Showing posts with label Statistics Science. Show all posts
Showing posts with label Statistics Science. Show all posts
Feb 20, 2011
Regresi Analysis
A. UNDERSTANDING REGRESSION
In general there are two kinds of relationship between two or more variables, namely the form of the relationship and the relationship. To determine the form of the relationshipused regression analysis. For the relationship can be identified by correlation analysis.Regression analysis was used to examine the relationship between two variables ormore, especially to trace the pattern of relationships that model is not known perfectly, orto find out how the variation of several independent variables affect the dependentvariable in a complex phenomenon. If X1, X2, ..., Xi are independent variables and Y is the dependent variable, then there is the functional relationship between X and Y, where the variation of X will be accompanied also by the variation of Y. The mathematicalrelationships above can be described as follows: Y = f (X1, X2, ..., Xi, e), where: Y is thedependent variable, X is the independent variable and e is the residual variable(disturbance term).
Related to this regression analysis, there are at least four four activities that can beimplemented in the regression analysis, including: (1) entered into estimates ofparameters based on empirical data, (2) examine how much variation of the dependentvariable can be explained by variations in the independent variables, (3) test whetherthe estimated parameters were significant or not, and (4) to see whether the sign andmagnitude of the estimated parameters match the theory (M. Nazir, 1983).
B. SIMPLE REGRESSION COEFFICIENT
Simple regression, aims to study the relationship between two variables. Simpleregression model is, where, is the dependent variable (bound), X is the independent variable, a is an estimator for intersap (α), b is an estimator for the regressioncoefficient (b), and α, b are parameters whose values are unknown so allegedly usingstatistical sampling.
Feb 15, 2011
Understanding Statistics
Understanding Statistics
STATISTICAL is a set of methods are discussed: (1) how to collect data that can provide optimal information, (2) how to summarize, process and present data, (3) how to conduct an analysis of the data set, so it arises from an analysis strategy -specific strategies, (4) how to draw conclusions and suggest that decisions should be taken, on the basis of the existing strategy, and (5) how to determine the risk of errors that might occur if we make a decision on the basis of the strategy.
STATISTICS, defined as a collection of facts that shaped figures arranged in the form of a list or table that illustrates a problem. Name statistics depend on the problems described by the statistic that, for example, population statistics, sales statistics, economic statistics and statistics education.
Statistical Classification
DESCRIPTIVE STATISTICAL (descriptive statistics), which discusses ways of collecting data, simplification of the figures obtained by observation (summarize and present), as well as measuring the concentration and distribution of data to obtain information that is more interesting, useful and easily understood. With descriptive statistics, collection of data obtained will be presented with a concise and neat and can provide the core information from existing data sets. The information can be obtained by descriptive statistics, among others, concentration for distributing data, and the tendency of a group of data. Included in the size of the convergence of data such as average, median, and mode. The size of the spread of such range, average deviation, variance, and standard deviation. In addition, the descriptive statistics is also included in the size of the location, such as quartiles, deciles and percentiles
STATISTICAL inference (inferential statistics), which discussed about how to analyze data and draw conclusions (related to parameter estimation and hypothesis testing). Method of statistical inference associated with the analysis of partial data to forecast or conclusion about the overall data. This method is often called inductive statistics because the conclusion drawn based on information from only partial data (samples). Statistical inference is divided into two groups, namely STATISTICAL STATISTICAL PARAMETRIC and nonparametric.
STATISTICAL PARAMETRIC (parametric statistics), the statistical inference that consider the value of one or more parameters of the population. Parametric statistics are usually associated with quantitative data (minimum scale measuring intervals). In addition, procedures for using parametric statistical analysis of data required to be normal distribution. Examples of parametric statistical analysis was the t test, analysis of Variety (ANOVA), Pearson correlation test and regression test (F test).
STATISTICAL nonparametric (nonparametric statistics) are part of statistical inference that does not pay attention to the value of one or more parameters of the population. Nonparametric statistical methods used to analyze data that can not be assumed normal distribution. Data needed more of a nominal or ordinal measurement scale (qualitative data). Examples of nonparametric statistical analysis: Chi Square Test for Freedom Two Variable Category, Spearman correlation coefficient, Wilcoxon rank sign test, Mann-Whitney test, Kruskal-Wallis, and Friedman Test.
Rounding Data
The result of rounding off a number such as 72.8 to the nearest unit is 73, because 72.8 is closer to 73 than at 72. Similarly, 72.8146 rounded to the nearest hundred or two decimal position is 72.81, because 72.81 72.8146 closer to than to 72.82.
In rounding off the nearest keratusan 72.465, we are faced with a problem as far as 72.465 from 72.46 and 72.47. Has become the custom in such cases made up into an even number that precedes 5. So 72.465 rounded to 72.46; 183.575 rounded to 183.58; 116 500 000 rounded to the nearest million is 116 million. This habit is especially useful in meperkecil error (error) cumulative rounding when it comes to a large number of operations.
Example:
Add numbers 4.35, 8.65, 2.95, 12.45, 6.65, 7.55, 9.75. (A) directly, (b) with the nearest kepuluhan rounding in accordance with the agreement "round fulfilled", (c) by rounding to enlarge the number before 5.
Completion:
(A) 4.35 + 8.65 + 2.95 + 12.45 + 6.65 + 7.55 + 9.75 = 52.35 (B) 4.4 + 8.6 + 3.0 + 12.4 + 6.6 + 7.6 + 9.8 = 52.4 (C) 4.4 + 8.7 + 3.0 + 12.5 + 6.7 + 7.6 + 9.8 = 52.7
Note that procedure (b) is superior to procedure (c), due to an error (error) cumulative rounding minimized in the procedure (b). Sum of procedure (b) closer to the sum of (a) compared with the procedure (c).
In rounding off the nearest keratusan 72.465, we are faced with a problem as far as 72.465 from 72.46 and 72.47. Has become the custom in such cases made up into an even number that precedes 5. So 72.465 rounded to 72.46; 183.575 rounded to 183.58; 116 500 000 rounded to the nearest million is 116 million. This habit is especially useful in meperkecil error (error) cumulative rounding when it comes to a large number of operations.
Example:
Add numbers 4.35, 8.65, 2.95, 12.45, 6.65, 7.55, 9.75. (A) directly, (b) with the nearest kepuluhan rounding in accordance with the agreement "round fulfilled", (c) by rounding to enlarge the number before 5.
Completion:
(A) 4.35 + 8.65 + 2.95 + 12.45 + 6.65 + 7.55 + 9.75 = 52.35 (B) 4.4 + 8.6 + 3.0 + 12.4 + 6.6 + 7.6 + 9.8 = 52.4 (C) 4.4 + 8.7 + 3.0 + 12.5 + 6.7 + 7.6 + 9.8 = 52.7
Note that procedure (b) is superior to procedure (c), due to an error (error) cumulative rounding minimized in the procedure (b). Sum of procedure (b) closer to the sum of (a) compared with the procedure (c).
Requirements for Data Analysis
Nonparametric test is used when the assumptions of parametric tests are not met. The most common assumption in the parametric test is a random sample from a normally distributed population, the data is homogeneous, and linear. If these assumptions are met, or at least a little deviation to the assumption, then the parametric test is still reliable. But if the assumptions are not met then an alternative nonparametric test. There are three assumptions of parametric statistical tests as described above, ie normality, homogeneity, and linearity data.
A. Normality Test Data
Testing normality conducted to determine whether or not a normal data distribution. It is important to know related to the election ketetapatan statistical test that will be used. Misalmya parametric test, data must berdistibusi mengsyaratkan normal. If the data distribution is not normal it is advisable to use a nonparametric test
Tests of normality has to be done if there is no theory which states that the variables studied were normal. In other words, if there is a theory which states that a normal variable under investigation, it is no longer needed test data normality.
Step work with normality test test test Liliefors
Arrange the data from small to large. Any data written once, although there is the same data.
Check the data, how many times have the appearance of numbers (the frequency must be written.)
From the frequency cumulative frequency stacking.
Based on cumulative frequency, calculate the proportion of empirical (observation).
Calculate the value of z to know Theoretical Proportion in table z.
Calculating Theoretical Proportion.
Compare with Theoretical Proportion Proportion empirical, then look for the biggest difference between observation points.
Make a conclusion, with the test criteria, reject H0 if D> D (n,?), With criteria:
H0: X follow a normal distribution.
H1: X does not follow a normal distribution.
B. Data Homogeneity
Parametric test requirements the second is the homogeneity of the data. The test is a test of homogeneity of variance-variance at least two or more distributions. Test of homogeneity that will be discussed in this paper is to test homogeneity of variance and test Burlett.
Test of homogeneity of variance were used to compare two predictor variables. Test criteria used were the two distributions are said to have a homogenous distribution when calculating the value of F smaller than the value of F with a particular table and dk1 = (n1-1) and dk2 = (n2 - 1). In other cases the distribution is not homogeneous / different.
Tests for homogeneity of data with Barlett test was to see whether the variance of k-variance group of predictor variables are the number of data per group may vary and are taken randomly from each population data are normally distributed, different or not (Ruseffendi, 1998: 297).
Test criteria used is when the count> table value, then H0 stating homogeneous variance is rejected, in other cases accepted. Formulas refer to the book source (Sambas Ali Muhidin. 2007. Correlation Analysis, Regression, and Path in the study. Bandung: Pustaka Setia).
The steps that can be done in testing the homogeneity with the Barlett test were:
Define groups of data, and calculate the variance for each group
Create a table helpers to facilitate the process of calculation
Calculate the combined variance.
Calculating the log of the variance combined.
Calculating the value of Barlett.
Calculating value
Determining the value and the critical point.
Make a conclusion.
C. Linearity Data
Checking linearity of regression is done through testing the null hypothesis, that the linear regression against a rival hypothesis that the regression is not linear. Step Test linearity of regression: See book seumber ((Sambas Ali Muhidin. 2007. Correlation Analysis, Regression, and Path in the study. Bandung: Pustaka Setia).
A. Normality Test Data
Testing normality conducted to determine whether or not a normal data distribution. It is important to know related to the election ketetapatan statistical test that will be used. Misalmya parametric test, data must berdistibusi mengsyaratkan normal. If the data distribution is not normal it is advisable to use a nonparametric test
Tests of normality has to be done if there is no theory which states that the variables studied were normal. In other words, if there is a theory which states that a normal variable under investigation, it is no longer needed test data normality.
Step work with normality test test test Liliefors
Arrange the data from small to large. Any data written once, although there is the same data.
Check the data, how many times have the appearance of numbers (the frequency must be written.)
From the frequency cumulative frequency stacking.
Based on cumulative frequency, calculate the proportion of empirical (observation).
Calculate the value of z to know Theoretical Proportion in table z.
Calculating Theoretical Proportion.
Compare with Theoretical Proportion Proportion empirical, then look for the biggest difference between observation points.
Make a conclusion, with the test criteria, reject H0 if D> D (n,?), With criteria:
H0: X follow a normal distribution.
H1: X does not follow a normal distribution.
B. Data Homogeneity
Parametric test requirements the second is the homogeneity of the data. The test is a test of homogeneity of variance-variance at least two or more distributions. Test of homogeneity that will be discussed in this paper is to test homogeneity of variance and test Burlett.
Test of homogeneity of variance were used to compare two predictor variables. Test criteria used were the two distributions are said to have a homogenous distribution when calculating the value of F smaller than the value of F with a particular table and dk1 = (n1-1) and dk2 = (n2 - 1). In other cases the distribution is not homogeneous / different.
Tests for homogeneity of data with Barlett test was to see whether the variance of k-variance group of predictor variables are the number of data per group may vary and are taken randomly from each population data are normally distributed, different or not (Ruseffendi, 1998: 297).
Test criteria used is when the count> table value, then H0 stating homogeneous variance is rejected, in other cases accepted. Formulas refer to the book source (Sambas Ali Muhidin. 2007. Correlation Analysis, Regression, and Path in the study. Bandung: Pustaka Setia).
The steps that can be done in testing the homogeneity with the Barlett test were:
Define groups of data, and calculate the variance for each group
Create a table helpers to facilitate the process of calculation
Calculate the combined variance.
Calculating the log of the variance combined.
Calculating the value of Barlett.
Calculating value
Determining the value and the critical point.
Make a conclusion.
C. Linearity Data
Checking linearity of regression is done through testing the null hypothesis, that the linear regression against a rival hypothesis that the regression is not linear. Step Test linearity of regression: See book seumber ((Sambas Ali Muhidin. 2007. Correlation Analysis, Regression, and Path in the study. Bandung: Pustaka Setia).
Direction of Hypothesis Testing
2-way hypothesis testing is used when investigators have no information regarding the trend of population characteristics that were observed. While the 1-way hypothesis test is used when investigators have information about the direction of trends of population characteristics that were observed. Example below may illustrate.
Example 1: A researcher wants to know the average achievement mahasiswa.Universitas X. According to a growing issue, the average achievement (GPA) of students at the University of X IN THE 3.5. Example 2: A researcher wants to know the average achievement of students at the University X. According to a growing issue, the average achievement (GPA) of students at the University of X is 3.5
Based on the two cases above, we see that in example 1, there is word ABOVE, while in case 2 there are no words that indicate larger or smaller, but directly on the CPI figure 3.5. This gives information that: GPA student at the University of X is located to the right in the normal curve. While in the example 2 means that the average GPA of students at the University of X in a circle (either to the left or to the right) of 3.5 GPA
Thus, in case 2 did not have 2 the possibility of trend / direction, while in case 1 there is a tendency towards (to the right). Therefore, the exact direction of the hypothesis testing for test case 1 is a 1-way (in H1 using a mark BIGGER inequalities), while in case 2 is testing 2-way (in H1 using the inequality sign "NOT THE SAME AS").
Preliminary studies?
A preliminary study is one activity or preparatory activities conducted by a researcher, in order to determine the object and the right of research subjects, which according to research themes that became the focus of the study investigators.
The object of study, related to the variables selected by the researcher, both variables problem (y) and the variables thought to be variables that affect the variables problem. Thus, determination of research variables through preliminary study is one effort of researchers to select appropriate variables, which empirically is a variable problem and the cause of the determinant variables, which affect the variables problem.
This means that in order to conduct research or obtain high-quality research results, useful and meaningful, then a researcher is not enough just based on theories alone in determining the study variables, not necessarily because the variables are selected based on earlier theory-terori , is the appropriate variables need to be researched empirically. Therefore it is recommended when a researcher in determining the title of his research, conducted preliminary studies in addition to studying the theory.
While the research subjects, deals with the respondent. Choosing the proper respondent is the necessity to obtain data / information that has a high accuracy and high precision. Therefore, investigators must establish a reliable respondents (reliable) in providing data / information needed to describe the problem under study.
Selecting respondents who trusted among others, by reviewing the characteristics inherent in these respondents, for example level of education, occupation, type of skill, gender, and so forth. Characteristics inherent in the respondents are then adjusted to the need for data / information that will be used to explain issues / variables studied
The object of study, related to the variables selected by the researcher, both variables problem (y) and the variables thought to be variables that affect the variables problem. Thus, determination of research variables through preliminary study is one effort of researchers to select appropriate variables, which empirically is a variable problem and the cause of the determinant variables, which affect the variables problem.
This means that in order to conduct research or obtain high-quality research results, useful and meaningful, then a researcher is not enough just based on theories alone in determining the study variables, not necessarily because the variables are selected based on earlier theory-terori , is the appropriate variables need to be researched empirically. Therefore it is recommended when a researcher in determining the title of his research, conducted preliminary studies in addition to studying the theory.
While the research subjects, deals with the respondent. Choosing the proper respondent is the necessity to obtain data / information that has a high accuracy and high precision. Therefore, investigators must establish a reliable respondents (reliable) in providing data / information needed to describe the problem under study.
Selecting respondents who trusted among others, by reviewing the characteristics inherent in these respondents, for example level of education, occupation, type of skill, gender, and so forth. Characteristics inherent in the respondents are then adjusted to the need for data / information that will be used to explain issues / variables studied
Role of Statistics in Quantitative Research
Paradigama research with quantitative approach is a research approach that rests on the view of positivism which essentially focuses on the things that are concrete, empirical tests and the real facts.
This paradigm believes that the only knowledge (knowledge) is valid is the science of knowledge (science), that is knowledge which originated and is based on experience (experience) are caught and processed through the senses by reason (reason). Therefore, in practice, research with this quantitative approach to give meaning through interpretation of statistical figures or not through language or culture.
Statistics in quantitative research approach is one of the main component in the research stages, ranging from the preparation of research, data collection techniques, data processing until the effort to make the decisions / conclusions scientifically. Thus the statistics in the study with quantitative approach has a fairly dominant role in expediting the achievement of research objectives.
With regard to the role of these statistics, then at least there are four roles in research, among others:
First, the role of statistics in the Determination of Sample Research. The purpose of sampling techniques is to produce a representative sample of the population and obtain an adequate sample size to do the research. In relation to this role, statistics provides techniques and specific formulas in order to obtain samples reperesentatif and adequate sample size.
Second, the role of statistics in the development of data retrieval tool. Before a person uses a device makers the data, he must have the assurance that the device he uses it with quality. The quality of data collection tools can be viewed from the side of validity and reliability. Therefore each data collection tools need to be tested by validity and relibilitasnya, and the best way to test vasliditas and reliability of data collection tools is to use statistical methods.
Third, the role of statistics in a Presenting data. Data collected through specific data collection technique is still raw data, therefore, that data was more communicative it must be presented in such a way that data is easy to read or understood. In connection with efforts to display the data to be easily read and understood, then the statistics provide specific techniques in processing data and presenting data, with descriptive statistical methods.
Fourth, the role of Statistics in Data Analysis or Testing Hypotheses. The ultimate goal in research is the conclusion as an ingredient to make a decision. In order to obtain results valid and reliable research, statistics have also developed a specific calculation techniques and develop various methods to test hypotheses that could help researchers. Statistical analysis of data that discuss or test this hypothesis is inferential statistical methods.
This paradigm believes that the only knowledge (knowledge) is valid is the science of knowledge (science), that is knowledge which originated and is based on experience (experience) are caught and processed through the senses by reason (reason). Therefore, in practice, research with this quantitative approach to give meaning through interpretation of statistical figures or not through language or culture.
Statistics in quantitative research approach is one of the main component in the research stages, ranging from the preparation of research, data collection techniques, data processing until the effort to make the decisions / conclusions scientifically. Thus the statistics in the study with quantitative approach has a fairly dominant role in expediting the achievement of research objectives.
With regard to the role of these statistics, then at least there are four roles in research, among others:
First, the role of statistics in the Determination of Sample Research. The purpose of sampling techniques is to produce a representative sample of the population and obtain an adequate sample size to do the research. In relation to this role, statistics provides techniques and specific formulas in order to obtain samples reperesentatif and adequate sample size.
Second, the role of statistics in the development of data retrieval tool. Before a person uses a device makers the data, he must have the assurance that the device he uses it with quality. The quality of data collection tools can be viewed from the side of validity and reliability. Therefore each data collection tools need to be tested by validity and relibilitasnya, and the best way to test vasliditas and reliability of data collection tools is to use statistical methods.
Third, the role of statistics in a Presenting data. Data collected through specific data collection technique is still raw data, therefore, that data was more communicative it must be presented in such a way that data is easy to read or understood. In connection with efforts to display the data to be easily read and understood, then the statistics provide specific techniques in processing data and presenting data, with descriptive statistical methods.
Fourth, the role of Statistics in Data Analysis or Testing Hypotheses. The ultimate goal in research is the conclusion as an ingredient to make a decision. In order to obtain results valid and reliable research, statistics have also developed a specific calculation techniques and develop various methods to test hypotheses that could help researchers. Statistical analysis of data that discuss or test this hypothesis is inferential statistical methods.
What level of Significance and Confidence Levels?
In the discussion the term statistical significance level (significance level) and level of confidence (confidence level) and is often used.
The level of significance (alpha) indicates the probability or the chance of errors set of researchers in making decisions to reject or support the null hypothesis, or can be defined as well as error rates or error rates are tolerated by the researchers, is caused by the possibility of error in sampling (sampling error .)
The level of significance is expressed in percent and dilambngkan with?. For example, set the level of significance? = 5% or? = 10%. That is, the researcher's decision to reject or support the null hypothesis has a probability of error of 5% or 10%. In some computer-based statistical programs, the level of significance is always included and is written as a Sig. (= Significance), or other computer programs written in the r-value. Value Sig or r - value, as described above, is the value of error probability is calculated or indicate the actual level of error probability. The error rate is used as a basis for making decisions in hypothesis testing.
While the level of trust basically shows how far the level of statistical reliability of sample to estimate the true population parameter and / or the extent of making a decision about the null hypothesis test results believed to be accurate.
In statistics, the level of confidence in its value ranges from 0 to 100% and is represented by 1 -?. Conventionally, researchers in the social sciences often determine the level of confidence ranged from 95% - 99%. If you say the level of confidence used was 95%, this means that the level of statistical certainty sample correctly estimate the population parameter is 95%, or level of confidence to reject or support the null hypothesis correctly was 95%.
The Concept Degrees of Freedom
The term number of degrees of freedom (degrees of freedom) is defined as the total number of observations in the sample (= N) minus the number of control (linear) free or limitation (restriction) is placed on earlier observations. In other words, the number degrees of freedom is the number of free observations of a total of observations N. So the general formula for determining the degrees of freedom (db) is the total observations (N) minus the number of parameters that are estimated or df = N - number of parameters estimated (k). (Gujarati, 1978).
Based on such understanding, it can be understood that the formula will be different degrees of freedom for the case of one observation with another observation case, and that makes the difference is depending on the number of estimated parameters. Therefore the formula of degrees of freedom can db = N - 2 or db = N -3 depending on the number of parameter (variable) had a crush. For example, if we want to examine two variables, the degree kebebasanya is db = N - 2. Why N - 2, because there are two variables.
Another thing that needs to be understood in the study of degrees of freedom is related to the research sample. The basic idea is every time we estimate the parameters (characteristics of the population), we will lose one degree of freedom. Therefore, degrees of freedom as told Gujarati (1978) will always N - k, not N. To understand this consider the following explanation: Suppose there is a population with an average (mean) is 10. Next we allowed to take a sample of 10 people from the population. The question is how many people we can take for free? For example, we take the first person freely, he has a score of 14. The second man is still free, he has a score of 8. Then the third consecutive person to person-to-nine were taken independently by score: 15, 6, 11, 14, 8, 6, and 5. What about the tenth? Was taken freely? Of course the answer is no. Ten people can not be taken freely again. If you already have 9 digits, numbers to ten no longer be determined freely in order to get the same estimate (ie mean = 10). For example, the number of scores from the nine people earlier were 87. In order that we get the same estimate, ie mean = 10, the tenth shall be determined by 13. Thus we can say we lost one degree of freedom. Well degrees of freedom is then used to see the value of a particular table, such as table t.
In our earlier calculations, we estimate only one parameter or estimate. Therefore, we only lost one degree of freedom, so the degrees of freedom that we have is N - 1, ie 10-1 = 9.
Feb 13, 2011
As Statistical Tools Decision Making Leaders
Abstrak
Importance of Statistics
Statistics have affected almost all aspects of human life and all the people involved and very concerned with that knowledge, including the leaders in the organization or company. Almost all public policy and decisions taken by leaders based on statistical methods, and the results of the analysis and interpretation of data, both quantitatively and qualitatively. Therefore, given the broad scope of responsibilities and strategic leadership positions within the organization, then a leader is concerned with statistics. Statistics are very important and useful for the leader, especially as a tool in decision-making process. Objective statistical characteristics can be used as the objective basis for making a decision.
Application of Statistical Methods in Decision Making Leadership
In front of this paper was submitted, that part of the work of a leader from the lower level until the top level leaders are making decisions (decision making). Making this decision is very closely related to the issue or problem faced by an organization to obtain a better condition, or even in order to make policy that is really new and could be considered a major contribution to the advancement organsisasi.
One of the tools that are considered could assist management in decision-making process is statitika. Why statistics? According to M. Nazir (1983) there are some non-scientific way of finding truths that can be used as the basis for making decisions, which are: (1) coincidence, (2) common sense (common sense), (3) by revelation, (4) intuitive, (5 ) trial and error, (6) speculation, and (7) authority. Statistics eliminate way decisions are not scientific or groping. By way of an objective statistical work and what it is, then it is very possible that the decision-making as objective as possible. This course is very helpful leader in order to make good decisions as well as a small risk when compared through nonilmiah process that may bias.
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