ONE WAY ANOVA USING SPSS

Hello everyone, In this post, we will be discussing that how to run the One Way ANOVA using SPSS. One-way analysis of variance is a statistical technique used for comparing means of more than two groups. This technique can be used in a situation where the data is measured either on interval or ratio scale. In one-way ANOVA, group means are compared by comparing the variability between groups with that of variability within the groups. This is done by computing an F-statistic. There are varieties of situations in which one-way analysis of variance can be used to compare the means of more than two groups.

Lets illustrate this with an example using SPSS. Imagine that a researcher is interested to see that if annual income level (in US$) is same or different across the four regions of a particular city e.g. New York. The regions in his study are east, west, north, and south. To check this, you need to follow the procedure of developing hypothesis, collection of data, running the One way ANOVA, and then based on the test results accepting or rejecting the hypothesis, and finally arriving on conclusion.

Suppose that researcher developed the following hypothesis

Null Hypothesis= H0= Annual income level of residents in the four regions of city are same.

Alternative Hypothesis= H1= Annual income level of residents in the four regions of city are statistically different.

To test this hypothesis, the researcher collects random annual income data from twenty people belonging to four regions. Let say the data collected is as under in US$ per annum.

East= 22000, 15000, 30000, 22000, 26000

West= 35000, 37000, 42000, 39000, 29000

North=45000, 39000, 35000, 45000, 29000

South=19000, 25000, 22000, 24000, 30000

To run the One Way ANOVA in SPSS, you need to first input the variables and data. For this study, you need to put two variables namely Annual Income in US$ and Region (For details on how to input the variables and data in to SPSS, please see our previous posts)

Once you have input the variables and data in to SPSS, now you are in position to run the one way ANOVA test by applying the following command.

Analyze---Compare Means---- One Way ANOVA

A dialogue box will appear which will show both variables Now take the ‘AnnualIncomeUS$’ to the ‘dependent list’, and ‘Region’ variable in to ‘Factor’ box. Then click on ‘Post Hoc’ option and check the ‘Scheffe’, click on continue. Then click on ‘Options’ and check the ‘Descriptive’ and ‘Means plot’ and click on continue, and then on ‘OK’.

 The results will appear in the ‘output window’ which can be interpreted as follow. 

The first table with the heading ‘Descriptive’ is only giving basic information including sample size for each group, mean, standard deviation, minimum, and maximum values. 

The second table with the heading ‘ANOVA’ will show the basic statistics such as F statistics, sig value and so on. In this example, the value of F is 11.229 with the Sig value of 0.000 which shows that there are significant mean differences between groups. In another words, the mean annual income in this example is statistically different among four groups namely east, west, north, and south. The F Statistics has some limitation as it only tells us that whether there are differences in means between different groups or not. Further, post hoc tests such as test Scheffe is used to identify the differences between means of individual groups.

The next table with the heading ‘Multiple Comparisons’ is based on the test Schefffe to discover that which groups have significant differences between them. Starting with the first row, you will find that here the reference point is east and further its comparison with west, north, and south is given. Here, the important point is the individual Sig value which shows that whether east has significant differences with other groups. So in this example, the value of Sig which is .012 in the first row shows that there are significant differences between annual income in US$ between east and west citizens. Similarly, in second row, the sig value of 0.003 shows that the average difference between east and north is also statistically significant. In the third row, the sig value of .993 shows that the mean annual income difference between the citizens of east and south are not statistically different; or in another words they are very similar (you can also check this by simply going through data visually)

Similarly, the comparison is also based on west, north, and south with other groups is given which can be interpreted accordingly.

(Note: if in Post hoc test, the sig value appears less than 0.05 then the interpretation will be that there are significant differences exist between those two groups; however, if sig value appears greater than 0.05, then the interpretation will be that there are insignificant differences exist between those two groups.)

The graph with heading ‘Mean Plot’ is used to visually see the differences between four groups. Its interpretation is also relatively simple, as you can see the average income on one axis and four groups on the other.

Finally, based on the value of F statistics and its Sig value given in the first table, we can accept the alternative hypothesis and reject the null hypothesis. Thus, the conclusion is that the average income in US$ in this city are statistically different among four regions.

(Note: If F statistics appears smaller and Sig value greater than 0.05, then we will reject the alternative hypothesis and accept the null hypothesis. Similarly, if F statistics appears greater than 4 and sig value appears less than 0.05, then we will accept the alternative hypothesis and reject the null hypothesis.)

Sample SPSS File is as under.
One Way ANOVA SPSS Practice file

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PAIRED SAMPLE T-TEST

In this post, we will be discussing that how paired sample t-test is conducted via SPSS. Paired Sample t-test is used when we want to test the hypothesis regarding the comparison of mean of same group mostly before and after situation. Lets illustrate this with an example. 

Suppose that you want to see that if sales (in US$) is increased after a massive advertising campaign. To check this, you need to follow the steps of developing hypothesis, collecting the data, running the pair sample t-test, accepting or rejecting the hypothesis, and then arriving on conclusion.

Lets say that you have developed the following hypothesis:

Null Hypothesis=H0= The average daily sale before and after the massive advertising campaign is same

Alternative Hypothesis=H1= The average daily sale before and after the massive advertising campaign is statistically different

Lets say that to test the above hypothesis, you have collected the daily sales data in US$ before and after the massive advertising campaign which is as under.

Before: 3000, 2500, 2000, 1500, 1800, 2500. 3300, 2600, 3300, 2900, 3200, 2200, 1900, 2000, 2000, 1900, 2200, 2200, 1500, 2400

After: 3100, 2700, 3200, 2900, 3200, 2900, 2200, 2400, 1900, 2500, 3000, 3200, 3500, 3500, 4000, 1900, 3900, 4400, 1900, 2300

To run the paired t-test on this data, you need to put it in the SPSS. So in SPSS, first create the variables of ‘before’ and ‘after’; and then input the data in to it (To learn about how to input the variables and data in to SPSS please see my previous posts).

 Once variables and data is fed it to the SPSS, now you are in position to test the following hypothesis by running the following command.

Analyze---Compare Means---Paired Samples T Test

A dialogue box will appear which will show the variables of ‘before’ and ‘after’. Now click on ‘before’ variable and shift it to ‘Variable1’ and ‘after’ to ‘Variable2’ and then simply click on ‘Ok’. 

The results will appear in ‘output window’ which can be interpreted as follow.The first table with the heading ‘Paired Samples Statistics’ simply provides the mean average, number of sample and standard deviation. So in this example, the mean value for before is 2345; while the mean value for after is 2930. Both of these values show the average sales in US$. Similarly, the standard deviation shows the dispersion of mean from its central value.

The second table heading ‘Paired Samples correlations’ show the correlation or association between both variables. In this example, the value of correlation which is -.270 shows that both before and after have negative association of 27%. 

Third table with the heading of ‘Paired Samples Test’ is the main table which shows that Mean difference between before and after is -585 US$. Similarly, the value of t and sig (2-tailed) is used to test the hypothesis. In this example, the t value of -2.560 and sig value of .019 shows that the sales difference between before and after is statistically different and thus, we reject the null hypothesis and accept the alternative hypothesis. So the conclusion is that the massive advertising is indeed brining significant positive difference in daily sales. 

(Note: To accept the alternative hypothesis, the value of t should be greater than 2; while, the value of Sig should be less than 0.05. In case, t value is less than 2 and sig value is greater than 0.05, then we will accept the alternative hypothesis and reject the alternative hypothesis.)

SPSS Practice file for Paired Sample T Test is as under.

SPSS Practice File

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INDEPENDENT SAMPLE T-TEST

In this post, we will be discussing that how independent sample t-test is conducted on SPSS. This test is used when we want to test the hypothesis regarding the means belonging to two separate groups. Lets illustrate this with an example.

Suppose that you are an HR Manager for a large organization and want to find out that if there is some wage differences between male and female salaries. To test this, you can follow the process by developing hypothesis, collecting data, running the independent sample t-test, accepting or rejecting the hypothesis, and then arriving on conclusion.

First you will develop the hypothesis, a sample is as under.
H0 (Null Hypothesis) = There is no differences between the male and female wages in this organization
H1 (Alternative Hypothesis) = There is significant differences between the male and female wages in this organization.Male= 1500, 2500. 3500, 1000, 2500, 1500, 2000, 2000, 2500, 3000 Female= 1000, 1000, 1500, 1000, 2000, 2500, 1500, 1000, 1500, 2000

To test the hypothesis, suppose you collect data from 30 respondents where 15 were male and 15 were female. The data for both groups is as under in US dollars weekly salary.

Now if you calculate simply the average for both groups, you will get average salary of male as US$ 2200, while average salary for female is US$ 1500. However, to test that whether these differences are really significant , you need to run the independent sample t-test.

First input the two variables namely Gender and Wages in US$ and relevant data in SPSS. (For details on how to input the variable and data in to SPSS, Please see my previous posts). 

Once you have setup the variables and data, then you are in position to actually run the test. 

 The command for running the independent sample t-test is as under.

Analyze---Compare Means--- Independent Sample t-test

A dialogue box will appear, where, you will be able to see the both variables.

 First, transfer the Wages variable in to Test Variable box. Then, transfer the Gender variable in to Grouping Variable box and then click on Define Groups. Another dialogue box will appear where simply write 1 and 2 in group 1 and 2 accordingly. Now click on Continue and then on OK. The results will appear in output window which can be interpreted as under.

The first table with the heading ‘Group Statistics’ is simply giving basic information on the mean of both groups. In this example, the average wages for both male and female are shown in this table which shows that for male the average salary is US$ 2200 and for female the average salary is US$ 1500. In next column, there is standard deviation given which is used to judge the measure of dispersion or the variation in the data from its mean point.

In the second table with the heading ‘Independent Samples Test’ there is various statistics given. The value of t and Sig (2-tailed) is used to test the hypothesis. In this example, the value of t is 2.409 which is greater than the standard test value of 2. Similarly, the value of sig is also less than 0.05; therefore, we can reject the null hypothesis and accept the alternative hypothesis. (Hypothesis is normally accepted when Sig value is less than 0.05. It is also called P value)Thus conclusion is that there is significant differences exist between the average salary of male and female in this organization.

Sample Practice File is as under.

Sample SPSS Practice File

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ONE SAMPLE T-TEST USING SPSS

There are different types of t-tests which are used in different situations. In this post, we will be discussing one sample t-test and relevant hypothesis procedure. One sample t-test is used when a researcher want to know that whether the mean value of a sample is same or different from the mean value of population. For this purpose, we construct hypothesis, collect the data from sample, conduct one sample t-test, then accept or reject the hypothesis and thus arrive on some conclusion. Let’s illustrate this with an example. 

Imagine that you are a manager of a busy fast food restaurant and you want to know that whether the average time of serving a customer is 30 Minutes or more or less than that. To test this, you collect data from 20 customers by observing serving times. Lets say that the data you collected is as follow: 45, 35, 35, 45, 50, 25, 22, 15, 20, 25, 35, 45, 35, 45, 50, 35, 25, 30, 20, and 25 (in Minutes Units)

If you calculate mean of these twenty values, you will get 33.10 Minutes; however, the question is that whether this 33.10 minutes is statistically different from the test value of 30 minutes. For this purpose, we run the one sample t-test. Here we develop the following null and alternative hypothesis. 

H0= The average serving time to the customers is 30 minutes

H1= The average serving time to the customers is different from 30 minutes

Now, just put this variable (Serving Time) and data (20 values) in to SPSS (For details on how to input variable and data in to SPSS, please see my previous posts). 

Once you have put the data, now just run the one sample t-test for which the command is as under.

Analyze---Compare Means---One Sample t-test

A dialogue box will appear which will show you the variables in to the left hand side. 

Now just select the variable (Serving time) and shift it to the selection box at right hand side. Then in the test value box just enter the test or hypothetical value which in this example is 30 minutes. And then just press OK.

Results will appear in Output Window in two tables. The first table with the heading ‘One-Sample Statistics’ provides some basic information. For example, the value of N shows that data consist of 20 samples. Similarly, the mean column shows the average or mean for full sample data which in this case is 33.10 minutes which we already calculated above. The standard deviation is also a regularly used measure which shows the data dispersion from its mean which in this case is 10.81. In this example, the mean serving time of 33.10 minutes with 10.81 standard deviation shows that there is some big variation in serving times (you can also see this from simply looking at data).

In second table heading ‘One-Sample Test’, there are various information. The value of t shows the t statistics value which is used to accept or reject the hypothesis. In this example, the value of t is 1.28 which is quite lower than the standard value of 2. The Sig value in the fourth column is also .215 which is greater than the standard value of .05. Therefore, based on this information we can reject the alternative hypothesis. Thus, conclusion is that average serving time is not statistically different from 30 minutes of serving. (Note: if t value is greater than 2 and sig value is less than 0.05 then you will reject the null hypothesis and accept the alternative hypothesis).

 Practice SPSS file is as under.

One Sample T-Test SPSS File

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REGRESSION ANALYSIS USING SPSS

In this post, I am going to tell you how to run single as well as multiple regression analysis using SPSS. Let’s illustrate this with an example. Imagine that you are conducting a survey and collecting data on the following matters of respondents.

1.      Gender

2.      Age

3.      Income in Dollars ($$)

4.      Brand Loyalty (Perceived)

5.      Service Quality (Experienced/Perceived)

First of all, you need to input the above mentioned variables in to SPSS. For details on how to enter/ input the variables in the SPSS please see my previous posts. Once, the variables and values are entered, now you are ready to enter the data. And once the data is entered in SPSS Data View window, now you are ready to run descriptive statistics, correlation test (Discussed in this post) or regression analysis (Discuss in this post)

In this example, the variable of Brand Loyalty is entered via likert scale with 1 refers to very  low brand loyalty, 2 refers to low, 3 refers to neutral, 4 refers to high, and 5 refers to very high brand loyalty. The variable of service quality is also based on likert scale with 1 refers to very poor service quality, 2 refers to poor, 3 refers to neutral, 4 refers to good, and 5 refers to very good service quality.  Since, regression analysis is mostly run when data is continuous (Based on likert scale); therefore, the data qualify for running normal correlation analysis.

The command for running regression analysis is as under.

Analyze---Regression----Linear

Now a dialogue box will open in front of you. In this box, on left hand side, you can see all of the variables. Select the dependent variable and transfer it in to Dependent box. Similarly, select the independent variable and transfer it in to independent variable box. 

In our example, we transfer, brand loyalty to the dependent box, and service quality in to the independent box. Then, just press OK.

The result will appear in new output window with four tables and some details.

 Here is how you will interpret these results. The first table with the heading ‘Variables Entered/Removed’ is only for information. It will show that the name of the variables entered in the regression analysis. Normally, we ignore this table.  In the second table with the heading ‘Model Summary’, the value of R, R Square, and Adjusted R Square are important for us. The value of R shows the correlation or association between the variables. In this case, the value of R is .431 which shows that both brand loyalty and service quality is 43.1% positively associated. Similarly, the value of R Square is .186 which means that the independent variable (service quality) is explaining 18.6% variation or change in the dependent variable (brand loyalty). The value of adjusted R square is an improved form of R Square as it adjusts for degree of freedom and interpretation is also similar to R Square. Thus, Adjusted R Square is considered a better indicator of model fitness over simple R Square.

Then in third table with the heading ‘ANOVA’, few values are important for us. The value of F shows that how fit the overall model is. In this example, the value of F is 4.10 which show that overall, the model is fit and can be considered satisfactory. Next to F value, there is Sig value which in this example is 0.058 which shows that the F statistics is significant (Its significant since P value is less than 0.10).

In the last or fourth table with the heading of ‘Coefficients’, there are various information. Mostly, we are interested in the value of B or beta for both constant and independent variable. Normally, we do not give much importance to the constant; however, its interpretation is that if everything else goes zero, still there will be some change in the dependent variable. Thus,  in this example, the beta value of 2.16 for the constant shows that if service quality is zero, still, there will be 2.16 units brand loyalty. The beta value of .407 written in the row of service quality shows that if there is one unit increase in the service quality, the brand loyalty will go up by .407 units. Similarly, other important information is t value which can be used to see if the effect of independent variable on the dependent variable is significant or insignificant. In this example, the value of 2.026 of t value shows that the results are significant (It’s significant since its bigger than 2). We can also check the significance by looking at the Sig value located next to t-value. The value of Sig is 0.058 which is less than 0.10 therefore, we can conclude  that the effect of service quality on brand loyalty are significant and if any hypothesis are constructed, then those hypothesis must be accepted based on the significant t or sig value.

So summing up all the things, normally we report the following things with this order in our report or thesis or article.

1.      Constant’s beta value, t value, and sig value

2.      Independent variable’s beta value, t value, and sig value

3.      R Value

4.      R Square value

5.      Adjusted R Square value

6.      F value with its sig value

    

Multiple Regression Analysis:

In multiple regression analysis, everything is similar to the simple regression analysis as discussed above with the exception that in multiple regression analysis there are more than single independent variable. So simply, when inputting the variables in the regression box, you add multiple variables and run the test.

SPSS Practice File is as under

SPSS Pracice File

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CORRELATION ANALYSIS USING SPSS

In this post, I am going to tell you how to run simple correlation analysis using SPSS. Let’s illustrate this with an example. Imagine, you are conducting a survey and collecting data on the following matters of respondents.

1. Gender

2. Age

3. Income in Dollars ($$)

4. Brand Loyalty (Perceived)

5. Service Quality (Experienced/Perceived)

First of all, you need to input the above mentioned variables in to SPSS. For details on how to enter/ input the variables in the SPSS please see my previous posts. Once, the variables and values are entered, now you are ready to enter the data. And once the data is entered in SPSS Data View window, now you are ready to run preliminary tests such as descriptive statistics (Previous posts) or Correlation Analysis (Discussed in this post)

In this example, the variable of Brand Loyalty is entered via likert scale with 1 refers to very low brand loyalty, 2 refers to low, 3 refers to neutral, 4 refers to high, and 5 refers to very high brand loyalty. The variable of service quality is also based on likert scale with 1 refers to very poor service quality, 2 refers to poor, 3 refers to neutral, 4 refers to good, and 5 refers to very good service quality. Since, correlation analysis is mostly run when data is continuous (based on likert scale); therefore, the data qualify for running normal correlation analysis.

The command for running correlation analysis is as under.

Analyze--- Correlate---Bivariate

Now select the variables which you want to correlate and move them to the selection window, and then Press OK. Results will appear.

The results will appear in table form with the heading of correlations. The interpretation is that if you go by column, you will see that in the first column there are different details but mainly the both variables with heading Pearson correlation, sig (2 tailed), and N for both variables. If we go by row, then first for brand loyalty, the value of Pearson correlation of .431 in third column shows that there is 43.1% association between brand loyalty and service quality. Moreover, the relationship between both variables is also significant since the value of sig (2-tailed) refers to the significance or P value and is slightly bigger than 0.05. The N shows the size of sample, which in this case is 20 meaning there were twenty respondents participated in this survey. 

Moving to the next row, you will also get almost same result but only with different position. This means that if you want to see the relationship between service quality and brand loyalty, so this is also 43.1% association between both variables. Moreover, the relationship is significant (p value <0.05) and N means sample size is also 20. The results for both variables is so same because actually, both results are one. Reason, if you compare potato with tomato, or tomato with potato, you will certainly get the same result. Hence, in correlation analysis, the value of correlation between any two variables comes twice but the value remains same.

Correlation between More Than Two Variables (Multiple Variable Correlation):

Lets assume that you run the correlation with same procedure as mentioned above with the exception that you entered three variables in correlation instead of two. The variables which you entered are Income, brand loyalty, and service quality. You will get new results.

Here in this new result table, let’s go with comparing brand loyalty with service quality and income. Going through the first row, the value of .431 shows that there is 43.1% association between brand loyalty and relationship is significant (p value=0.058). Similarly, the value of .351 in income column shows that the brand loyalty and income has 35.1% association while the relationship is insignificant (p value is greater than 0.05). Similarly, you can go to second row and see the relationship between service quality and other two variables, and same procedure for third row with income.

Note: 

1. you can add more than two variables and can get reasonable results up to 10 to 15 variables. 

2. Significant value of P should be less than 0.10 to be moderate significant, less than 0.05 to be significant, and less than 0.01 to be highly significant.

Sample Example SPSS file is as under.
Sample SPSS Practice File

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