19.3.2019

Overview of Quantitative Data Analysis Methods in SPSS

Data analysis methods in SPSS
Juho Pesonen
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Analytical thinking in marketing is critical. If marketing is both art and science, the numbers play a big role in the science of marketing. In our Tourism Marketing and Management programme, we study analytical thinking in many courses. One of those is our Practical Tourism Research course. During the course, our students study big data, survey research, online data sets, experimental research and sensor technology as a source of quantitative data. Our main data analysis software is SPSS.

To help our students learn data analysis methods in SPSS, I have collected (From SPSS manual) functionalities and use examples for most common data analysis methods in SPSS. This provides a one-page overview of different data analysis methods and helps to find the correct one for different use cases. Hopefully, the reads of this blog will find this helpful!

SPSS Analyze path

 Functionality

Example

Descriptive Statistics
Analyze -> Descriptive statistics -> Frequencies Provides statistics and graphical displays that are useful for describing many types of variables, how many of what are there in your data. The Frequencies procedure is a good place to start looking at your data. What is the distribution of a company’s customers by industry type? From the output, you might learn that 37.5% of your customers are in government agencies, 24.9% are in corporations, 28.1% are in academic institutions, and 9.4% are in the healthcare industry. For continuous, quantitative data, such as sales revenue, you might learn that the average product sale is $3,576, with a standard deviation of $1,078.
Analyze -> Descriptive statistics -> Descriptives Displays univariate summary statistics for several variables in a single table and calculates standardized values (z scores). Variables can be ordered by the size of their means (in ascending or descending order), alphabetically, or by the order in which you select the variables (the default). If each case in your data contains the daily sales totals for each member of the sales staff (for example, one entry for Bob, one entry for Kim, and one entry for Brian) collected each day for several months, the Descriptives procedure can compute the average daily sales for each staff member and can order the results from highest average sales to lowest average sales.
Analyze -> Descriptive statistics -> Explore The Explore procedure produces summary statistics and graphical displays, either for all of your cases or separately for groups of cases. There are many reasons for using the Explore procedure–data screening, outlier identification, description, assumption checking, and characterizing differences among subpopulations (groups of cases). The exploration may indicate that you need to transform the data if the technique requires a normal distribution. Or you may decide that you need nonparametric tests. Look at the distribution of maze-learning times for rats under four different reinforcement schedules. For each of the four groups, you can see if the distribution of times is approximately normal and whether the four variances are equal. You can also identify the cases with the five largest and five smallest times. The boxplots and stem-and-leaf plots graphically summarize the distribution of learning times for each of the groups.
Analyze -> Descriptive statistics -> Crosstabs The Crosstabs procedure forms two-way and multiway tables and provides a variety of tests and measures of association for two-way tables. The structure of the table and whether categories are ordered determine what test or measure to use. Are customers from small companies more likely to be profitable in sales of services (for example, training and consulting) than those from larger companies? From a crosstabulation, you might learn that the majority of small companies (fewer than 500 employees) yield high service profits, while the majority of large companies (more than 2,500 employees) yield low service profits.

Compare Means
Analyze- > Compare means -> Means The Means procedure calculates subgroup means and related univariate statistics for dependent variables within categories of one or more independent variables. Optionally, you can obtain a one-way analysis of variance, eta, and tests for linearity. Measure the average amount of fat absorbed by three different types of cooking oil, and perform a one-way analysis of variance to see whether the means differ.
Analyze- > Compare means -> One-Sample T Test The One-Sample T Test procedure tests whether the mean of a single variable differs from a specified constant. A researcher might want to test whether the average IQ score for a group of students differs from 100. Or a cereal manufacturer can take a sample of boxes from the production line and check whether the mean weight of the samples differs from 1.3 pounds at the 95% confidence level.
Analyze- > Compare means -> Independent Samples T Test The Independent-Samples T Test procedure compares means for two groups of cases. Ideally, for this test, the subjects should be randomly assigned to two groups, so that any difference in response is due to the treatment (or lack of treatment) and not to other factors. This is not the case if you compare average income for males and females. A person is not randomly assigned to be a male or female. In such situations, you should ensure that differences in other factors are not masking or enhancing a significant difference in means. Differences in average income may be influenced by factors such as education (and not by sex alone). Patients with high blood pressure are randomly assigned to a placebo group and a treatment group. The placebo subjects receive an inactive pill, and the treatment subjects receive a new drug that is expected to lower blood pressure. After the subjects are treated for two months, the two-sample t test is used to compare the average blood pressures for the placebo group and the treatment group. Each patient is measured once and belongs to one group.
Analyze- > Compare means -> Paired Samples T Test The Paired-Samples T Test procedure compares the means of two variables for a single group. The procedure computes the differences between values of the two variables for each case and tests whether the average differs from 0. In a study on high blood pressure, all patients are measured at the beginning of the study, given a treatment, and measured again. Thus, each subject has two measures, often called before and after measures. An alternative design for which this test is used is a matched-pairs or case-control study, in which each record in the data file contains the response for the patient and also for his or her matched control subject. In a blood pressure study, patients and controls might be matched by age (a 75-year-old patient with a 75-year-old control group member).
Analyze- > Compare means -> One-Way ANOVA The One-Way ANOVA procedure produces a one-way analysis of variance for a quantitative dependent variable by a single factor (independent) variable. Analysis of variance is used to test the hypothesis that several means are equal. This technique is an extension of the two-sample t test.

In addition to determining that differences exist among the means, you may want to know which means differ. There are two types of tests for comparing means: a priori contrasts and post hoc tests. Contrasts are tests set up before running the experiment, and post hoc tests are run after the experiment has been conducted. You can also test for trends across categories.

 Doughnuts absorb fat in various amounts when they are cooked. An experiment is set up involving three types of fat: peanut oil, corn oil, and lard. Peanut oil and corn oil are unsaturated fats, and lard is a saturated fat. Along with determining whether the amount of fat absorbed depends on the type of fat used, you could set up an a priori contrast to determine whether the amount of fat absorption differs for saturated and unsaturated fats.

Compare Means
Analyze- > Compare Means-> Bivariate Correlations The Bivariate Correlations procedure computes Pearson’s correlation coefficient, Spearman’s rho, and Kendall’s tau-b with their significance levels. Correlations measure how variables or rank orders are related. Before calculating a correlation coefficient, screen your data for outliers (which can cause misleading results) and evidence of a linear relationship. Pearson’s correlation coefficient is a measure of linear association. Two variables can be perfectly related, but if the relationship is not linear, Pearson’s correlation coefficient is not an appropriate statistic for measuring their association. Is the number of games won by a basketball team correlated with the average number of points scored per game? A scatterplot indicates that there is a linear relationship. Analyzing data from the 1994–1995 NBA season yields that Pearson’s correlation coefficient (0.581) is significant at the 0.01 level. You might suspect that the more games won per season, the fewer points the opponents scored. These variables are negatively correlated (–0.401), and the correlation is significant at the 0.05 level.
Analyze- > Compare Means -> Partial The Partial Correlations procedure computes partial correlation coefficients that describe the linear relationship between two variables while controlling for the effects of one or more additional variables. Correlations are measures of linear association. Two variables can be perfectly related, but if the relationship is not linear, a correlation coefficient is not an appropriate statistic for measuring their association. Is there a relationship between healthcare funding and disease rates? Although you might expect any such relationship to be a negative one, a study reports a significant positive correlation: as healthcare funding increases, disease rates appear to increase. Controlling for the rate of visits to healthcare providers, however, virtually eliminates the observed positive correlation. Healthcare funding and disease rates only appear to be positively related because more people have access to healthcare when funding increases, which leads to more reported diseases by doctors and hospitals.
Analyze- > Compare Means -> Distances This procedure calculates any of a wide variety of statistics measuring either similarities or dissimilarities (distances), either between pairs of variables or between pairs of cases. These similarity or distance measures can then be used with other procedures, such as factor analysis, cluster analysis, or multidimensional scaling, to help analyze complex datasets. Is it possible to measure similarities between pairs of automobiles based on certain characteristics, such as engine size, MPG, and horsepower? By computing similarities between autos, you can gain a sense of which autos are similar to each other and which are different from each other. For a more formal analysis, you might consider applying a hierarchical cluster analysis or multidimensional scaling to the similarities to explore the underlying structure.

Generalized Linear Models
Analyze- > Generalized Linear Models -> Generalized Linear Models The generalized linear model expands the general linear model so that the dependent variable is linearly related to the factors and covariates via a specified link function. Moreover, the model allows for the dependent variable to have a non-normal distribution. It covers widely used statistical models, such as linear regression for normally distributed responses, logistic models for binary data, loglinear models for count data, complementary log-log models for interval-censored survival data, plus many other statistical models through its very general model formulation. A shipping company can use generalized linear models to fit a Poisson regression to damage counts for several types of ships constructed in different time periods, and the resulting model can help determine which ship types are most prone to damage.

 

A car insurance company can use generalized linear models to fit a gamma regression to damage claims for cars, and the resulting model can help determine the factors that contribute the most to claim size.

 

Medical researchers can use generalized linear models to fit a complementary log-log regression to interval-censored survival data to predict the time to recurrence for a medical condition.

 

Regression
Analyze -> Regression -> Linear Linear Regression estimates the coefficients of the linear equation, involving one or more independent variables, that best predict the value of the dependent variable. For example, you can try to predict a salesperson’s total yearly sales (the dependent variable) from independent variables such as age, education, and years of experience. Is the number of games won by a basketball team in a season related to the average number of points the team scores per game? A scatterplot indicates that these variables are linearly related. The number of games won and the average number of points scored by the opponent are also linearly related. These variables have a negative relationship. As the number of games won increases, the average number of points scored by the opponent decreases. With linear regression, you can model the relationship of these variables. A good model can be used to predict how many games teams will win.
Analyze -> Regression -> Binary Logistics Logistic regression is useful for situations in which you want to be able to predict the presence or absence of a characteristic or outcome based on values of a set of predictor variables. It is similar to a linear regression model but is suited to models where the dependent variable is dichotomous. Logistic regression coefficients can be used to estimate odds ratios for each of the independent variables in the model. Logistic regression is applicable to a broader range of research situations than discriminant analysis. What lifestyle characteristics are risk factors for coronary heart disease (CHD)? Given a sample of patients measured on smoking status, diet, exercise, alcohol use, and CHD status, you could build a model using the four lifestyle variables to predict the presence or absence of CHD in a sample of patients. The model can then be used to derive estimates of the odds ratios for each factor to tell you, for example, how much more likely smokers are to develop CHD than nonsmokers.
Analyze -> Regression -> Multinomial Logistic Regression Multinomial Logistic Regression is useful for situations in which you want to be able to classify subjects based on values of a set of predictor variables. This type of regression is similar to logistic regression, but it is more general because the dependent variable is not restricted to two categories. In order to market films more effectively, movie studios want to predict what type of film a moviegoer is likely to see. By performing a Multinomial Logistic Regression, the studio can determine the strength of influence a person’s age, gender, and dating status has upon the type of film they prefer. The studio can then slant the advertising campaign of a particular movie toward a group of people likely to go see it.
Analyze -> Regression -> Ordinal Regression Ordinal Regression allows you to model the dependence of a polytomous ordinal response on a set of predictors, which can be factors or covariates. The design of Ordinal Regression is based on the methodology of McCullagh (1980, 1998), and the procedure is referred to as PLUM in the syntax. Ordinal Regression could be used to study patient reaction to drug dosage. The possible reactions may be classified as none, mild, moderate, or severe. The difference between a mild and moderate reaction is difficult or impossible to quantify and is based on perception. Moreover, the difference between a mild and moderate response may be greater or less than the difference between a moderate and severe response.
Analyze -> Regression -> Probit This procedure measures the relationship between the strength of a stimulus and the proportion of cases exhibiting a certain response to the stimulus. It is useful for situations where you have a dichotomous output that is thought to be influenced or caused by levels of some independent variable(s) and is particularly well suited to experimental data. This procedure will allow you to estimate the strength of a stimulus required to induce a certain proportion of responses, such as the median effective dose. How effective is a new pesticide at killing ants, and what is an appropriate concentration to use? You might perform an experiment in which you expose samples of ants to different concentrations of the pesticide and then record the number of ants killed and the number of ants exposed. Applying probit analysis to these data, you can determine the strength of the relationship between concentration and killing, and you can determine what the appropriate concentration of pesticide would be if you wanted to be sure to kill, say, 95% of exposed ants.

Classify
Analyze -> Classify -> K-Means Cluster Analysis This procedure attempts to identify relatively homogeneous groups of cases based on selected characteristics, using an algorithm that can handle large numbers of cases. However, the algorithm requires you to specify the number of clusters. You can specify initial cluster centers if you know this information. You can select one of two methods for classifying cases, either updating cluster centers iteratively or classifying only. You can save cluster membership, distance information, and final cluster centers. Optionally, you can specify a variable whose values are used to label casewise output. You can also request analysis of variance F statistics. While these statistics are opportunistic (the procedure tries to form groups that do differ), the relative size of the statistics provides information about each variable’s contribution to the separation of the groups. What are some identifiable groups of television shows that attract similar audiences within each group? With k-means cluster analysis, you could cluster television shows (cases) into k homogeneous groups based on viewer characteristics. This process can be used to identify segments for marketing. Or you can cluster cities (cases) into homogeneous groups so that comparable cities can be selected to test various marketing strategies.
Analyze -> Classify -> Hierarchical Cluster Analysis This procedure attempts to identify relatively homogeneous groups of cases (or variables) based on selected characteristics, using an algorithm that starts with each case (or variable) in a separate cluster and combines clusters until only one is left. You can analyze raw variables, or you can choose from a variety of standardizing transformations. Distance or similarity measures are generated by the Proximities procedure. Statistics are displayed at each stage to help you select the best solution. Are there identifiable groups of television shows that attract similar audiences within each group? With hierarchical cluster analysis, you could cluster television shows (cases) into homogeneous groups based on viewer characteristics. This can be used to identify segments for marketing. Or you can cluster cities (cases) into homogeneous groups so that comparable cities can be selected to test various marketing strategies.
Analyze -> Classify -> Discriminant Discriminant analysis builds a predictive model for group membership. The model is composed of a discriminant function (or, for more than two groups, a set of discriminant functions) based on linear combinations of the predictor variables that provide the best discrimination between the groups. The functions are generated from a sample of cases for which group membership is known; the functions can then be applied to new cases that have measurements for the predictor variables but have unknown group membership.

Note: The grouping variable can have more than two values. The codes for the grouping variable must be integers, however, and you need to specify their minimum and maximum values. Cases with values outside of these bounds are excluded from the analysis.

 

 On average, people in temperate zone countries consume more calories per day than people in the tropics, and a greater proportion of the people in the temperate zones are city dwellers. A researcher wants to combine this information into a function to determine how well an individual can discriminate between the two groups of countries. The researcher thinks that population size and economic information may also be important. Discriminant analysis allows you to estimate coefficients of the linear discriminant function, which looks like the right side of a multiple linear regression equation. That is, using coefficients a, b, c, and d, the function is:

D = a * climate + b * urban + c * population + d * gross domestic product per capita

 

If these variables are useful for discriminating between the two climate zones, the values of D will differ for the temperate and tropic countries. If you use a stepwise variable selection method, you may find that you do not need to include all four variables in the function.

 

Dimension Reduction
Analyze -> Dimension Reduction -> Factor Analysis Factor analysis attempts to identify underlying variables, or factors, that explain the pattern of correlations within a set of observed variables. Factor analysis is often used in data reduction to identify a small number of factors that explain most of the variance that is observed in a much larger number of manifest variables. Factor analysis can also be used to generate hypotheses regarding causal mechanisms or to screen variables for subsequent analysis (for example, to identify collinearity prior to performing a linear regression analysis).

The factor analysis procedure offers a high degree of flexibility:

• Seven methods of factor extraction are available.

• Five methods of rotation are available, including direct oblimin and promax for nonorthogonal rotations.

• Three methods of computing factor scores are available, and scores can be saved as variables for further analysis.

 

 What underlying attitudes lead people to respond to the questions on a political survey as they do? Examining the correlations among the survey items reveals that there is significant overlap among various subgroups of items–questions about taxes tend to correlate with each other, questions about military issues correlate with each other, and so on. With factor analysis, you can investigate the number of underlying factors and, in many cases, identify what the factors represent conceptually. Additionally, you can compute factor scores for each respondent, which can then be used in subsequent analyses. For example, you might build a logistic regression model to predict voting behavior based on factor scores.
Analyze -> Dimension Reduction -> Correspondence Analysis One of the goals of correspondence analysis is to describe the relationships between two nominal variables in a correspondence table in a low-dimensional space, while simultaneously describing the relationships between the categories for each variable. For each variable, the distances between category points in a plot reflect the relationships between the categories with similar categories plotted close to each other. Projecting points for one variable on the vector from the origin to a category point for the other variable describe the relationship between the variables.

An analysis of contingency tables often includes examining row and column profiles and testing for independence via the chi-square statistic. However, the number of profiles can be quite large, and the chi-square test does not reveal the dependence structure. The Crosstabs procedure offers several measures of association and tests of association but cannot graphically represent any relationships between the variables.

Factor analysis is a standard technique for describing relationships between variables in a low-dimensional space. However, factor analysis requires interval data, and the number of observations should be five times the number of variables. Correspondence analysis, on the other hand, assumes nominal variables and can describe the relationships between categories of each variable, as well as the relationship between the variables. In addition, correspondence analysis can be used to analyze any table of positive correspondence measures.

 

 Correspondence analysis could be used to graphically display the relationship between staff category and smoking habits. You might find that with regard to smoking, junior managers differ from secretaries, but secretaries do not differ from senior managers. You might also find that heavy smoking is associated with junior managers, whereas light smoking is associated with secretaries.

Reliability Analysis
Analysis -> Scale -> Reliability Analysis Reliability analysis allows you to study the properties of measurement scales and the items that compose the scales. The Reliability Analysis procedure calculates a number of commonly used measures of scale reliability and also provides information about the relationships between individual items in the scale. Intraclass correlation coefficients can be used to compute inter-rater reliability estimates. Does my questionnaire measure customer satisfaction in a useful way? Using reliability analysis, you can determine the extent to which the items in your questionnaire are related to each other, you can get an overall index of the repeatability or internal consistency of the scale as a whole, and you can identify problem items that should be excluded from the scale.

Are you looking for an international tourism-focused master’s degree programme in business? Tourism Marketing and Management programme by University of Eastern Finland provides a unique learning experience for students who have finished their bachelor’s degree and are looking for new skills and knowledge in developing tourism industry in a sustainable way. Read more about the programme at www.uef.fi/tmm.