Interpretive of Inferential Statistics

When you are working on a research paper, statistics which support your hypothesis are very important. Once you are done with the collection of data, the next crucial step is accurate interpretation of the same. Interpretive statistics allow inferences to be drawn about the similarities or differences between the sample and the population, or between samples or subsets of a sample. The Statistics Help and dissertation consulting services by Dissertation India guide you with this task, making it easy for you and saving time:

This part is an indispensable segment of PhD Dissertation Consulting. Our statisticians prepare reports that are detailed and explain all aspects of the analysis, thus making the inference clear. This is how a sample report looks like:

Factor analysis

The factor analysis is carried out in SPSS and the output is given below:

Total Variance Explained

Extraction Method: Principal Component Analysis.

The table given above lists the Eigenvalues associated with each linear component before extraction, after extraction and after rotation. Before extraction, we can see 11 linear components. That is, Factor 1 explains 22.796% of total variance, Factors 1 and 2 jointly explain 36.718% of total variance and so on. Also, we see that subsequent factors explain only small variances. Therefore, those factors are excluded from the model (the factors for which Eigenvalues are less than 1). The factors which are selected for the model iteration are listed under the heading 'Rotation Sum of Squared Loadings'.

Scree Plot

The scree plot shown below indicates the point of inflexion on the curve. This curve is difficult to interpret because curve begins to tail off after two factors, but there is another drop after 5th factor before a stable plateau is reached. Therefore, we could probably justify retaining either one or four factors.

Rotated Component Matrix

Extraction Method: Principal Component Analysis.

Rotation Method: Varimax with Kaiser Normalization.

Component Transformation Matrix

Extraction Method: Principal Component Analysis.

Rotation Method: Varimax with Kaiser Normalization.

Discriminant Analysis

Summary of Canonical Discriminant Functions

Eigenvalues

First 1 canonical discriminant functions were used in the analysis.

An Eigenvalue indicates the proportion of variance explained. (Between-groups sums of squares divided by within-groups sums of squares). A large Eigen value is associated with a strong function. .

The canonical relation is a correlation between the discriminant scores and the levels of the dependent variable. A high correlation indicates a function that discriminates well. The present correlation of 0.15 is not very low (1.00 is perfect)

Wilks' Lambda

Wilks' Lambda is the ratio of within-groups sums of squares to the total sums of squares. This is the proportion of the total variance in the Discriminant scores not explained by differences among groups. A lambda of 1.00 occurs when observed group means are equal (all the variance is explained by factors other than difference between those means), while a small lambda occurs when within-groups variability is small compared to the total variability. A small lambda indicates that group means appear to differ. The associated significance value indicates whether the difference is significant. Here, the Lambda of 0.977 has an insignificant value (Sig. = 0.484); thus, the group means do not appear to differ.

Canonical Discriminant Function Coefficients

Unstandardized coefficients

A Canonical Discriminant function coefficient indicates the unstandardized scores concerning the independent variables. It is the list of the coefficients of the unstandardized distribution. Each subject's Discriminant score would be computed by entering his or her variable values for each of the variables in the equation. The canonical Discriminant function coefficients for REGR factor score (2 for analysis 1) and REGR factor score (3 for analysis 1) are greater than 0.5

Functions at Group Centroids

Unstandardized canonical Discriminant functions evaluated at group means

'Functions at Group Centroids' indicate the average Discriminant score for subjects in the two groups; more specifically, the Discriminant scores for each group when the variable means are entered into the Discriminant equation. The score for Local Convenience Store (0.122) is significantly greater than the Super Markets score (-0.187). .

Classification Statistics

Classification Processing Summary

Prior Probabilities for Groups

Classification Resultsa

Classification results are a simple summary of the number and per cent of subjects classified correctly and incorrectly. The leave-one-out classification is a cross validation method, of which results are to be presented.

From the above Classification results table, we see that 59.5% of original grouped cases are classified correctly.

Another Example report

Hypothesis testing:

In order to test whether there is a significant mean difference between the Fiscal Incentives and the cost of utilities, we carry out independent sample 'T' test. The null and alternate hypotheses are given below:

Null Hypothesis: H0: μ1 = μ2

That is, there is no significant mean difference between the Fiscal Incentives and the cost of utilities

Alternate Hypothesis: H0: μ1 ≠ μ2

That is, there is a significant mean difference between the Fiscal Incentives and the cost of utilities

The output of the independent sample 'T' test is given below

t-Test: Two-Sample Assuming Equal Variances

From the above output table, we see that the value of the 'T' test statistic is 4.43152344 and its corresponding p-value is 1.4284E-05.

Since the p-value of the test statistic is less than 0.05, there is sufficient evidence to reject the null hypothesis and conclude that there is a significant mean difference between the Fiscal Incentives and the cost of utilities.

Also, we see that the correlation coefficient between the two variables Fiscal Incentives and the cost of utilities is positive and equal to 0.687126. This indicates that there exists a moderate positive linear relationship between the two variables Fiscal Incentives and the cost of utilities.