SPSS On-Line Training Workshop

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Data Types and Possible Analysis Techniques

We will cover: Types of Statistics  Descriptive & Graphical Inferential Variable Relationships Statistical Modeling Data Dimension Reduction Nonparametric Methods Quality Control Time Series Survival Modeling ROC Curve

Data Types General speaking, statistical techniques are determined by the type of data. A basic understanding about the data types is helpful for choosing statistical procedures. In SPSS, a column is for a variable and a row is for a case. There are, generally speaking, two major types of data: Qualitative variables: The data values are non-numeric categories. Examples: Blood type, Gender. Quantitative variables: The data values are counts or numerical measurements. A quantitative variable can be either discrete such as # of students receiving an 'A' in a class, or continuous such as GPA, salary and so on. Another way of classifying data is by the measurement scales. In statistics, there are four generally used measurement scales: Nominal data: data values are non-numeric group labels. For example, Gender variable can be defined as male = 0 and female =1. Ordinal data (we sometimes call 'Discrete Data'): data values are categorical and may be ranked in some numerically meaningful way. For example, strongly disagree to strong agree may be defined as 1 to 5. Continuous data: Interval data : data values are ranged in a real interval, which can be as large as from negative infinity to positive infinity. The difference between two values are meaningful, however, the ratio of two interval data is not meaningful. For example temperature, IQ. Today is 1.2 times hotter than yesterday is not much useful nor meaningful. Ratio data: Both difference and ratio of two values are meaningful. For example, salary, weight. NOTE: The statistical procedures mentioned below are demonstrated using movie clips in the Statistical Procedures Page.

	Descriptive statistics: Summary statistics: mean median standard deviation percentile frequency Summary graphic tools pie charts histograms boxplots scatterplots
	Inferential statistics: used to make comparisons between two or more groups or study relationships Estimation Confidence interval Hypothesis testing
	Statistical Modeling: used to modeling one response variable (dependent variable) based on a list of potential predictors (independent variables, or to modeling multivariate response variables using a set of potential predictors. Common modeling techniques include Multiple regression Logistic regression Generalized linear models Mixed models General log-linear models Survival models
	Dimension reduction techniques: In many statistical applications, one often have many variables. Many of them are either not very useful or redundant for the study. It is, in many cases, important to perform data reduction by 'combining' information of a group of variables into a few smaller number of 'new' variables or by deleting statistically redundant variables prior to conducting advanced analysis. Many of these techniques are available in what has been known as 'data mining techniques. In this SPSS online training, we will only discuss some of those techniques that are considered more 'traditional' statistical techniques: Clustering analysis for grouping variables or cases. Factor analysis for reducing number of variables.
	Statistical Process Control techniques: These techniques are commonly used for monitoring and improving the quality of a process. Typically used techniques include: X-bar R-Charts for variable data p-, np-charts for attribute data that follows binomial rules c- & u-charts for attribute data that follows Poisson process Capability analysis for studying the performance of a process prior and after any process improvement.
	Time Series Modeling: used to model the time series pattern of data. Typical techniques are ARIMA models and ARIMA models with seasonal adjustment.
	Survival modeling: used for data that are truncated. In this online workshop, we will talk about two survial modeling techniques: Kaplan-Meier survival models Cox regression models
	ROC Curve: A graphical technique for comparing the performances of different classification models. This technique is a model selection technique that is often used for selecting models with response variable being categorical.
	Design of Experimental techniques: Data are usually collected either observationally (such as survey, existing sources, etc.) or through an experiment that follows some statistical designs such as Factorial Designs, Complete Randomized Block Designs, Incomplete Block Designs, Composite Designs, Orthogonal Arrays, etc.). In this online workshop, we will not discuss techniques of experimental designs. Instead, we focus on data analysis.

	For nominal data: Frequency, Crosstabs, bar charts and pie charts are common tools.
	For ordinal data: Frequency, Crosstabs, and descriptive statistics, bar charts, pie charts, stem-leaf plots are common tools.
	For continuous data: Descriptive statistics, histograms, boxplots, and scatterplots for two variables are common tools.

For Nominal or ordinal data: Use crosstabs.

For continuous data: First, check to see if the variable is normal. To check Normality, go to 'Analyze' then to 'Descriptive Statistics' then choose 'Explore' procedure. Second, if you compare two or more groups, check the homogeneity of the variances among groups.  To do so, you also use the 'Explore' procedure. For two group comparison, use Independent t-test. For three or more group comparison, use one-way analysis of variance. For two or more factors, use multiway analysis of variance. If there are factors and covariates, use analysis of covariance. If the same subject is measured more than one time, it is a repeated measure problem.

	For nominal data, use crosstabs, and choose proper tests for nominal data.
	For ordinal data, use crosstabs, bivariate correlation such as Spearman correlation coefficient..
	For continuous data, use bivariate correlation such as Pearson correlation.

	For nominal data, if the response is a binary variable (that is only two possible values such as graduate in four years or not), then, use Logistic regression model.  If the response has more than two categories, use multinomial logistic regression.
	For ordinal data, if the response follows Poisson distribution, use Poisson regression model.  In general, one can use log-linear models for ordinal data.
	In many applications, the relationship between response variable and predictors are not linear, but may be linearized. Generalized linear modeling techniques are useful.
	Some applications involves certain structure of relationship between response and predictor variables. Mixed models may be useful for some of these problems.
	Many medical data or reliability data involves with data values that are not completely observed at the end of the study (right-truncated), or some data have already evolving before the study started (left-truncated). The analysis requires special attention regarding to the information of data being 'truncated'. Survival modeling techniques are useful for modeling these types of data.
	Most of statistical techniques require certain assumptions. Typically, for continuous response, the assumptions may include normality of the response variable, homogeneity of variance and the relationship between Y and X's being linear or not. One should take appropriate data transformation as needed when building statistical mdodels.

Classification techniques, which are often called as 'supervised techniques', are techniques involve with classifying cases of a categorical response variable based on a set of independent variables (also called Input variables) by building a model. The model is then applied to classify future cases into one of the categories of the response based on the observed data values of the independent variables.

While cluster analysis does not involve with the modeling. You have a set of k variables, each with n cases. The cluster analysis for cases will group the cases into small number of groups of cases based on the similarity of the independent variables. The cluster analysis for variables will group the variables into small number of subsets of variables based on the similarity of cases.

For example, in the technology survey, we collect 16 variables related to the difficulty faced by faculty when using classroom technology. Using Factor Analysis, we are able to combine these 16 different types of difficulties into four general groups of difficulty (factors). These are difficulties related to: (1) Computer hardware and software, (2) Media technology, (3) Instructor's technology need in office, and (4) Classroom instructional technology need.

	Chi-square
	Two Independent Samples Comparison: The similar parametric procedure is independent t-test.
	K Independent Samples Comparison : The similar parametric procedure is Analysis of Variance.
	Two Related Samples: The similar parametric procedure is the paired t-test.
	K Related Samples: The similar parametric procedure is the Repeated Measure Analysis.

Statistical quality control techniques are commonly used in monitoring the process quality. There are typically two major sources of variations occurred in a process. One is the variation due to special causes, and the other is the variation due to system causes. Control charts are commonly used for monitoring the variation due to special causes. Capability analysis is typically used to evaluate the performance of the existing system. Once the capability of a system is assessed, one can then, design further investigation to study the possible factors (causes) that may result in the system variation.  There are various tools available in SPSS for quality control, include:

	Capability Analysis for evaluating the performance of the quality characteristic in interval scale.  Typical capability indices include Cp, Cpu, Cpl, Cpk, CpM.
	Variable control charts: X-bar/R charts and X-bar/S charts for monitoring variable data (interval data). X-bar chart monitors the average performance of the quality characteristic along the time. The range/s-charts monitor the variability of the quality catachrestic along the time. The assumption is the quality characteristic follows a normal distribution. Caution should be taken for situations where the normality assumption is highly violated.
	Variable control charts: Individual, Moving Range charts for monitoring variable (interval) measurement where each sample is taken only from one individual unit. The point represents the moving average or moving range of at least two consecutive individual measurements. Typical assumption is the number of defectives in a random sample of n items follows a binomial distribution
	Attribute control charts: p-, np-charts for monitoring proportion (p-chart) or number ( np-chart) of defectives of the quality characteristic in each batch of a random sample along the time.
	Attribute control charts: c, u-charts for monitoring the number of defects in the sample (c-chart) or the mean number of defects in one unit of sample (u-chart). The typical assumption is the number of defects in a sample follows a Poisson distribution.

To performance Quality Control procedure in SPSS,

There are two commonly used time series modeling techniques included in SPSS:

	Exponential smoothing for modeling the time series exponential smoothing technique.
	ARIMA model for modeling the time series using autoregressive and moving average techniques. Seasonal effect can be considered. The ARIMA model also allows for covariates.
	SPSS also provides an Expert Modeler to assist users choosing the 'best' ARIMA model for the time series.

To performance time series modeling in SPSS,

Survival modeling techniques are commonly used for modeling life time data or reliability data that may involve with censored data. SPSS provides four procedures for survival modeling:

	Life table: Life table is created by subdividing the study period into smaller time intervals, and count the number of cases being lasted for at least to the time period. The counts are used to estimate the overall probability of the event occurring at different time points and displayed in a tabular form.
	Kaplan-Meier model. This is a nonparametric technique. It is also known as product-limit method for the reason that the method is based on estimating conditional probabilities at each time when an event occurs and computes the product limit of these conditional probabilities to estimate the survival rates at the time. This technique is often used for comparing the effects of treatments on the survival time.
	Cox Regression model: This is a parametric modeling technique that can take into account of covariates. A survival predictive model is built. It is also known as proportional hazard model for the reason that the model assumes that the covariate effects on a hazard function is the same for different factor levels for all time points.
	Cox regression with Time-dependent covariates: This extends the original Cox regression model by allowing covariates that are time-dependent.

To perform a survival analysis in SPSS, go to Analyze, scroll down to Survival Analysis, select the procedure appropriate for your survival data.

ROC Curve:

ROC Curve is useful for evaluating and comparing the performance of classification models where the response variable is binary (often labeled as Positive and Negative). This is a two-dimensional curve with the Y-axis the sensitivity measure and  X-axis (1-specificity). These sensitivity and (1-specificity) measures are computed based a a sequence of cut-off points to be applied to the model for predicting observations into Positive or Negative.

Prior to create the ROC curve, users have already have performed and built more than one predictive models and choose to use ROC Curve for comparing the performance of the models, and have obtained and saved the predicted responses from these competing models.

To create the ROC Curve in SPSS,go to Analyze, scroll down to ROC Curve.

We In this workshop, we attempt to cover most of the statistical procedures available in SPSS 16.  The bottom line is, when you have questions about your design and analysis, contact a statistical consultant for help.