wiley, 1966.

Freeman, L. C. Elementary Applied Statistics for Students in Behavioral Science. New York: Wiley, 1965.

Harshbarger, T. R. Introductory Statistics: A Decision Map. New York: Macmillan, 1971.

Hays, W. L. Statistics for the Social Sciences. Second edition. New York: Holt, Rinehart, and Winston, 1973.

Krippendorf, K. Bivariate agreement coefficients for reliability of data. In Sociological Methodology: 1970, edited by E. F. Borgatta and G. W. Bohrnstedt. San Francisco: Jossey-Bass, 1970.

Mayer, L. S., and Robinson, J. A. Measures of association for multiple regression models with ordinal predictor variables. In Sociological Methodology 1978, edited by K. F. Schuessler. San Francisco: JosseyBass, 1977.

McNemar, Q. Psychological Statistics. Fourth edition. New York: Wiley 1969.

Nunnally, J. C. Psychometric Theory. Second edition. New York: McGraw-Hill, 1978.

Robinson, W. S. The statistical measurement of agreement. American Sociological Review 22 (1957).

http://www.socialresearchmethods.net

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