相关系数种类(Types of correlation coefficients)

相关系数种类（Types of correlation coefficients）

Types of correlation coefficients

(I) Pearson product difference correlation (K. Pearson

product-moment correlation; R)

1. X variables: isometry, ratio variables (continuous

variables)

2. Y variables: isometry, ratio variables (continuous

variables)

3. formula:

4. characteristics: numerical stability, standard error.

5. cases: the relationship between working hours and income.

(two) Spearman rank correlation (Spearman rank correlation;

RS)

1. X variables: ordinal variables

2. Y variables: ordinal variables

3. formula:

(1) without the same rank: (D is the rank difference of two

variable symmetry)

(2) people with the same grade:

T: the number of people who receive the same grade.

4. features: suitable for two raters to evaluate N pieces, or

the same rater, two times to evaluate N pieces.

5. cases: evaluation of N students' works by two reviewers.

(three) Kendall rank correlation (Kendall's coefficient of

rank correlation; (tau))

1. X variables: human order variables

2. Y variables: human order variables

3. formula: S: rank ordinal quantity; N: the number of persons

evaluated or the number of works

4. features: quite simple

5. cases: evaluation of N students' works by two reviewers.

(four) Kendall concordance coefficient (the Kendall's

coefficient of concordance; W)

1. X variables: ordinal variables

2. Y variables: ordinal variables

3. formula:

(1) without the same grade:;

(2) people with the same grade:;;

K: the number of raters; N: the number of persons being

evaluated or the number of entries

4. features: especially for the inter rater reliability

(interjudge reliability); test the consistency of the

evaluation of N works by many reviewers.

5. cases: evaluation of N students' works by multi site

evaluation.

(five) Kappa consistency coefficient (K coefficient of

agreement; K)

1. X variables: categorical variables

2. Y variables: categorical variables

The 3. formula: the Kappa consistency coefficient is the ratio

of the percentage of the actual evaluation of the raters to the

percentage of the maximum possible number of raters evaluated

by the raters (Lin Wei, 1992). Formula for:

P (A): the percentage of K rater ratings;

N: total number; K: rater number; m: rating category; N: fine

grid data

P (E): K score raters can theoretically assess the percentage

of consistency; when the rater's rating is exactly the same,

then K=1, when the rater's rating is completely inconsistent,

then K=0.

； ；

4. characteristics: the Kendeer harmony coefficient, the score

is limited in the evaluation object can be evaluated. That is,

can list the order. However, in some cases cannot be assessed

object list rank order, and can only be classified in a category,

at this time, you must use Kappa to indicate the consistency

coefficient, the consistency of the relationship between the

score.

5. cases: K psychiatrists, N patients were classified into m

categories of mental illness after diagnosis.

(six) two series correlation (biserial correlation; RBIs)

1. X variables: anthropogenic two variables (nominal

variables)

2. Y variables: continuous variables (isometric, ratio

variables)

3. formula:

4. features: use in project analysis; standard error is large;

RBIs may be greater than 1.

5. cases: the relationship between IQ and academic achievement

or not.

(seven) point two series correlation (point-biserial

correlation; rpq)

1. X variables: real two variables (nominal variables)

2. Y variables: continuous variables

3. formula:

Table 1: the average of the first class; the mean of the first

class; St: the standard deviation of the total fraction;

P: Table 1 percentage of the number of people; Q: percentage

of people in table second.

4. characteristic: standard error is smaller than rbis.

5. cases: the relationship between gender (male, female) and

income.

(eight) correlation (phi coefficient;)

1. X variables: real two variables (nominal variables)

2. Y variables: real two variables (nominal variables)

A

B

C

D

3. formula:

4. characteristics: closely related to Chi square test.

5. cases: parental parenting style (authoritative,

democratic).

(nine) contingency correlation (contingency coefficient; C)

1. X variables: real two or more nominal variables

2. Y variables: real two or more nominal variables

3. formula: the maximum value of C is N, and the total number

is

4. characteristics: closely related to Chi square test.

5. cases: the attitude of the people (teachers and students)

towards the implementation of the policy (agreement, no opinion,

no agreement).

(ten) four point correlation (tetrachoric correlation; TET)

1. X variables: human two nominal variables (raw data are

equidistant variables)

2. Y variables: human two nominal variables (raw data are

equidistant variables)

A

B

C

D

3. formula:

4. cases: academic achievement (pass, fail) and IQ (high, low)

relationship.

(eleven) net correlation (Partial correlation; r12.3)

1. X variables: continuous variables

2. Y variables: continuous variables

3. formula: (significant test t =)

The 4. characteristic: removing the important influence

factors related to the two variables, the relationship between

the two variables can be obtained.

5.: get rid of the influence of intelligence, for mathematics

and Chinese achievement related.

(twelve) curve correlation or correlation ratio (correlation

ratio;)

1. X variables: continuous variables

2. Y variables: continuous variables

3. formula:

The 4. characteristic: with the increase of X variables, the

Y variable increases first, and then begins to decline after

being added to a certain stage. The relationship between the

two variables is called curve correlation or correlation ratio.

5. cases: the relationship between work efficiency and anxiety.

The correlation coefficient of the variable type, were

summarized as shown in table 14-1:

Table for details of all relevant variables 14-1 finishing

X

Y

Nominal variable

Order variable

Variables above equidistant

Nominal variable

Contingency correlation

Related

Kappa consistency coefficient

Four points correlation

Point two series correlation

Two series correlation

Multiple series correlation

Order variable

Spearman rank correlation

Kendall rank correlation

Kendall concordance coefficient

Variables above equidistant

Point two series correlation

Two series correlation

Multiple series correlation

Pearson product moment correlation

Net correlation

Correlation ratio

The characteristics of product difference correlation

coefficient

(I).

(two) the value of correlation coefficient is closely related

to the number of N (number).

1. it is known from the formula that N is one of the important

factors determining the R value of correlation coefficient.

2. the magnitude of the R value does not mean that there is a

high correlation or low correlation between the two variables

(because it is likely to be caused by the probability), and the

size of the sample (N) and the significant level should be

considered again.

(1) in general, the smaller the N, the correlation coefficient

r value must be larger, can say the relationship between the

two variables; on the contrary, the greater the N, the

correlation coefficient cannot be too large, we have two

variables related to existence.

(2) the smaller the value, the greater the value of the phase

relationship, and the relative existence. As shown in table

14-2:

Tables 14-2, N and R

N

DF

=.05

=.01

Three

One

.997

.999

Five

Three

.979

.959

Ten

Eight

.632

.765

Thirty

Twenty-eight

.361

.463

One hundred and two

One hundred

.195

.254

(three) the degree of correlation is not proportional to R. The

correlation coefficient is only an index indicating whether the

two variables are closely related, so the correlation

coefficient can not be regarded as a ratio or an isometry

variable. Such as: r1=.80, r2=.20, can not be said that the

value of R1 is four times of r2.

(four) there is a relationship, but does not mean that there

is a causal relationship. Two events occur at the same time,

or happen before and after, we can only say that the two events

are related, but not necessarily there is a causal relationship

exists.

One