# **Interpreting a Reliability Analysis in SPSS**

**CASE STUDY: RELIABILITY AND PRINCIPAL COMPONENTS SPSS**

__Part 1__

The objective of this part is to construct two scales based on the database “shelter1990”. One of the scales will measure the *level of satisfaction* of an individual, and the other the *level of depression*. In order to construct these scales, a number of items from the survey will be used. For the first scale, questions “nb26a” through “nb26j” will be used. For the second scale, questions “ra95”, “ra120”, and “ra121” will be used.

__Level of Satisfaction Scale__:

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First of all, an initial descriptive statistics analysis of the variables involved is performed

It is noticeable that all the questions have a very variable number of valid responses. Specifically, the question *Satisfied-job services* has a very low number of valid responses compared to the other questions. This may be due to the different nature of the questions which may deal with issues that are more sensitive for some people.

A more detailed summary of descriptive statistics is shown below:

__Cronbach’s Alpha__

It is required to check whether the data is multidimensional or one-dimensional. In other words, we need to know if the proposed scale measures the same, or it measures more than one thing. The Cronbach’s alpha is shown below:

The value of Cronbach’s Alpha is equal to, which means that the scale is one-dimensional (the value of the alpha is greater than 0.7, the commonly accepted cutoff value for Cronbach’s alpha).

Since Cronbach’s shows one-dimensionality it makes sense to construct a scale. The scale is only calculated for people who responded at least 8 out of the 10 questions.

- The average of the 10 questions was computed and recorded as
*Satisf_scale*on the SPSS dataset. The descriptive statistics of the scale are shown below:

The scale was calculated for 240 subjects.

The sample mean is, and the sample standard deviation is. The median is, and the range is 8. The histogram is shown below:

The histogram is clearly right skewed, which indicates a sign of departure from a normal distribution. In fact, a normality test is shown below:

This indicates that the p-value is *p* = 0.000, which is a strong evidence that the scale is not normally distributed.

__Level of Depression Scale__:

First, an initial overview of the descriptive statistics analysis of the variables involved is shown below:

- There is not a great variability in the number of valid answers for each question.

A detailed summary of descriptive statistics is shown below:

** Descriptive Statistics**

__Cronbach’s Alpha__

The one-dimensionality check is performed using Cronbach’s alpha. The results are shown below (SPSS output)

The value of Cronbach’s Alpha is equal to, which is not greater than 0.7, the commonly accepted cutoff value for Cronbach’s alpha. Furthermore, negative value for Cronbach's Alpha indicate that some items required reverse recoding.

A Principal Components analysis will be performed:

The table above shows that only one component was extracted, and hence we can consider the items as one-dimensional. The scale is only calculated for people who responded all the three questions.

- The average of the 3 questions was computed and recorded as
*Dep_scale*on the SPSS dataset. The descriptive statistics of the scale are shown below:

- The scale was calculated for 231 subjects.

The sample mean is, and the sample standard deviation is. The median is, and the range is 4. The histogram is shown below:

The histogram is slightly left-skewed, which indicates a sign of departure from a normal distribution. In fact, a normality test is shown below:

This indicates that the p-value of the test is *p* = 0.000, which means that we reject the null hypothesis of normality.

- Finally the age of the respondents was recorded on the dataset as
*age*. The descriptive statistics are shown below:

The histogram is

__Part 2__:

**Research Questions**

(1) *Do men and women have the same levels of satisfaction?*

We need to test the following:

This corresponds to a t-test. The results, using SPSS are shown below:

The t-statistics is *t* = 1.746, and the corresponding *p*-value is *p* = 0.079, which means that we fail to reject the null hypothesis. In other words, we don’t’ have enough evidence to claim that men and women have different levels of satisfaction

(2) *Is marital status (“ns36”) is associated with level of satisfaction.*

We need to test the following hypotheses:

This corresponds to an ANOVA. Using SPSS, the following results are obtained:

This means that the F-statistics is *F* = 0.961, and the corresponding p-value is *p* = 0.443. This means that there is not enough evidence to claim that there is a difference between the means, at the 0.05 significance level.

(a) *Are those who are least distressed about not having a regular place to stay (“nb33”) are the most satisfied with the shelter*

First we need to test the following hypotheses:

This corresponds to an ANOVA. Using SPSS, the following results are obtained:

The F-statistics is *F* = 0.069, and the corresponding p-value is *p* = 0.993, *which implies that we fail to reject the null hypothesis*. This means that there is not enough evidence to claim that there is a difference between the means, at the 0.05 significance level. (There is no need to perform a Post Hoc analysis)

(b) *Are those looking for work (“na155”) more satisfied than those who are not?*

We need to test the following:

This corresponds to a t-test. The results, using SPSS are shown below:

The t-statistics is *t* = 0.646, and the corresponding *p*-value is *p* = 0.519, which means that we fail to reject the null hypothesis. In other words, we don’t have enough evidence to claim that those who are looking for jobs have different mean levels of satisfaction than those who are not.

(4) *Is satisfaction with the shelter negatively associated with age?*

We perform a correlation analysis to settle this question. Using SPSS we get

Both the parametric and nonparametric analysis shows that there is not a significant association between *Satisfaction Level *and *age.*

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