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878 results in Statistics for social sciences, behavioral sciences and law

Page 23 of 44

  • Chapter 4 - Models of Central Tendency and Variability

  • Russell T. Warne, Utah Valley University
  • Book:
    Statistics for the Social Sciences
    Published online:
    06 August 2018
    Print publication:
    14 December 2017, pp 77-102

  • Summary

    The last chapter showed the most common ways to create visual representations of data, the histogram being the most popular model. Visual models are helpful for understanding data, but they have their limitations. In a large dataset, for example, it can be cumbersome – even with the aid of a computer – to create a histogram for every single variable. For this reason statisticians have created two families of statistical models that describe the characteristics of a dataset. These are statistical models of central tendency and models of variability – both of which are types of descriptive statistics.

    Learning Goals

  • • Calculate the four major models of central tendency: the mode, median, mean, and trimmed mean.

  • • Calculate the four major models of variability: the range, interquartile range, standard deviation, and variance.

  • • Explain the complementary nature of models of central tendency and variability.

    • Models of Central Tendency

    Models of central tendency are statistical models that are used to describe where the middle of the histogram lies. For many distributions, the model of central tendency is at or near the tallest bar in the histogram. (We will discuss exceptions to this general rule in the next chapter.) These statistical models are valuable in helping people understand their data because they show where most scores tend to cluster together. Models of central tendency are also important because they can help us understand the characteristics of the “typical” sample member.

    Mode. The most basic (and easiest to calculate) statistical model of central tendency is the mode. The mode of a variable is the most frequently occurring score in the data. For example, in the Waite et al. (2015) study that was used as an example in Chapter 3, there were four males (labeled as Group 1) and nine females (labeled as Group 2). Therefore, the mode for this variable is 2, or you could alternatively say that the mode sex of the sample is female. Modes are especially easy to find if the data are already in a frequency table because the mode will be the score that has the highest frequency value.

    Calculating the mode requires at least nominal-level data. Remember from Chapter 2 that nominal data can be counted and classified (see Table 2.1).

  • Chapter 3 - Visual Models

  • Russell T. Warne, Utah Valley University
  • Book:
    Statistics for the Social Sciences
    Published online:
    06 August 2018
    Print publication:
    14 December 2017, pp 35-76

  • Summary

    Biology has equipped humans to process a great deal of information through their senses, especially vision. For many people one of the easiest ways to remember that information is through pictures and other visual aids. A well-designed image can often help others understand complex and abstract ideas (Robinson & Kiewra, 1995). The benefits of a picture even extend into the world of statistics, though we will use the term visual models to refer to these images.

    In Chapter 1, a model was defined as a simplified version of reality. This chapter focuses on visual models, which are pictures that people create so that they can understand their data better. Like all models, visual models are simplified, which means that they are inaccurate to some extent. Nevertheless, visual models can help data analysts understand their data before any analysis actually happens.

    Learning Goals

  • • Create a frequency table and histogram from raw data.

  • • Describe histograms in terms of their skewness, kurtosis, and number of peaks.

  • • Correctly choose an appropriate visual model for a dataset.

  • • Identify the similarities and differences that exist among histograms, bar graphs, frequency polygons, line graphs, and pie charts.

  • • Read a scatterplot and understand how each person in a dataset is represented in a scatterplot.

    • Sample Data

    To illustrate the most common visual models, we will use data from the same study that we first saw in Chapter 1. This is a study that one of my students conducted on the relationships that people have with their sibling diagnosed with an autism spectrum disorder (Waite et al., 2015). Some of the data in the study are displayed in Table 3.1.

    The table shows six variables: ID, sex, age, sibling age, the level of agreement that the subject has with the statement “I feel that my sibling understands me well,” and the level of language development in the sibling with autism. The table also shows how to interpret each number in the table. For example, for the sex variable, male respondents are labeled as “1,” and female respondents are “2.”

    Frequency Tables

    One of the simplest ways to display data is in a frequency table. To create a frequency table for a variable, you need to list every value for the variable in the dataset and then list the frequency, which is the count of how many times each value occurs.

  • Chapter 10 - Unpaired Two-Sample t-Tests

  • Russell T. Warne, Utah Valley University
  • Book:
    Statistics for the Social Sciences
    Published online:
    06 August 2018
    Print publication:
    14 December 2017, pp 241-274

  • Summary

    Social science students naturally have a lot of questions. Are college students majoring in the humanities more social than students majoring in the physical sciences? Are religious societies happier than secular societies? Do children with divorced parents have more behavioral problems than children with married parents? Are inmates who attended school in prison less likely to reoffend than inmates who do not receive education?

    These questions compare two groups (e.g., children of divorced parents and children of married parents) and ask which group has a higher score on a variable (e.g., number of behavioral problems). These kind of questions are extremely common in the social sciences, so it should not surprise you that there is a statistical method developed to answer them. That method is the unpaired two-sample t-test, which is a comparison of scores from two different unrelated groups. The topic of this chapter is the unpaired two-sample t-test, one of the most common statistical methods in the social sciences.

    Learning Goals

  • • Explain when an unpaired two-sample t-test is an appropriate NHST procedure.

  • • Conduct an unpaired two-sample t-test.

  • • Calculate an effect size (i.e., Cohen's d) for an unpaired two-sample t-test.

  • • Show how the unpaired two-sample t-test is a member of the general linear model (GLM).

  • • Correctly find and interpret a p-value.

    • Making Group Comparisons

    Answering the questions at the beginning of the chapter requires comparing two scores. When these groups are unrelated to one another, an unpaired-samples t-test is an appropriate method of analyzing data. You may remember in Chapter 9 we paired scores, the two sets of scores formed pairs across the datasets (e.g., pre-test and post-test data, or scores about a pair of siblings). This allowed us to simplify the two sets of scores into one group of difference scores and to conduct a one-sample t-test with the difference scores.

    However, in the social sciences our scores are often unrelated to one another. For example, a sociology student interested in the happiness levels in different societies would collect data on happiness levels from people in both religious and non-religious societies. After these data are collected, she would have two sets of scores – but there would be no logical reason to pair individuals from one group with individuals from another group because the people in the two groups had nothing to do with each other.

  • Chapter 14 - Chi-Squared Test

  • Russell T. Warne, Utah Valley University
  • Book:
    Statistics for the Social Sciences
    Published online:
    06 August 2018
    Print publication:
    14 December 2017, pp 403-442

  • Summary

    One of the most famous ocean disasters was the sinking of the RMS Titanic on April 15, 1912. This catastrophe has captured the imaginations of millions of people for the past century through books, films, documentaries, and other works inspired by the infamous “unsinkable ship.” When I first learned about the Titanic years ago, I heard that the first-class passengers – the wealthiest passengers – were more likely to survive than the people in second class (less wealthy passengers) and third class (the poorest group of passengers), and that third-class passengers were the most likely to die. This seemed odd to me because, of the 498 surviving passengers, approximately onethird were from each group. I thought that if first-class passengers really were the most likely to survive, there would be more survivors from that group than any other. (I was wrong, and you will see why later in this chapter.)

    To determine whether a group of individuals is more likely to experience an outcome – surviving or dying in the example of the Titanic – it is necessary to look beyond the raw numbers and instead conduct a statistical test. This test is called the chi-squared test. In this chapter, I will explain the chi-squared test, which is named after the Greek letter χ, which is pronounced to rhyme with “fly.” We will also use the chi-squared test to determine whether first-class passengers on the Titanic were more likely to survive than less wealthy passengers.

    Learning Goals

  • • Determine the appropriate situation for a one-way or two-way chi-squared test.

  • • Conduct a one-variable chi-squared test and two-variable chi-squared test.

  • • Calculate and interpret an effect size for a chi-squared test: the odds ratio and relative risk.

    • Nominal Outcomes

    Every null hypothesis test discussed so far in this textbook has had a dependent variable that was either interval- or ratio-level data. This was necessary either to calculate a correlation coefficient (in Chapter 12) or test a null hypothesis that means were equal (in Chapters 7–11). However, dependent variables (i.e., outcomes) are not always interval- or ratio-level data. The Titanic is a perfect example of an outcome of this sort: whether a passenger survived or perished is a nominal variable.

  • Chapter 1 - Statistics and Models

  • Russell T. Warne, Utah Valley University
  • Book:
    Statistics for the Social Sciences
    Published online:
    06 August 2018
    Print publication:
    14 December 2017, pp 1-20

  • Summary

    “Why do I need to take statistics?”

    Every semester that I teach statistics I have students asking this question. It's a fair question to ask. Most of my students want to work as therapists, social workers, psychologists, anthropologists, sociologists, teachers, or in other jobs that seem far removed from formulas and numbers. As students majoring in the social sciences, almost all of them are more interested in people than they are in numbers. For many students (including me, a long time ago), statistics is something to get out of the way so that they can devote their attention to the stuff they really want to do (Rajecki, Appleby, Williams, Johnson, & Jeschke, 2005).

    The purpose of this chapter is to show you why students majoring in the social sciences have to take statistics. This chapter will also explore some introductory concepts and terminology that are necessary to understand the book. The most important concept introduced in this chapter is models, which many experts use to understand their statistical results. Because my goal is to help you think about statistics like a professional, I will use that perspective throughout the book.

    Learning Goals

  • • Explain why students in the behavioral sciences need statistics to be successful in their majors.

  • • Outline the general process for designing and executing a research study.

  • • Describe the benefits of using models to understand reality.

  • • Demonstrate why using a model – even if it is not completely accurate – is useful for people working in the social sciences.

  • • Identify the three types of models and describe their characteristics.

    • Why Statistics Matters

    Although many students would not choose to take a statistics course, nearly every social science department requires its students to take a statistics course (e.g., Norcross et al., 2016; Stoloff et al., 2010). Why? Apparently, the professors in these departments think that statistics is essential to their students’ education, despite what their students may think.

    The main reason that many students must take statistics is that research in the social sciences is dominated by methodologies that are statistics-based; this family of methods is called quantitative research. Researchers who use quantitative research convert their data into numbers for the purpose of analysis, and the numbers are then analyzed by statistical methods.

  • Chapter 8 - One-Sample t-Tests

  • Russell T. Warne, Utah Valley University
  • Book:
    Statistics for the Social Sciences
    Published online:
    06 August 2018
    Print publication:
    14 December 2017, pp 181-214

  • Summary

    One of my favorite stories from ancient mythology is the tale of Hercules fighting the Hydra – a monster with several heads. During the fight Hercules cut off several of its heads. But every time he did, two heads grew in the place of each severed head.

    I like this story because learning statistics is like fighting the Hydra; learning a statistical method gives me a feeling of accomplishment (not unlike Hercules may have felt after cutting off a head of the ferocious Hydra), but after mastering a statistical method, it becomes clear that the method has limitations. Overcoming those limitations requires learning more statistical methods – much like conquering one head of the Hydra means defeating two more.

    The z-test was the first head of our statistical Hydra. However, it often cannot be used because our data frequently do not meet the assumptions required to use it. In this chapter we will discuss the limitations of the z-test and learn a new method to replace it, much like a new head on the Hydra. This new method is called the one-sample t-test.

    Learning Goals

  • • Explain the differences between a z-test and a one-sample t-test and how the two methods are related.

  • • Recognize the situations in which it is more appropriate to use a one-sample t-test than a z-test.

  • • Conduct a one-sample t-test.

  • • Describe the purpose of a confidence interval (CI).

  • • Calculate the CI of a mean.

    • Shortcomings of the z-Test – and a Solution

    The z-test is the simplest type of NHST, which makes it a suitable starting point for learning other NHST procedures. In Chapter 7 we learned that a z-test has three assumptions. They are (1) the variable consists of interval- or ratio-level data, (2) μ is known, and (3) σ is known. The first assumption is rather easy to meet because often the level of the data that are collected is under the researcher's control. The second assumption is sometimes difficult to meet, but often reasonable approximations of μ are known. The last assumption – having a known σ – can be difficult to meet. Therefore, it was necessary to invent an NHST procedure that could be used when σ was unknown. That procedure is the one-sample t-test.

  • Chapter 12 - Correlation

  • Russell T. Warne, Utah Valley University
  • Book:
    Statistics for the Social Sciences
    Published online:
    06 August 2018
    Print publication:
    14 December 2017, pp 329-368

  • Summary

    Video games are one of the most popular forms of multimedia entertainment available today. Because of their popularity, social scientists have been studying the effects of video games for over 30 years. However, for the first 20 years or so, this research was focused on the negative effects of video gaming, such as a theorized link between playing violent video games and engaging in aggressive behavior in the real world (e.g., Browne & Hamilton-Giachritis, 2005). But since the turn of the millennium more social scientists have recognized the potentially positive benefits of video games. These researchers have found evidence that playing video games may increase players’ ability to shift their focus of attention (e.g., Bavelier, Achtman, Mani, & Föcker, 2012), foster collaboration among players, and improve planning and goal-directive behavior (Granic, Lobel, & Engels, 2014).

    One intriguing finding is that people who obtain high scores on some video games have higher intelligence test scores (e.g., Ángeles Quiroga et al., 2015; Foroughi, Serraino, Parasuraman, & Boehm-Davis, 2016). Two of my students decided to test this finding for themselves, and so they collected two variables from a sample. The first variable was the average score on a simple video game, and the second variable was the subjects’ scores on a brief intelligence test. When my students wanted to analyze their data, they discovered that they couldn't use an ANOVA or an unpaired-samples t-test. These statistical analysis methods require a nominal independent variable that divides the sample into groups. However, one variable that my students collected (video game scores) was ratio-level, and the second variable (intelligence test scores) was interval-level. Therefore, they needed a different analysis method to analyze their data. That statistical method is called the correlation, and it is the topic of this chapter.

    Learning Goals

  • • Explain the purpose of a correlation and when it is appropriate to use.

  • • Calculate Pearson's r to measure the strength of the relationship between two variables.

  • • Interpret the effect size (r2) for a correlation.

    • Purpose of the Correlation Coefficient

    My students’ example of video game scores and intelligence test scores is typical of the types of data that social scientists calculate correlations for. Since both variables are interval-level data, it is usually not feasible to use any previous NHST procedures because there are not discrete groups (e.g., two sets of scores created by a nominal data) with interval-level data.

  • Chapter 15 - Applying Statistics to Research, and Advanced Statistical Methods

  • Russell T. Warne, Utah Valley University
  • Book:
    Statistics for the Social Sciences
    Published online:
    06 August 2018
    Print publication:
    14 December 2017, pp 443-484

  • Summary

    As you have progressed through this book, you have learned seven inferential statistics methods. However, even the most mathematically savvy student can sometimes have difficulty applying what they have learned to real-life research situations. Students – and some professionals – often have two challenges in applying these statistical methods:

  • • Selecting an appropriate statistical method to analyze their data.

  • • Understanding complex statistical methods.

    • This chapter is designed to help you overcome these two hurdles to using statistics with real data. As a result, it is structured differently from the other chapters in this textbook. Rather than a thorough exploration of relevant statistical procedures, this chapter is designed to be a reference guide that students can turn to when they are using statistics to analyze their own data. Therefore, this chapter does not include the mathematical, step-by-step procedures; instead, it relies more on interpretation and the use of software. You will also notice that the software guides in this chapter are dispersed throughout the chapter – rather than being placed at the end.

    Learning Goals

  • • Select an appropriate statistical method for a given research question.

  • • Explain how multiple regression fits into the general linear model (GLM).

  • • Interpret multiple regression results.

  • • Define nonparametric statistics and recognize when their use is appropriate.

  • • Distinguish between univariate and multivariate statistical methods.

    • How to Choose a Statistical Method

    With the seven statistical methods that we have discussed so far in this textbook – and with the many more methods available – sometimes one of the biggest challenges is just to know which statistical procedure to use. Many students are surprised to learn that the choice of statistical methods depends mostly on two characteristics of the data: (1) the number of independent and dependent variables, and (2) the levels of data for the different variables. Yet, this makes sense because, as we have progressed from one null hypothesis test to another (Chapters 7–13), we have had to tweak the eight steps of statistical significance testing to accommodate different types of data.

    Figure 15.1 is a chart to guide you through the process of choosing an appropriate statistical analysis procedure. The first five columns of boxes represent the characteristics of the data that influence what statistical procedure to adopt.

Page 23 of 44