Selasa, 30 September 2014

UJI HIPOTESIS KORELATIF

# TEST HYPOTHESES CORRELATION


Correlation A.Mengenal
What exactly is the correlation? Correlation is an analytical technique that is included in one measurement techniques associations / relationships (measures of association). Measurement of association is a general term that refers to a group of techniques in bivariate statistics used to measure the strength of the relationship between the two variables. Among the many techniques of measurement of the association, there are two very popular correlation techniques until now, namely the Pearson Product Moment Correlation and Spearman Rank Correlation. Measurement of the association was wearing a numeric value to determine the level of association or the strength of the relationship between variables. Two variables are said to be associated if one variable affects the behavior of other variables. If there is no effect, then the two variables are called independent.
Correlation helpful to measure the strength of the relationship between two variables (sometimes more than two variables) with certain scales, such as the data Pearson must scale interval or ratio; Spearman and Kendal using ordinal scale. Strong weak relationship was measured using the distance (range) 0 to 1. Correlations have the possibility of testing hypotheses two-way (two-tailed). Correlation unidirectional if the value of the correlation coefficient was found positive; otherwise if the value of the correlation coefficient is negative, correlation is called not unidirectional. What is meant by the correlation coefficient is a statistical measurement kovariasi or association between two variables. If the correlation coefficient is found not equal to zero (0), then there is a relationship between two variables. If the correlation coefficient was found +1. then the relationship is referred to as a perfect correlation or perfect linear relationship with a slope (slope) is positive. On the contrary. if the correlation coefficient is found -1. then the relationship is referred to as a perfect correlation or perfect linear relationship with a slope (slope) is negative. In a perfect correlation is not needed anymore testing hypotheses about the significance between variables are correlated, because the two variables have a perfect linear relationship. This means that the variable X has a very strong relationship with the variable Y. If the correlation is equal to zero (0), then there is no relationship between the two variables.
B.Kegunaan
Correlation measurements are useful to measure the strength (strength) and the direction of the relationship the relationship between two or more variables. Example: measure the relationship between variables, for example: work motivation and productivity and the quality of service and customer satisfaction. This measurement is the relationship between two variables for each case will result in a decision, including: a) The relationship between the two variables do not exist; b) The relationship between the two variables is weak; c) The relationship between the two variables is strong enough; d) strong relationship between the two variables; and e) The relationship between the two variables is very kuat.Penentuan is based on criteria that indicate if the relationship is close to 1, then the relationship is getting stronger; conversely if the relationship is close to 0, then the relationship is getting weaker

C.Konsep Linearity and Correlation
There is a close relationship between the understanding of correlation and linearity. Pearson, for example, shows the strength of the linear relationship in the two variables. Yet if the normality assumption is wrong then the correlation value will not be sufficient to prove a link linearity. The assumption of linearity means in a straight line relationship between the variables. Linearity between the two variables can be assessed through observation bivariate scatterplots. If both normally distributed variables and relate linearly, then the scatterplot oval; if not normal scatterplot is not oval.
In praktinya sometimes the data used will produce a high correlation but the relationship is not linear; or conversely a low correlation but a linear relationship. Thus, in order linearity of the relationship are met, then the data used must have a normal distribution. In other words, the correlation coefficient is only a summary statistic that can not be used as a means to check the data individually.

D.Asumsi - Assumptions In Correlation
Assumption - the basic assumptions of correlation among them are: The two variables are independent of one another, meaning that each of the variables are independent and not dependent on each other. No terms dependent and independent variables. Data for both variables normal distribution. Data that have a normal distribution of data means that distribution is perfectly symmetrical. If used in common parlance is called a bell-shaped curve.

Correlation E.Karakteristik
Correlations have characteristics such as:
  1. Correlation Range: Range (range) correlations ranging from 0 to 1. The correlation can be positive and can also be negative.
  2. Equals Zero Correlation: Correlation is equal to 0 has the meaning there is no relationship between the two variables.
  3. Correlation Equals One: correlation equal to + 1 means that the two variables have a perfect linear relationship (straight line) is positive. Perfect correlation like this has meaning if the value of X goes up, then Y also rose.
  4. Correlation equals minus one: that the two variables have a perfect linear relationship (straight line) is negative. Perfect correlation like this has meaning if the value of X rises, the Y down and vice-versa.

F.Pengertian correlation coefficient
The correlation coefficient is the covariance statistical measurements or association between two variables. The magnitude of the correlation coefficient ranges from +1 s / d -1. The correlation coefficient indicates the strength (strength) linear relationship and the direction of the relationship between two random variables. If the correlation coefficient is positive, then the two variables have a unidirectional relationship. This means that if the value of the variable X is high, then the value of the variable Y will be high anyway. Conversely, if the correlation coefficient is negative, then the two variables have an inverse correlation. This means that if the value of the variable X is high, then the value of the variable Y will be low and vice-versa. To facilitate interpretation of the strength of the relationship between two variables, the authors provide the following criteria (Sarwono: 2006):
0
> 0 to 0.25
> From 0.25 to 0.5
> 0.5 to 0.75
> 0.75 to 0.99
1
There is no correlation between the two variables
The correlation is very weak
correlation enough
The strong correlation
The correlation is very strong
perfect correlation

G.Signifikansi / Probability / Alpha
What is the significance of it? In common English, the word "significant" has an important meaning; is in the statistical sense of the word has the meaning of "right" is not based on chance. The research results can be correct but not essential. Significance / probable / α gives an overview of how the results of the research have the opportunity to correct. If we choose a significance of 0.01, then it means we determine the results of the research have the opportunity to correct it later at 99% and for one of 1%. 99% is called the level of interest (confidence interval); was 1% is called fault tolerance.
Generally we use the figure of significance of 0.01; 0.05 and 0.1. Consideration of the use of these figures are based on a confidence level (confidence interval) desired by the researcher. Figures 0,01 significance has the sense that the level of trust or common language our desire to obtain truth in our research is at 99%. If the figure of significance of 0.05, then the confidence level is 95%. If the significance of the figure of 0.1, the confidence level is 90%.
Another consideration is regarding the amount of data (sample) to be used in research. The smaller the number of significance, then the sample size will be even greater. Conversely the greater the number of significance, then the sample size will be smaller. Unutuk scored significance, there are generally required sample size is large. For testing in IBM SPSS used the following criteria:
  1. If the figures of significance to research <0.05, significant relationship between both variables.
  2. If significant numbers of research results of> 0.05, then the relationship between the two variables were not significant

H.Membuat Interpretation In Correlation
There are three interpretations correlation analysis, covering: First, look at the strength of relationship between two variables; second, the significance of the relationship; and third, see the direction of the relationship.
To make an interpretation the strength of the relationship between two variables is done by looking at the correlation coefficient calculations using the following criteria: a) If the number of correlation coefficient indicates 0, then the two variables do not have a relationship; b) If the number of correlation coefficient close to 1, then the two variables have a stronger relationship; c) If the number of correlation coefficient close to 0, then the two variables have a relationship growing weaker; d) If the number of the correlation coefficient is equal to 1, then the two variables have a perfect positive linear relationship; e) If the number of correlation coefficient equal to -1, then these two variables have a perfectly negative linear relationship.
The next interpretation of the significance of the relationship between two variables based on the significance of the numbers resulting from the calculation under the conditions as discussed above. This interpretation will prove whether the relationship between the two variables is significant or not.
The third interpretation see the direction of correlation. In correlation there is a two-way correlation, ie one way and not unidirectional. At IBM SPSS it is characterized by two tailed message. Directions correlation seen from the figures the correlation coefficient. If the correlation coefficient is positive, then the relationship between the two variables in the same direction. Unidirectional means that if the variable X value is high, then the variable Y is also high. If the correlation coefficient is negative, then the relationship between the two variables is not unidirectional. No way it means that if the variable X value is high, then the variable Y will be low.
In the case of, for example, the relationship between customer satisfaction and loyalty of 0.86 with a significance of the numbers 0 will have a meaning that the relationship between the variables of customer satisfaction and loyalty is very strong, significant, and direction. Conversely in the case of the relationship between the variables with the price of buying interest at -0.86, with a significance of the numbers 0; then the relationship between the two variables is very strong, significant and not the direction.

I.Korelasi Pearson
Pearson Product Moment Correlation, a parametric measurement, will produce a correlation coefficient which serves to measure the strength of the linear relationship between two variables. If the relationship of two variables is not linear, then the Pearson correlation coefficient does not reflect the strength of the relationship between two variables being studied; although the two variables have a strong relationship. The symbol for the Pearson correlation is "p" when measured in the population and the "r" when measured in the sample. Pearson has a range between -1 to + 1. If the correlation coefficient is -1, then the two variables studied had a perfectly negative linear relationship. If the correlation coefficient is +1, then the two variables studied have a perfect positive linear relationship. If the correlation coefficient shows the number 0, then there is no relationship between the two variables studied. If a perfect linear relationship of two variables, the distribution of these data will form a straight line. Yet in fact we will be difficult to find data that can form a linear line perfectly.
The data used in the Pearson correlation should meet the requirements, including the following: a) Scale interval / ratio, b) Variable X and Y must be independent of one another, c) quantitative variables must be symmetrical. Assumptions in Pearson, including the following: a) There is a linear relationship between X and Y, b) normally distributed data, c) variables X and Y symmetrical. Variable X does not function as the independent variable and Y as the dependent variable, d) Sampling representative, c) the second variant of the same variable
Pearson Correlation Procedures
In this case we will look at the relationship between a variable number of visits to point cellular telephone service providers X with the level of satisfaction. To see these relationships we are making steps as below:
First: prepare the data
Second: create a design variable
Third: entering data start numbers 1 through 11 as below
Fourth: perform analytical procedures as below:
    • Analyse> Correlate> Select the sub menu bivariate
    • Move variables to visit and satisfaction to the Variable column
    • Correlation Coefficient: select Pearson
    • Test of Significance: select Two Tailed> Check Flag significant correlation
    • Option: Missing Values, choices: Exclude cases pairwise, press Continue
    • click Ok
    • Once processed, then out the output of analytical results.
Fifth: make interpretation
How to make an interpretation as follows:
  1. First: Seeing the strength of the relationship between the variable product and sales. Figures obtained by making a cross-tabulation between the Product and Sales as below:
From the table, visible figure Pearson correlation coefficient of .881 **. That is a big correlation between a variable number of visits and the satisfaction rate is at 0.881 or very strong because of approaching the number 1. Signs two stars (**) means significant at the significance correlation of 0.01 and have the possibility of two-way (two-tailed). (Note: If there is no sign of the two stars, it automatically significance of 0.05)
  1. Second: Seeing the significance of relations between the two variables. The numbers are as follows:
Based on the criteria of existing relationship between the two variables is significant because the numbers significance of 0.000 <0.001. (If there is no sign of the two stars, it automatically significance of 0.05). Relations between the two variables have two-way (two-tailed), which may be one way and not unidirectional.
  1. Third: Looking at the correlation between the two variables. Directions correlation seen from the figures the correlation coefficient is positive or negative result. Because the number of correlation coefficient is positive, namely 0.881; the correlation of the two variables are unidirectional. It means if the value of the high number of visits, then the value will be high levels of satisfaction anyway.
  2. In conclusion: The correlation between variable number of visits and the satisfaction level is very strong, significant, and direction.

J.Korelasi Spearman
Spearman's correlation is a non-parametric measurements. The correlation coefficient r mempuyai symbol (rho). Measurements using Spearman correlation coefficient was used to assess how well their monotonic function (a function of the corresponding command) arbitrarily used to describe the relationship between two variables without making assumptions frequency distribution of the variables studied. The value of the correlation coefficient and the assessment criteria strength of relationship between two variables the same as those used in the Pearson correlation. Calculations done in the same way with Pearson, the difference lies in the conversion of data into a form ranking before the calculated correlation coefficient. That is why this correlation is referred to as Spearman Rank Correlation
The data used for the Spearman correlation should ordinal scale. Unlike the Pearson correlation, Spearman Correlation does not require the assumption of a linear relationship in the variables measured and does not need to use the data interval scale, but simply by using ordinal scale data. The assumptions used in this correlation is level (rank) next must indicate the position of the same distance on the measured variables. If using a Likert scale, then the distance scale used must be the same. Also, data should not normally distributed.
Spearman's correlation procedure
In this case we will look at the relationship between the variables attitude towards work performance. To see these relationships we are making steps as below:
First: prepare the data
Second: create a design variable
* Give Values ​​with the following conditions: a very negative attitude-code 1, negative-code 2, neutral-code 3, 4 and the positive-code-code is very positive 5
** Give Values ​​with the following conditions: extremely low stance give the code 1, the low-code 2, please give a code 3, 4 and high-code-code is very high 5
Third: entering data start numbers 1 to 30 as below
Fourth: perform analytical procedures as below:
    • Analyse> Correlate> Select the sub menu bivariate
    • Move variables to the attitude and performance to Variable column
    • Correlation Coefficient: select Spearman
    • Test of Significance: select Two Tailed> Check Flag significant correlation
    • Option: Missing Values, choices: Exclude cases pairwise, press Continue> Click Ok
    • Once processed, then out the output of analytical results.
Fifth: interpret results
How to make an interpretation as follows:
  1. First: Seeing the strength of the relationship between the variables attitude towards work with employee performance. Figures obtained by making a cross-tabulation between the two variables is shown below:
From the table, visible figure Spearman correlation coefficient of .329. That is a big correlation between variable variable attitude towards work with the employee's performance is at .329 or strong enough. Correlations have the possibility of two-way (two-tailed).
  1. Second: Seeing the significance of relations between the two variables. The numbers are as follows:
Based on the criteria of existing relations between the two variables is not significant because the number of significance for 0.076> 0.05. (If there is no sign of the two stars, it automatically significance of 0.05). Relations between the two variables have two-way (two-tailed), which may be one way and not unidirectional.
  1. Third: Looking at the correlation between the two variables. Directions correlation seen from the figures the correlation coefficient is positive or negative result. Because the number of correlation coefficient is positive, namely 0.329; the correlation of the two variables are unidirectional. It means if a positive attitude towards work (4), then the performance will be high (4).
  2. In conclusion: The correlation between variable variable attitude towards work with the employee's performance is strong enough, not significant and direction.
K.Korelasi Kendall's Tau
Kendall's Tau correlation is used to measure the strength of relationship between two variables. The same correlation with Spearman correlations were categorized as non-parametric statistics. The data used ordinal scale and does not have normal distribution.
Kendall's Tau correlation procedure
In this case we will look at the relationship between the variables attitude towards work performance. To see these relationships we are making steps as below:
First: prepare the data
Second: create a design variable
Third: entering data start numbers 1 to 30 as below
Fourth: do the analysis with the following procedures:
  • Analyse> Correlate> Select the sub menu bivariate
  • Move variables to price and buy into the Variable column
  • Correlation Coefficient: select Kendall's Tau
  • Test of Significance: select Two Tailed> Check Flag significant correlation
  • Option: Missing Values, choices: Exclude cases pairwise, press Continue
  • click Ok
  • Once processed, the exit output analysis results.
Fifth: make interpretation
How to make an interpretation as follows:
  1. First: Seeing the strength of the relationship between price and variable attitudes toward buying decision. Figures obtained by making a cross-tabulation between the variables attitude towards the price and the buying decision as below:
From the table above, looks figures Pearson correlation coefficient of .459 **. That is a big correlation between a variable number of visits and the satisfaction level is equal to 0,459 or strong enough. Sign two stars (**) means significant at the significance correlation of 0.01 and have the possibility of two-way (two-tailed). (Note: If there is no sign of the two stars, it automatically significance of 0.05)
  1. Second: Seeing the significance of relations between the two variables. The numbers are as follows:
Based on the criteria contained significant relationship between the two variables because the number of significance 0.006 <0.001. (If there is no sign of the two stars, it automatically significance of 0.05). Relations between the two variables have two-way (two-tailed), which may be one way and not unidirectional.
  1. Third: Looking at the correlation between the two variables. Directions correlation seen from the figures the correlation coefficient is positive or negative result. Because the number of correlation coefficient is positive, ie 0,459; the correlation of the two variables are unidirectional. That is if the attitude of the high prices, the decision to buy will be higher as well.
  2. In conclusion: The correlation between price and variable attitudes toward buying decision is quite strong, significant, and direction.

Partial L.Korelasi
Partial correlation is a correlation between two variables when the effects of one or more variables related to the role as a third variable controlled or diparsialkan. The aim is to obtain a unique variant in the relationship between the two variables are correlated and eliminate variance third variable that can affect the relationship between the two variables. Variables examined must kontinus and interval scale. The relationship between variables is linear and the data should be normally distributed. Partial correlation is only used if a third variable is linked to one of the variables that we have correlated.
Partial Correlation Procedures
In this case we will look at the relationship between the variables visits to the service points for the organizer mobile phone X with the level of satisfaction while getting services by controlling the variable responses given by the employees of the service point. To see these relationships we are making steps as below:
First: prepare the data
Second: create a design variable
Third: entering data start numbers 1 through 11 as below
Fourth: do the analysis with the following procedures:
To perform the analysis lakukankanlah steps as follows:
  • Analyse> Correlate> Partial
  • Move variables visits and satisfaction to the Variable column
  • Move the variable response to the column Controlling For
  • Test of Significance: select Two Tailed
  • Option: Statistics select Zero Order Correlation and the Missing Values, select Exclude cases pairwise, press Continue
  • Click Ok to be processed
  • Once processed, the output (output) the results of the analysis as follows:
Fifth: make interpretation
Interpretation of the results of the partial correlation can be performed using the figures in the table below.
The correlation between the variable number of visits and the level of satisfaction - 0,641. This means that both variables have a strong relationship, but not the direction. Not unidirectional means if the number of visits to the point of service used by the organizers to accommodate complaints - customer complaints is high, then the level of satisfaction with the service will be low. The third variable customer responses, if not controlled will affect the relations between the two variables such as the significance of shows at 0.046 <0.05. This means that the presence of the three variables are significant for it to be beyond our control; because the level of satisfaction is not only related to the number of visits but also relates to how employees respond to customer complaints that come to the point of the service.
M.SOAL EXERCISE
  1. Correlation is ...
  2. Correlation measurement is useful for ...
  3. What is the Correlation Coefficient
  4. Significance / probable / α is
  5. The significance criteria for testing the correlation in SPSS is ...
  6. Pearson Product Moment Correlation, which is p
  7. Spearman correlations were used to ...
  8. Mention the steps Spearman correlation analysis ...
  9. Correlation Keanall Tau used to ...
  10. Partial correlation is ...