HOW TO MAKE INFERENTIAL STATISTICS WITH SPSS
October 13 2018, By Chidi Rafael
When decisions or judgements are to be made from a study or a descriptive data, it is imperative to adopt various techniques for inferences.
One way to make inferences is by formulating a Hypothesis. A hypothesis may be needed in a study for users to decide appropriately on whether an assumption is true or false.
To make this tutorial simple and straight forward for a beginner, I will stick with these areas where Inferential Statistics could be applied in research. These four areas are:
 Relationships.
 Association.
 Correlation.
 Variance.
Before we go deep into these four major areas mentioned above, it is necessary to know the Decision Rule when Using the Statistical Package for Social Sciences (SPSS) for judgements.
Using a 95% Confidence Level, the decision is pegged at 0.05. (p =0.05). This simply implies that when p (the Significance level) is less than or equal to 0.05, we should accept (i.e. it is Significant Statistically).
On the other hand, when p is greater than 0.05, we should reject the hypothesis (i.e. it is not Significant Statistically).
The table below represents the Decision Rule:
Result 
Decision 
p< or = 0.05 
Accept (Significant) 
p> 0.05 
Reject (Not Significant) 
Figure 1.0
*This is dependent on a significance level of 0.05.
A) Relationships: Applying Linear Regression in SPSS
To measure relationship(s) between two or more variables linearly, we can use the Linear Regression. The example below illustrates how this can be applied using SPSS.
Illustration 1
The following data shows the Income and Expenditure pattern of Mr. Okoro from January to June 2018.
MR OKORO 

INCOME AND EXPENDITURE REPORT FROM JANJUNE 2018 

MONTH 
INCOME (NGN) 
EXPENDITURE (NGN) 
JAN 
35,000 
32,500 
FEB 
50,000 
43,000 
MAR 
53,000 
50,000 
MAY 
61,000 
58,000 
JUNE 
74,000 
73,000 
Figure 2.0
Objective
To compute the data in Figure 2.0 in SPSS and test if there is a Significant Relationship between Income and Expenditure.
Solution to Illustration 1 Using SPSS
 Open the SPSS Software and click on Variable View
 Name your Variables (No spaces Accepted) as shown below:
Credit: IBM SPSS Statistics
 Click on Data View button to enter the values or results gotten from the study. See below:
Credit: IBM SPSS Statistics
 Click on Analyze > Regression > Linear.
 Move the Income Variable to the Independent(s) and Expenditure Variable to Dependent using the Arrow button
Credit: IBM SPSS Statistics
 Click OK for the result to display in the SPSS Output Screen.
Click to Download SPSS Software
Interpreting the Result
Our emphasis will be on 3 major tables:
 Model Summary.
 ANOVA.
 Coefficients.
Credit: IBM SPSS Statistics
Model Summary
The model Summary shows the relationship between the variables. R of 0.991 shows the strength of the relationship between the Independent Variable/Predictor (Income) and the Dependent Variable (Expenditure) in Decimal or Percentage form.
From the above example, Income accounts for 0.991 or 99.1% change in Expenditure. In other words, 99.1% change in Expenditure can be explained by the Predictor (Income).
ANOVA
The ANOVA table is used to check for Fitness of data in the model. To decide whether there is a statistically significant relationship between variables, we will look at the heighted in the Sig. Column above.
The Sig. Column of 0.001 is less than 0.05 (See Figure 1.0 for Decision Rule). This implies that there is a Statistically Significant relationship between Income and Expenditure.
Coefficients
The Coefficients table provides us with information to predict Expenditure from Income.
The highlighted above shows that 1 unit increase in Income will result to 1.057 increase in Expenditure.
B) ASSOCIATIONS: APPLYING CHISQUARE IN SPSS
ChiSquare can be used to test for Association between two or more variables. The ChiSquared test measures if there is a significant difference between Expected Frequency (EF) and the Observed Frequency (OF).
Illustration 2
A survey was conducted on the reading preference of Undergraduate Students in The University of Abuja. With a Sample Size (n) of 20, the following results were gotten:
Gender 
Preferred Reading Method 
Total 

Book 
Online 

Male 
3 
7 
10 
Female 
6 
4 
10 


Total 
20 
Figure 3.0
Objective
From the above data in Figure 3.0, You are required to compute the results in SPSS and test for Association between Gender and Preferred Reading Method using ChiSquare.
Solution to Illustration 2 in SPSS
 Enter the Data (As shown in Figure 2.0) in the Data View as shown below:
Credit: IBM SPSS Statistics
NOTE: A little Data Coding is required in the Variable View. Data Type for Gender should be changed to ‘String’, and ‘1’ should be used to represent ‘Book’, 2 should represent ‘Online’.
 Click on Analyze > Descriptive > Cross Tabs
 Use the Arrow Button to move the Gender Variable to Row(s) and Reading_Method Variable to Column(S).
Credit: IBM SPSS Statistics
 Click on the Statistics button. Select ChiSquare and Phi and Cramer’s V, then Click on Continue .
Credit: IBM SPSS Statistics
 Click on the Cells button. Select Observed, Row Column and Total. Click Continue .
Credit: IBM SPSS Statistics
 Finally, Click the OK button for the Result.
Credit: IBM SPSS Statistics
Interpreting the Result
The Crosstabulation Table
This table simply illustrates the frequency distributions of Gender Versus Reading Method Preferences of the Respondents used for the study.
ChiSquare Tests
This is the most important table used for measuring Association between variables used for the study.
From the table, the Pearson ChiSquare (p) = 0.178. since p > 0.05, we can conclude that there is no Statistically Significant association between Gender and the reading preference of Undergraduates in the University of Abuja.
C) APPLYING CORRELATION IN SPSS
The Pearson Correlation test measures the strength and direction of two variables. We will use the illustration below to demonstrate this.
Illustration 3
The following data shows the Income and Expenditure pattern of Mr. Okoro from January to June 2018.
MR OKORO 

INCOME AND EXPENDITURE REPORT FROM JANJUNE 2018 

MONTH 
INCOME (NGN) 
EXPENDITURE (NGN) 
JAN 
35,000 
32,500 
FEB 
50,000 
43,000 
MAR 
53,000 
50,000 
MAY 
61,000 
58,000 
JUNE 
74,000 
73,000 
Figure 4.0
Objective
You are to compute the data in Figure 4.0 using SPSS and test if there is a Significant Correlation between Income and Expenditure.
Solution to Illustration 3 in SPSS
 Properly Name your variables (Income and Expenditure) in the Variable View and Enter your data on the Data View as shown below:
Credit: IBM SPSS Statistics
 Click on Analyze > Correlate > Bivariate
 Use the Arrow button to move both variables to the Variables Box.
Credit: IBM SPSS Statistics
 Click OK
Interpreting the Result
The table above presents a mix of the Pearson Correlation, the Significance Value (Sig.) and the Sample Size (N) in a matrix form.
The Pearson Correlation (r) = 0.991 with p = 0.001. This implies that there is a significant Correlation between Income and Expenditure, since p < 0.05.
D) TEST FOR VARIANCE: APPLYING ONE WAY ANOVA IN SPSS
One way to test for variance is through OneWay ANOVA. Oneway ANOVA compares the means between two or more variables to test for a statistically significant difference.
Oneway ANOVA is most suitable for testing variance between two or more unrelated groups.
Click to Download SPSS Software
Illustration 4
A Quiz was set for two groups (Male and Female) in a class to determine if there is a significant difference between Gender and Academic Performance. With a sample size(n) of 10, the results below were gotten.
Name 
Gender 
Score 
John 
Male 
20.01 
Mark 
Male 
15.98 
Andrew 
Male 
43 
Peter 
Male 
21.4 
Solomon 
Male 
32.4 
Joy 
Female 
20.12 
Amaka 
Female 
13.5 
Rose 
Female 
56.1 
Cynthia 
Female 
18.7 
Emem 
Female 
45.2 
Figure 5.0
Objective
You are Required to Compute the Data in Figure 5.0 using SPSS and test for Variance using the OneWay ANOVA.
Solution to Illustration 4 in SPSS
 Enter the data properly in SPSS. You Data View should look like this:
Credit: IBM SPSS Statistics
 Click on Analyze > Compare Means > OneWay ANOVA.
 Use the Arrow Button to move the Dependent Variable (Score) to the Dependent List, and the Independent Variable (Gender) to the ‘Factor’ Field.
Credit: IBM SPSS Statistics
 Click on OK .
Interpreting the Result
The ANOVA table represents the results between Groups and within Groups used for the study. p= 0.680 shows that there is no statistically significant difference between Gender and Academic Performance of students used for the study.
Click to Download SPSS Software
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