SPSS Data Analysis for Univariate, Bivariate, and Multivariate Statistics

Daniel J. Denis

• Editorial: Wiley
• Año: 2018
• ISBN:
  9781119465782
• Edición: 1
• Categoría: Matemáticas
• Categoría: Probabilidad y estadística

Enables readers to start doing actual data analysis fast for a truly hands-on learning experience

This concise and very easy-to-use primer introduces readers to a host of computational tools useful for making sense out of data, whether that data come from the social, behavioral, or natural sciences. The book places great emphasis on both data analysis and drawing conclusions from empirical observations. It also provides formulas where needed in many places, while always remaining focused on concepts rather than mathematical abstraction.

SPSS Data Analysis for Univariate, Bivariate, and Multivariate Statistics offers a variety of popular statistical analyses and data management tasks using SPSS that readers can immediately apply as needed for their own research, and emphasizes many helpful computational tools used in the discovery of empirical patterns. The book begins with a review of essential statistical principles before introducing readers to SPSS. The book then goes on to offer chapters on: Exploratory Data Analysis, Basic Statistics, and Visual Displays; Data Management in SPSS; Inferential Tests on Correlations, Counts, and Means; Power Analysis and Estimating Sample Size; Analysis of Variance – Fixed and Random Effects; Repeated Measures ANOVA; Simple and Multiple Linear Regression; Logistic Regression; Multivariate Analysis of Variance (MANOVA) and Discriminant Analysis; Principal Components Analysis; Exploratory Factor Analysis; and Non-Parametric Tests. This helpful resource allows readers to:

• Understand data analysis in practice rather than delving too deeply into abstract mathematical concepts
• Make use of computational tools used by data analysis professionals.
• Focus on real-world application to apply concepts from the book to actual research

Assuming only minimal, prior knowledge of statistics, SPSS Data Analysis for Univariate, Bivariate, and Multivariate Statistics is an excellent "how-to" book for undergraduate and graduate students alike. This book is also a welcome resource for researchers and professionals who require a quick, go-to source for performing essential statistical analyses and data management tasks.

1
Review of Essential Statistical Principles: Big Picture on Statistical Modeling and Inference

The purpose of statistical modeling is to both describe sample data and make inferences about that sample data to the population from which the data was drawn. We compute statistics on samples (e.g. sample mean) and use such statistics as estimators of population parameters (e.g. population mean). When we use the sample statistic to estimate a parameter in the population, we are engaged in the process of inference, which is why such statistics are referred to as inferential statistics, as opposed to descriptive statistics where we are typically simply describing something about a sample or population. All of this usually occurs in an experimental design (e.g. where we have a control vs. treatment group) or nonexperimental design (where we exercise little or no control over variables).

As an example of an experimental design, suppose you wanted to learn whether a pill was effective in reducing symptoms from a headache. You could sample 100 individuals with headaches, give them a pill, and compare their reduction in symptoms to 100 people suffering from a headache but not receiving the pill. If the group receiving the pill showed a decrease in symptomology compared with the nontreated group, it may indicate that your pill is effective. However, to estimate whether the effect observed in the sample data is generalizable and inferable to the population from which the data were drawn, a statistical test could be performed to indicate whether it is plausible that such a difference between groups could have occurred simply by chance. If it were found that the difference was unlikely due to chance, then we may indeed conclude a difference in the population from which the data were drawn. The probability of data occurring under some assumption of (typically) equality is the infamous p‐value, usually set at 0.05. If the probability of such data is relatively low (e.g. less than 0.05) under the null hypothesis of no difference, we reject the null and infer the statistical alternative hypothesis of a difference in population means.

Much of statistical modeling follows a similar logic to that featured above – sample some data, apply a model to the data, and then estimate how good the model fits and whether there is inferential evidence to suggest an effect in the population from which the data were drawn . The actual model you will fit to your data usually depends on the type of data you are working with. For instance, if you have collected sample means and wish to test differences between means, then t‐test and ANOVA techniques are appropriate. On the other hand, if you have collected data in which you would like to see if there is a linear relationship between continuous variables, then correlation and regression are usually appropriate. If you have collected data on numerous dependent variables and believe these variables, taken together as a set, represent some kind of composite variable, and wish to determine mean differences on this composite dependent variable, then a multivariate analysis of variance (MANOVA) technique may be useful. If you wish to predict group membership into two or more categories based on a set of predictors, then discriminant analysis or logistic regression would be an option. If you wished to take many variables and reduce them down to fewer dimensions, then principal components analysis or factor analysis may be your technique of choice. Finally, if you are interested in hypothesizing networks of variables and their interrelationships, then path analysis and structural equation modeling may be your model of choice (not covered in this book). There are numerous other possibilities as well, but overall, you should heed the following principle in guiding your choice of statistical analysis:

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The type of statistical model or method you select often depends on the types of data you have and your purpose for wanting to build a model. There usually is not one and only one method that is possible for a given set of data. The method of choice will be dictated often by the rationale of your research. You must know your variables very well along with the goals of your research to diligently select a statistical model.

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1.1 Variables and Types of Data

Recall that variables are typically of two kinds – dependent or response variables and independent or predictor variables. The terms “dependent” and “independent” are most common in ANOVA‐type models, while “response” and “predictor” are more common in regression‐type models, though their usage is not uniform to any particular methodology. The classic function statement Y = f(X) tells the story – input a value for X (independent variable), and observe the effect on Y (dependent variable). In an independent‐samples t‐test, for instance, X is a variable with two levels, while the dependent variable is a continuous variable. In a classic one‐way ANOVA, X has multiple levels. In a simple linear regression, X is usually a continuous variable, and we use the variable to make predictions of another continuous variable Y. Most of statistical modeling is simply observing an outcome based on something you are inputting into an estimated (estimated based on the sample data) equation.

Data come in many different forms. Though there are rather precise theoretical distinctions between different forms of data, for applied purposes, we can summarize the discussion into the following types for now: (i) continuous and (ii) discrete. Variables measured on a continuous scale can, in theory, achieve any numerical value on the given scale. For instance, length is typically considered to be a continuous variable, since we can measure length to any specified numerical degree. That is, the distance between 5 and 10 in. on a scale contains an infinite number of measurement possibilities (e.g. 6.1852, 8.341 364, etc.). The scale is continuous because it assumes an infinite number of possibilities between any two points on the scale and has no “breaks” in that continuum. On the other hand, if a scale is discrete, it means that between any two values on the scale, only a select number of possibilities can exist. As an example, the number of coins in my pocket is a discrete variable, since I cannot have 1.5 coins. I can have 1 coin, 2 coins, 3 coins, etc., but between those values do not exist an infinite number of possibilities. Sometimes data is also categorical, which means values of the variable are mutually exclusive categories, such as A or B or C or “boy” or “girl.” Other times, data come in the form of counts, where instead of measuring something like IQ, we are only counting the number of occurrences of some behavior (e.g. number of times I blink in a minute). Depending on the type of data you have, different statistical methods will apply. As we survey what SPSS has to offer, we identify variables as continuous, discrete, or categorical as we discuss the given method. However, do not get too caught up with definitions here; there is always a bit of a “fuzziness” in learning about the nature of the variables you have. For example, if I count the number of raindrops in a rainstorm, we would be hard pressed to call this “count data.” We would instead just accept it as continuous data and treat it as such. Many times you have to compromise a bit between data types to best answer a research question. Surely, the average number of people per household does not make sense, yet census reports often give us such figures on “count” data. Always remember however that the software does not recognize the nature of your variables or how they are measured. You have to be certain of this information going in; know your variables very well, so that you can be sure SPSS is treating them as you had planned .

Scales of measurement are also distinguished between nominal, ordinal, interval, and ratio. A nominal scale is not really measurement in the first place, since it is simply assigning labels to objects we are studying. The classic example is that of numbers on football jerseys. That one player has the number 10 and another the number 15 does not mean anything other than labels to distinguish between two players. If differences between numbers do represent magnitudes, but that differences between the magnitudes are unknown or imprecise, then we have measurement at the ordinal level. For example, that a runner finished first and another second constitutes measurement at the ordinal level. Nothing is said of the time difference between the first and second runner, only that there is a “ranking” of the runners. If differences between numbers on a scale represent equal lengths, but that an absolute zero point still cannot be defined, then we have measurement at the interval level. A classic example of this is temperature in degrees Fahrenheit – the difference between 10 and 20° represents the same amount of temperature distance as that between 20 and 30; however zero on the scale does not represent an “absence” of temperature. When we can ascribe an absolute zero point in addition to inferring the properties of the interval scale, then we have measurement at the ratio scale. The number of coins in my pocket is an example of ratio measurement, since zero on the scale represents a complete absence of coins. The number of car accidents in a year is another variable measurable on a ratio scale, since it is possible, however unlikely, that there were no accidents in a given year.

The first step in choosing a statistical model is knowing what kind of data you have, whether they are continuous, discrete, or categorical and with some attention also devoted to whether the data are nominal, ordinal, interval, or ratio. Making these decisions can be a lot trickier than it sounds, and you may need to consult with someone for advice on this before selecting a model. Other times, it is very easy to determine what kind of data you have. But if you are not sure, check with a statistical consultant to help confirm the nature of your variables, because making an error at this initial stage of analysis can have serious consequences and jeopardize your data analyses entirely.

1.2 Significance Tests and Hypothesis Testing

In classical statistics, a hypothesis test is about the value of a parameter we are wishing to estimate with our sample data. Consider our previous example of the two‐group problem regarding trying to establish whether taking a pill is effective in reducing headache symptoms. If there were no difference between the group receiving the treatment and the group not receiving the tr...