Analysis of variance (ANOVA) is a statistical technique that was invented by Fisher, and it is therefore sometimes called Fisher’s analysis of variance (ANOVA). In survey research, analysis of variance (ANOVA) is used to compare the means of more than two populations. Analysis of variance (ANOVA) technique can be used in the case of two sample means comparison.
Additionally, it can be used in cases of two samples analysis of variance (ANOVA) and results will be the same as the t-test. For example, if we want to compare income by gender group. In this case, t-test and analysis of variance (ANOVA) results will be the same. In the case of more than two groups, we can use t-test as well, but this procedure will be long. Thus, analysis of variance (ANOVA) technique is the best technique when the independent variable has more than two groups. Before performing the analysis of variance (ANOVA), we should consider some basics and some assumptions on which this test is performed:
Assumptions:
1. Independence of case: Independence of case assumption means that the case of the dependent variable should be independent or the sample should be selected randomly. There should not be any pattern in the selection of the sample.
2. Normality: Distribution of each group should be normal. The Kolmogorov-Smirnov or the Shapiro-Wilk test may be used to confirm normality of the group.
3. Homogeneity: Homogeneity means variance between the groups should be the same. Levene's test is used to test the homogeneity between groups.
If particular data follows the above assumptions, then the analysis of variance (ANOVA) is the best technique to compare the means of two populations, or more than two populations. Analysis of variance (ANOVA) has three types.
One way analysis of variance (ANOVA): When we are comparing more than three groups based on one factor variable, then it said to be one way analysis of variance (ANOVA). For example, if we want to compare whether or not the mean output of three workers is the same based on the working hours of the three workers, then it said to be one way analysis of variance (ANOVA).
Two way analysis of variance (ANOVA): When factor variables are more than two, then it is said to be two way analysis of variance (ANOVA). For example, based on working condition and working hours, we can compare whether or not the mean output of three workers is the same. In this case, it is said to be two way analysis of variance (ANOVA).
K way analysis of variance (ANOVA): When factor variables are k, then it is said to be the k way of analysis of variance (ANOVA).
Key terms and concepts:
Sum of square between groups: For the sum of the square between groups, we calculate the individual means of the group, then we take the deviation from the individual mean for each group. And finally, we will take the sum of all groups after the square of the individual group.
Sum of squares within group: In order to get the sum of squares within a group, we calculate the grand mean for all groups and then take the deviation from the individual group. The sum of all groups will be done after the square of the deviation.
F –ratio: To calculate the F-ratio, the sum of the squares between groups will be divided by the sum of the square within a group.
Degree of freedom: To calculate the degree of freedom between the sums of the squares group, we will subtract one from the number of groups. The sum of the square within the group’s degree of freedom will be calculated by subtracting the number of groups from the total observation.
BSS df = (g-1) for BSS is between the sum of squares, where g is the group, and df is the degree of freedom.
WSS df = (N-g) for WSS within the sum of squares, where N is the total sample size.
Significance: At a predetermine level of significance (usually at 5%), we will compare and calculate the value with the critical table value. Today, however, computers can automatically calculate the probability value for F-ratio. If p-value is lesser than the predetermined significance level, then group means will be different. Or, if the p-value is greater than the predetermined significance level, we can say that there is no difference between the groups’ mean.
Analysis of variance (ANOVA) in SPSS: In SPSS, analysis of variance (ANOVA) can be performed in many ways. We can perform this test in SPSS by clicking on the option “one way ANOVA,” available in the “compare means” option. When we are performing two ways or more than two ways analysis of variance (ANOVA), then we can use the “univariate” option available in the GLM menu. SPSS will give additional results as well, like the partial eta square, Power, regression model, post hoc, homogeneity test, etc. The post hoc test is performed when there is significant difference between groups and we want to know exactly which group has means that are significantly different from other groups.
Extension of analysis of variance (ANOVA):
MANOVA: Analysis of variance (ANOVA) is performed when we have one dependent metric variable and one nominal independent variable. However, when we have more than one dependent variable and one or more independent variable, then we will use multivariate analysis of variance (MANOVA).
ANCOVA: Analysis of covariance (ANCOVA) test is used to know whether or not certain factors have an effect on the outcome variable after removing the variance for quantitative predictors (covariates).
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Monday, April 6, 2009
Wednesday, April 1, 2009
Dissertation Statistics Help
Dissertations can be very frustrating for aspiring students and scholars everywhere. Students who wish to attain their degree often feel much anxiety and stress. It can feel close to impossible for a student to even decide upon a topic, let alone conclude one. In such instances where it looks as if there is no way out, there is dissertation statistics help to assist the students with all that they need! Dissertation statistics help is aid provided to students on dissertations and theses. Dissertation statistics help has relieved many students of their dissertation woes. It has catered to a large number of students and has ensured and secured high grades and scores for them.
Most importantly, dissertation statistics help builds confidence for students, for students are assured of the success of their dissertations. Dissertation statistics help provides specialized services for the students through various means and methods. Below is a list of the processes of dissertation statistics help:
· Dissertation statistics help assists the student in first deciding on a topic.
· The consultant plans and designs the statistical method.
· The analysts and consultants also help the student in preparing hypotheses. Additionally, they help to design a survey and an investigation that answers all the research questions.
· The dissertation statistics help interprets the results and submits the results based on the findings and utilizes tables and graphs.
· Some consultants do the editing of the entire report as well.
· Dissertation statistics help also ensures that the consultants prepare and groom the students for their oral presentations and reports of the dissertation, giving them much more confidence and poise.
Dissertation statistics help has proven to be very constructive for the students. Through dissertation statistics help, students become more prepared and more confident when they meet with their authorities and the teaching faculty concerned. The students, after taking dissertation statistics help, can more clearly comprehend their findings.
Dissertation statistics help can be derived from statisticians who are well trained and experts in the field. Such help can be sought from professors as well as statistical consultants who know the subject at length. Such professionals must have sufficient communication skills so that a proper understanding and mutual cooperation may exist between the two parties. Again, the concerned body must be equipped with a keen interest in science, they must be statistically adept, and must also be computer proficient. Their computer proficiency enables them to use various computer statistical software that exists today. Besides theses skills, they must also be invested in teamwork and cooperation. This is crucial to the overall success of the project. Clearly dissertation statistics help is necessary, as without it, the student would be at a loss and would not know how to go about the entire process.
Statistics is a very important subject and plays an important role in many domains and fields. It is applied to almost every subject. Thus, for those who do not possess the required and necessary skills, dissertation statistics help is of the essence. Dissertation statistics help is priced at reasonable rates and consultants ensure that the clients get their money’s worth. In other words, hiring a statistical consultant is money well spent. It guides the student in the right direction through expert management. Dissertation statistics help focuses on quality and excellence. Customized reports are also guaranteed through dissertation statistics help. Statistics (attained with help and expertise from statistics help) has assured itself as one of the most reliable and efficient methods to validate the thesis and report. Budget, cost, expenses, deadlines and requisites concerning the project are also to be considered by the firm so that they are in accordance with the clients’ needs and requirements.
Dissertation statistics help has opened a plethora of avenues for students. While it is important for the student to be cautious and perform a thorough check on the background and repute of the company, it is also necessary for the student to be able to trust the consultant with the work. Dissertation statistics help is vital in the present day and will continue reach milestones in the future.
Most importantly, dissertation statistics help builds confidence for students, for students are assured of the success of their dissertations. Dissertation statistics help provides specialized services for the students through various means and methods. Below is a list of the processes of dissertation statistics help:
· Dissertation statistics help assists the student in first deciding on a topic.
· The consultant plans and designs the statistical method.
· The analysts and consultants also help the student in preparing hypotheses. Additionally, they help to design a survey and an investigation that answers all the research questions.
· The dissertation statistics help interprets the results and submits the results based on the findings and utilizes tables and graphs.
· Some consultants do the editing of the entire report as well.
· Dissertation statistics help also ensures that the consultants prepare and groom the students for their oral presentations and reports of the dissertation, giving them much more confidence and poise.
Dissertation statistics help has proven to be very constructive for the students. Through dissertation statistics help, students become more prepared and more confident when they meet with their authorities and the teaching faculty concerned. The students, after taking dissertation statistics help, can more clearly comprehend their findings.
Dissertation statistics help can be derived from statisticians who are well trained and experts in the field. Such help can be sought from professors as well as statistical consultants who know the subject at length. Such professionals must have sufficient communication skills so that a proper understanding and mutual cooperation may exist between the two parties. Again, the concerned body must be equipped with a keen interest in science, they must be statistically adept, and must also be computer proficient. Their computer proficiency enables them to use various computer statistical software that exists today. Besides theses skills, they must also be invested in teamwork and cooperation. This is crucial to the overall success of the project. Clearly dissertation statistics help is necessary, as without it, the student would be at a loss and would not know how to go about the entire process.
Statistics is a very important subject and plays an important role in many domains and fields. It is applied to almost every subject. Thus, for those who do not possess the required and necessary skills, dissertation statistics help is of the essence. Dissertation statistics help is priced at reasonable rates and consultants ensure that the clients get their money’s worth. In other words, hiring a statistical consultant is money well spent. It guides the student in the right direction through expert management. Dissertation statistics help focuses on quality and excellence. Customized reports are also guaranteed through dissertation statistics help. Statistics (attained with help and expertise from statistics help) has assured itself as one of the most reliable and efficient methods to validate the thesis and report. Budget, cost, expenses, deadlines and requisites concerning the project are also to be considered by the firm so that they are in accordance with the clients’ needs and requirements.
Dissertation statistics help has opened a plethora of avenues for students. While it is important for the student to be cautious and perform a thorough check on the background and repute of the company, it is also necessary for the student to be able to trust the consultant with the work. Dissertation statistics help is vital in the present day and will continue reach milestones in the future.
Dissertation Statistics Tutoring
Dissertation writing is a very critical step in the process of acquiring your degree. All students who are writing their dissertations have to go through many hurdles for which they need both guidelines and a helping hand. Because their advisors are not available to help them every time, they can struggle with direction and at times can find themselves at a complete loss. In such situations, students cannot do anything but turn in circles as they struggle with their dissertations. Even if the students have done their papers and the required readings throughout the year, when it comes to writing the dissertations, students can find themselves unsure of where to even begin. Despite their best efforts, they could most definitely use professional guidance. This need for help only intensifies while dealing with the statistical part of the dissertation. Authoring a dissertation is a tough task in and of itself, but doing the statistical part of dissertation is absolutely a different level of complexity. And this certainly requires expert help! As it is, exam time is a difficult and tiring period by itself. This is because of the papers one has to write and the amount of reading the student has to finish. Adding the stress of a dissertation on top of all of this work does not help. The frustration the student feels gets intensified when their proposals or finished dissertations get rejected because of insufficient data or lack of innovation in the student’s idea. This is where dissertation statistics tutoring comes into the picture. Dissertation statistics tutoring benefits students who have to complete their dissertations to attain their degree. Dissertation statistics tutoring is invaluable as it facilitates the entire process of composing the thesis or dissertation for the student.
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-Dissertation Statistics tutoring provides help in preparing tables and graphs.
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Dissertation Statistics Tutors have a thorough knowledge of research designs and statistics. Dissertations Statistics tutoring provides professionals who are experts at making you choose the proper type of analysis such as, t-tests, ANOVA, MANOVA, regression analysis, factor analysis, cluster analysis, etc. for your research question. If you hire a tutor from the dissertation statistics tutoring services in the beginning of your research, he/she can easily spot the loopholes in your research design and help you do the corrections needed to get the perfect design of study. The best part about dissertation statistics tutoring is that they have tutors who can transcribe the complex literature into understandable prose and assist you in writing a comprehensible and error free dissertation. Many dissertation statistics consultants do not do the editing work but there are few others who are willing to check spelling and grammar as a part of their writing assistance.
In this fast-paced world, students have a lot of things to worry about. Dissertation Statistics tutoring services can be a good source of relief if hired with all the necessary precautions. While hiring the services of dissertation statistics tutoring, one should make sure that they are capable and that they have the required expertise to carry out the task assignment as per the clients’ requirements. Students should always check their available services as well as the feedback from the people who have made use of their services. Students should also respect the policies and constructive criticism that they receive in the course of their dissertation statistics tutoring. Some students might find the dissertation statistics tutoring a bit challenging but they should remember that the experience and unique information gained from the dissertation statistics tutor is invaluable.
Dissertation statistics tutoring is of great use for all students if utilized efficiently and without any communication gap between the tutor and student. The exchange of ideas should be clear-cut and precise and should be followed up by a mutual understanding between both parties. Dissertation statistics tutoring is without a doubt indispensable and effective.
Tuesday, March 31, 2009
Cronbach’s Alpha Rule of Thumb
To examine reliability and internal consistency Cronbach’s alpha tests were conducted using the survey subscales: communication, organizational commitment, organizational justice, organizational citizenship, affect based trust, cognition based trust and resistance to change. George and Mallery (2003) suggest the following rules of thumb for evaluating alpha coefficients, “> .9 excellent, > .8 good, > .7 acceptable, > .6 questionable, > .5 poor, < .5 unacceptable.” The measure (alpha or α) assumes that items measuring the same thing will be highly correlated (Welch & Comer, 1988). Click here for dissertation statistics help
Number of Components to Extract
There are a number of ways to determine the number of factors to extract. The Kaiser criterion suggests that one should retain any factors with eigenvalues greater than one. Scanning the Total Variance Explained (see Appendix C), the first eleven components (λ or eigenvalues) are above one. The total variance explained for the first two components is 27.683 and 7.598 percent of the variance, respectively. The total variance explained for the first two factors is 5.281 percent. Total variance explained by the first eleven factors is 72.012 percent. The Kaiser technique is only reliable, however, when the number of variables is less than thirty and the communalities are greater than .7. Inspection of the communalities shows twenty three of the 54 communality coefficients are greater than .7. Communalities (h2) “represent how much of the variance of a measured variable was useful in delineating the extracted factors” (Thompson, 2004, p. 61). These communalities also represent the R-square (R2) between the factor scores (latent variable scores) and measured scores on the measured variable.
The Catell (1996) technique suggests keeping factors above the elbow in the Scree plot (see Figure 1 in Appendix B). In this study, the scree plot suggests two factors be retained. Breaks also appear for 3, 4, 5, and 7 components. The seven factor solution supports the theoretical model with seven factors. When this model was specified, however, the majority of the variables loaded onto the first factor and the model made no theoretical sense. Theoretical considerations supported a nine factor model. The pattern matrix is shown in Table 4.
The items cluster cleanly into the communication, commitment, citizenship, cognition based trust, and resistance to change factors. Nearly all the affect based trust measures hang together with the exception of abt6 (This person approaches his/her job with professionalism and dedication. (ABT-6)) which is strongly correlated with the items that measure cognition based trust. The variable, organizational justice, includes three subfactors, fairness, employee voice and justification. The first four items for fairness cluster together and appear to measure that concept. The questions are shown below. Survey questions Orgjv6, Orgjv7, Orgjv8 and OrgjJ11 cluster together to form the Employee Voice measure. Similarly, Orgjv5, Orgjv8, and OrgjJ10 load onto Justification. These subscales will be utilized as one scale, organization justice, in the computation of Cronbach’s alpha.
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The Catell (1996) technique suggests keeping factors above the elbow in the Scree plot (see Figure 1 in Appendix B). In this study, the scree plot suggests two factors be retained. Breaks also appear for 3, 4, 5, and 7 components. The seven factor solution supports the theoretical model with seven factors. When this model was specified, however, the majority of the variables loaded onto the first factor and the model made no theoretical sense. Theoretical considerations supported a nine factor model. The pattern matrix is shown in Table 4.
The items cluster cleanly into the communication, commitment, citizenship, cognition based trust, and resistance to change factors. Nearly all the affect based trust measures hang together with the exception of abt6 (This person approaches his/her job with professionalism and dedication. (ABT-6)) which is strongly correlated with the items that measure cognition based trust. The variable, organizational justice, includes three subfactors, fairness, employee voice and justification. The first four items for fairness cluster together and appear to measure that concept. The questions are shown below. Survey questions Orgjv6, Orgjv7, Orgjv8 and OrgjJ11 cluster together to form the Employee Voice measure. Similarly, Orgjv5, Orgjv8, and OrgjJ10 load onto Justification. These subscales will be utilized as one scale, organization justice, in the computation of Cronbach’s alpha.
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Univariate Outliers
Outliers can cause serious problems for any regression-based test such as SEM. Due to distance separation from the normal data swarm outliers tend to make the regression line deviate in the direction of the outlier. Outliers can appear in both univariate and multivariate situations but Tabachnick and Fidell (2001) suggest first assessing univariate outliers. Outliers can be assessed using bivariate scatterplots or boxplots. Examination of the boxplots revealed some variables have outliers that are between 1.5 and three box lengths from the top or bottom edge of the box. The boxplots are in Appendix A. The data were reexamined to check for accuracy. All values were within the expected range and appeared to be a legitimate part of the sample so will remain in the analysis.
Factor analysis has also been articulated by numerous seminal authors as a vital component of a model’s validity. Churchill (1979) stated, “Factor analysis can then be used to confirm whether the number of dimensions can be verified empirically” (p. 69). Nunnally (1978) also stated, “factor analysis is intimately involved with questions of validity…Factor analysis is at the heart of the measurement of psychological constructs” (pp. 112-113). The factor-analytic stage (EFA) therefore, is an assessment of one aspect of model validity.
Principle components analysis transforms the original measures into a smaller set of linear combinations with all of the variance being used (Pallant, 2003). Factor analysis (FA) is similar; however it uses a mathematical model and only analyzes shared variance. Tabachnick and Fidell (2001) described the difference between EFA and FA: “If you are interested in a theoretical solution uncontaminated by unique and error variability, FA is your choice. If on the other hand you want an empirical summary of he data set, PCA is the better choice” (p. 611). In addition, PCA yields components whereas FA provides factors. Sometimes they are used interchangeably. This study will follow the factor analysis guidelines of Mertler and Vannatta (2005).
There are two basic requirements to factor analysis: sample size and the strength of the relationship of the measures. The sample size of 286 is close to the 300 recommended by Tabachnick and Fidell (2001) and is sufficient. The authors also caution that a matrix that is factorable should include correlations in excess of .30. If none are found, reconsider use of factor analysis.
An inspection of the correlation matrix in Table 3 shows less than half the values < .3 as recommended by Tabachnick and Fidell (2001). Principal axis factoring with Promax rotation was performed to see if the items that were written for the survey to index the seven constructs (communication, commitment, organizational justice, organizational citizenship, affect based trust, cognition based trust and resistance to change) actually do hang together. That is, are the participants’ responses to the communication questions more similar to each other than their responses to the commitment items? The Kaiser-Meyer-Olkin (Kaiser, 1970, 1974) Measure of Sampling Adequacy (KMO) value of .891 exceeds the recommended value of .6 and the Bartlett’s Test of Sphericity (Bartlett, 1954) reached statistical significance (Chi-square = 11,880.86 (p < .001; df = 1431)) supporting the factorability of the correlation matrix. Examination of the correlation matrix revealed some collinearity (Determinant = 0.000) between variable pairs. In example, the correlation between cmit6 and comu4 was .72. The first analysis resulted in eleven factors, however, these made no theoretical sense, but were based on Eigenvalues greater than one. For instance, factor 11 included no variables. These results are shown in Appendix B. To determine which questions load on a factor, the cutoff of .278 was chosen (twice the significant correlation of a sample of 350 at the .01 level). However, when the question loading magnitude was much greater on another factor, the question was identified loading just on that factor. The variables from the following questions have been reverse coded: Organizational Justice (ORGJ-1), (ORG-2), (ORG-6), (ORG-7) (ORG-9), and (ORG-11). The variables from the following questions have been reverse coded: Resistance to Change (RCHG-2) and (RCHG-6). Click here for dissertation statistics help
Factor analysis has also been articulated by numerous seminal authors as a vital component of a model’s validity. Churchill (1979) stated, “Factor analysis can then be used to confirm whether the number of dimensions can be verified empirically” (p. 69). Nunnally (1978) also stated, “factor analysis is intimately involved with questions of validity…Factor analysis is at the heart of the measurement of psychological constructs” (pp. 112-113). The factor-analytic stage (EFA) therefore, is an assessment of one aspect of model validity.
Principle components analysis transforms the original measures into a smaller set of linear combinations with all of the variance being used (Pallant, 2003). Factor analysis (FA) is similar; however it uses a mathematical model and only analyzes shared variance. Tabachnick and Fidell (2001) described the difference between EFA and FA: “If you are interested in a theoretical solution uncontaminated by unique and error variability, FA is your choice. If on the other hand you want an empirical summary of he data set, PCA is the better choice” (p. 611). In addition, PCA yields components whereas FA provides factors. Sometimes they are used interchangeably. This study will follow the factor analysis guidelines of Mertler and Vannatta (2005).
There are two basic requirements to factor analysis: sample size and the strength of the relationship of the measures. The sample size of 286 is close to the 300 recommended by Tabachnick and Fidell (2001) and is sufficient. The authors also caution that a matrix that is factorable should include correlations in excess of .30. If none are found, reconsider use of factor analysis.
An inspection of the correlation matrix in Table 3 shows less than half the values < .3 as recommended by Tabachnick and Fidell (2001). Principal axis factoring with Promax rotation was performed to see if the items that were written for the survey to index the seven constructs (communication, commitment, organizational justice, organizational citizenship, affect based trust, cognition based trust and resistance to change) actually do hang together. That is, are the participants’ responses to the communication questions more similar to each other than their responses to the commitment items? The Kaiser-Meyer-Olkin (Kaiser, 1970, 1974) Measure of Sampling Adequacy (KMO) value of .891 exceeds the recommended value of .6 and the Bartlett’s Test of Sphericity (Bartlett, 1954) reached statistical significance (Chi-square = 11,880.86 (p < .001; df = 1431)) supporting the factorability of the correlation matrix. Examination of the correlation matrix revealed some collinearity (Determinant = 0.000) between variable pairs. In example, the correlation between cmit6 and comu4 was .72. The first analysis resulted in eleven factors, however, these made no theoretical sense, but were based on Eigenvalues greater than one. For instance, factor 11 included no variables. These results are shown in Appendix B. To determine which questions load on a factor, the cutoff of .278 was chosen (twice the significant correlation of a sample of 350 at the .01 level). However, when the question loading magnitude was much greater on another factor, the question was identified loading just on that factor. The variables from the following questions have been reverse coded: Organizational Justice (ORGJ-1), (ORG-2), (ORG-6), (ORG-7) (ORG-9), and (ORG-11). The variables from the following questions have been reverse coded: Resistance to Change (RCHG-2) and (RCHG-6). Click here for dissertation statistics help
MVA Analysis
The SPSS missing value analysis (MVA) was used to analyze the data for both MAR and MCAR data loss using an expectation maximization technique. Little’s (Little & Rubin, 2002) MCAR resulted in a Chi-square = 1852.25 (p = 0.099; df = 1778). This significance denotes that the missing data is MCAR and the data loss pattern is not systematic.
The SPSS MVA module also incorporates an expectation-maximization (EM) algorithm for generation of imputed values used to fill in all the missing data. Since the data is MCAR, listwise deletion is a better alternative than pairwise deletion which may cause covariance matrix issues due to unequal numbers of cases (Kline, 2005).
The AMOS application is unique in that it can be used to analyze data that includes missing data. AMOS incorporates a special form of maximum likelihood estimation (Special ML) which partitions all cases with the same missing data patterns. Peters and Enders (2002) found that this method for analyzing datasets with incomplete data “outperformed traditional (available case) methods” (cited in Kline, 2005, p. 56). Tabachnick and Fidell (2001) suggest using both methods (with and without missing data) but favor the EM imputation method and listwise methods (if data is ignorable) over mean substitution or pairwise deletion. Tabachnick and Fidell (2001) state, “The decision about to handle missing data is important. At best, the decision is among several bad alternatives” (p. 59).
Caution should be exercised with any method using a dataset with a high percentage of missing values (> 5%). Nunnally and Bernstein (1994) suggest that when there is a high percentage of missing values any of these methods may be unsatisfactory. Incorporating listwise deletion may be the best option for MCAR data since EM imputation may cause distorted coefficients of association and correlations (Kalton & Kasprzyk, 1982). In the present data set, listwise deletion resulted in a final sample size of 286 respondents.
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The SPSS MVA module also incorporates an expectation-maximization (EM) algorithm for generation of imputed values used to fill in all the missing data. Since the data is MCAR, listwise deletion is a better alternative than pairwise deletion which may cause covariance matrix issues due to unequal numbers of cases (Kline, 2005).
The AMOS application is unique in that it can be used to analyze data that includes missing data. AMOS incorporates a special form of maximum likelihood estimation (Special ML) which partitions all cases with the same missing data patterns. Peters and Enders (2002) found that this method for analyzing datasets with incomplete data “outperformed traditional (available case) methods” (cited in Kline, 2005, p. 56). Tabachnick and Fidell (2001) suggest using both methods (with and without missing data) but favor the EM imputation method and listwise methods (if data is ignorable) over mean substitution or pairwise deletion. Tabachnick and Fidell (2001) state, “The decision about to handle missing data is important. At best, the decision is among several bad alternatives” (p. 59).
Caution should be exercised with any method using a dataset with a high percentage of missing values (> 5%). Nunnally and Bernstein (1994) suggest that when there is a high percentage of missing values any of these methods may be unsatisfactory. Incorporating listwise deletion may be the best option for MCAR data since EM imputation may cause distorted coefficients of association and correlations (Kalton & Kasprzyk, 1982). In the present data set, listwise deletion resulted in a final sample size of 286 respondents.
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MIssing Values
According to Tabachnick and Fidell (2001), “Missing data is one of the most pervasive problems in data analysis “ (p. 58). Missing data can have serious effects on the reliability, validity and generalizability of the data (Tabachnick & Fidell, 2001). Missing data can be indicative of lack of knowledge, fatigue or sensitivity, or interpretation by the respondent of the questionnaire relevance. When the number of missing cases is small (< 5%) it is common to exclude the cases from the analysis (Tabachnick & Fidell, 2001). In the present analysis, every variable is missing at least 16% of the responses. The univariate statistics are shown below in Table 2.
Before exploratory factor analysis it must be determined if missing data is systematic (represents bias) or is ignorable. Missing data also has other important ramifications, especially in factor analysis. Factor analysis using listwise deletion should not be conducted unless the missing data is at least missing completely at random (MCAR).
Before exploratory factor analysis it must be determined if missing data is systematic (represents bias) or is ignorable. Missing data also has other important ramifications, especially in factor analysis. Factor analysis using listwise deletion should not be conducted unless the missing data is at least missing completely at random (MCAR).
Normality
Data normality is focused on the premise that data is from one or more normally distributed populations. Characteristics of a distribution can be described by its moments (the average of its values which are then raised to a certain power). The normal distribution in standard form has a first moment (mean) of zero, a second moment (variance) of one, a third moment (skewness) of zero and a fourth moment (kurtosis) of three. Many statistical programs like SPSS subtract the three from the kurtosis value to normalize to zero for reporting purposes. These statistics are based on the distribution curve as a whole and not on individual cases. Data normality is usually focused on skewness and kurtosis which are measures of shape. A skewness and kurtosis of zero is indicative of a normal distribution. Skewness is associated with the symmetry of the distribution. Kurtosis is associated with how peaked or flat the distribution is. A kurtosis above zero is indicative of a peaked distribution while a negative value is indicative of a flat distribution. Some authors suggest that univariate values approaching at least 2.0 for skewness and 7.0 for kurtosis should be suspect (West et al., 1995; Yuan & Bentler, 1999). The descriptive statistics, including skewness and kurtosis are shown below in Table 1. Examination of the distributions indicated only one variable, cmit8 has a high negative skew, -2.179. Computing the log transformation reduced the skew to .851 and the kurtosis to.247. The transformed variable will be used in further analyses.
Screening of the Data
Careful analysis of data applicability after collection and before analysis is probably the most time-consuming part of data analysis (Tabachnick & Fidell, 2001). This step is, however, of utmost importance as it provides the foundation for any subsequent analysis and decision-making which rests on the accuracy of the data. Incorrect analysis of the data during purification, including EFA, and before conducting confirmatory SEM analysis may result in poor fitting models or, worse, models that are inadmissible.
Data screening is important when employing covariance-based techniques such as structural equation modelling where assumptions are stricter than for the standard t-test. Many of the parametric statistical tests (based on probability distribution theory) involved in this study assume that: (a) normally distributed data – the data are from a normally distributed population, (b) homogeneity of variance – the variances in correlational designs should be the same for each level of each variable, (c) interval data – data where the distance between any two points is the same and is assumed in this study for Likert data, and (d) independence – the data from each respondent has no effect on any other respondent’s scores.
Many of the common estimation methods in SEM (such as maximum-likelihood estimation) assume: (a) “all univariate distributions are normal, (b) joint distribution of any pair of the variables is bivariate normal, and (c) all bivariate scatterplots are linear and homoscedastic” (Kline, 2005, p. 49). Unfortunately, SPSS does not offer an assessment of multivariate normality but Field (2005) and others (Kline, 2005; Tabachnick & Fidell, 2001) recommend first assessing univariate normality. The data were checked for plausible ranges and examination was satisfactory. There were no data out of range.
Data screening is important when employing covariance-based techniques such as structural equation modelling where assumptions are stricter than for the standard t-test. Many of the parametric statistical tests (based on probability distribution theory) involved in this study assume that: (a) normally distributed data – the data are from a normally distributed population, (b) homogeneity of variance – the variances in correlational designs should be the same for each level of each variable, (c) interval data – data where the distance between any two points is the same and is assumed in this study for Likert data, and (d) independence – the data from each respondent has no effect on any other respondent’s scores.
Many of the common estimation methods in SEM (such as maximum-likelihood estimation) assume: (a) “all univariate distributions are normal, (b) joint distribution of any pair of the variables is bivariate normal, and (c) all bivariate scatterplots are linear and homoscedastic” (Kline, 2005, p. 49). Unfortunately, SPSS does not offer an assessment of multivariate normality but Field (2005) and others (Kline, 2005; Tabachnick & Fidell, 2001) recommend first assessing univariate normality. The data were checked for plausible ranges and examination was satisfactory. There were no data out of range.
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