{"title":"Formula Guide","authors":"","doi":"10.1017/9781108894319.024","DOIUrl":"https://doi.org/10.1017/9781108894319.024","url":null,"abstract":"","PeriodicalId":334587,"journal":{"name":"Statistics for the Social Sciences","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116762733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Linear Transformations and z-Scores","authors":"","doi":"10.1017/9781108894319.006","DOIUrl":"https://doi.org/10.1017/9781108894319.006","url":null,"abstract":"","PeriodicalId":334587,"journal":{"name":"Statistics for the Social Sciences","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131586632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"z-Table","authors":"","doi":"10.1017/9781108894319.017","DOIUrl":"https://doi.org/10.1017/9781108894319.017","url":null,"abstract":"","PeriodicalId":334587,"journal":{"name":"Statistics for the Social Sciences","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124884346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Models of Central Tendency and Variability","authors":"","doi":"10.1017/9781108894319.004","DOIUrl":"https://doi.org/10.1017/9781108894319.004","url":null,"abstract":"","PeriodicalId":334587,"journal":{"name":"Statistics for the Social Sciences","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116081437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Levels of Data","authors":"Russell T Warne","doi":"10.1017/9781108894319.003","DOIUrl":"https://doi.org/10.1017/9781108894319.003","url":null,"abstract":"","PeriodicalId":334587,"journal":{"name":"Statistics for the Social Sciences","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133450574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Analysis of Variance","authors":"R. Bethea, R. Rhinehart","doi":"10.1142/9789811200410_0006","DOIUrl":"https://doi.org/10.1142/9789811200410_0006","url":null,"abstract":" continuous probability distribution skewed to the right variable values on horizontal axis are 0 area under the curve represents probability horizontal asymptote – extends to infinity along positive horizontal axis curve gets closer to horizontal axis but does not touch it as X gets large The shape of the F distribution is determined by two values for “degrees of freedom”. The degrees of freedom are both written as subscripts. The theoretical mathematical formula for the F probability distribution is a ratio, so the two values for degrees of freedom are associated with the numerator and the denominator of the ratio. The “first” number for degrees of freedom is associated with the numerator; The “second” number for degrees of freedom is associated with the denominator. Notation F df for “numerator”, df for “denominator”","PeriodicalId":334587,"journal":{"name":"Statistics for the Social Sciences","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117249198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Probability and the Central Limit Theorem","authors":"Russell T Warne","doi":"10.1017/9781316442715.007","DOIUrl":"https://doi.org/10.1017/9781316442715.007","url":null,"abstract":"Everything in the preceding chapters of this book has been about using models to describe or represent data that have been collected from a sample – which we learned is a branch of statistics called descriptive statistics. Describing data is an important task. (It would be difficult to learn about data without describing it!) But it is often of limited usefulness because almost all datasets are collected from samples – and most researchers and practitioners in the social sciences are interested in the population as a whole. After all, if a psychologist says, “I have discovered that 35 out of 50 people in my sample got better after therapy,” that isn't very interesting to anyone who isn't a friend or family member of the people in the sample. The vast majority of social science researchers are interested in how their data from their sample applies to a population. But drawing conclusions about an entire population (which may consist of millions of people) based on a sample that consists of a tiny fraction of the population is a difficult logical leap to make. Yet, that leap is not impossible. In fact, the process of how to draw conclusions about a population from sample data was worked out in the early twentieth century, and it is now common in the social sciences to draw these conclusions about populations. This chapter provides the necessary theory of this process. The rest of the chapters in this textbook will discuss the nuts and bolts of actually performing the calculations needed to learn valuable information about a population with just sample data. Learning Goals • Calculate the probability that a particular outcome will occur in a set of events. • Construct a probability distribution based on theoretical probabilities or empirical probabilities and describe why the differences between the two distribution types occur. • Explain the process of generalizing a conclusion based on sample data to the entire population. • Differentiate between a sample histogram, a sampling distribution, and a probability distribution. • Explain the Central Limit Theorem (CLT) and why it permits estimation of the population mean and standard deviation. • Estimate a population mean and standard deviation by taking multiple samples from the population. Basic Probability Statistics is based entirely on a branch of mathematics called probability , which is concerned with the likelihood of outcomes for an event.","PeriodicalId":334587,"journal":{"name":"Statistics for the Social Sciences","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129153678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Null Hypothesis Statistical Significance Testing and z-Tests","authors":"Russell T Warne","doi":"10.1017/9781316442715.008","DOIUrl":"https://doi.org/10.1017/9781316442715.008","url":null,"abstract":"In the previous chapter, we learned about the theory of statistical inference. This theory provides statisticians, researchers, and students with the background information they need to make inferences about a population based on sample data. This chapter builds upon that theoretical foundation by teaching about the simplest possible inferential statistics procedure: the z -test. Although z-tests are not common in social science research, learning the z -test is still important. Mastering a z -test will make the more complicated procedures discussed in later chapters easier to learn because those procedures are variations of a z -test that have been adapted to other types of data and research situations. Learning Goals • Execute the eight steps of null hypothesis statistical significance testing (NHST). • Conduct a z-test and explain how it fits into the general linear model (GLM). • Recognize how effect sizes can compensate for some of the weaknesses of the decision to reject or retain a null hypothesis. • Calculate and interpret Cohen's d for a z -test. • Define Type I and Type II errors and explain why it is always possible to commit one or the other when conducting a null hypothesis statistical significance test. Null Hypothesis Statistical Significance Testing The main purpose of this chapter is to transition from the theory of inferential statistics to the application of inferential statistics. The fundamental process of inferential statistics is called null hypothesis statistical significance testing (NHST) . All procedures in the rest of this textbook are a form of NHST, so it is best to think of NHSTs as statistical procedures used to draw conclusions about a population based on sample data. There are eight steps to NHST procedures: 1. Form groups in the data. 2. Define the null hypothesis (H0). The null hypothesis is always that there is no difference between groups or that there is no relationship between independent and dependent variables. 3. Set alpha (α). The default alpha = .05. 4. Choose a one-tailed or a two-tailed test. This determines the alternative hypothesis (H1). 5. Find the critical value, which is used to define the rejection region. 6. Calculate the observed value. 7. Compare the observed value and the critical value. If the observed value is more extreme than the critical value, then the null hypothesis should be rejected. Otherwise, it should be retained. 8. Calculate an effect size.","PeriodicalId":334587,"journal":{"name":"Statistics for the Social Sciences","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131123256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Unpaired Two-Sample t-Tests","authors":"Russell T Warne","doi":"10.1017/9781316442715.011","DOIUrl":"https://doi.org/10.1017/9781316442715.011","url":null,"abstract":"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.","PeriodicalId":334587,"journal":{"name":"Statistics for the Social Sciences","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122013307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Chi-Squared Test","authors":"A. Culyer","doi":"10.1017/9781108894319.015","DOIUrl":"https://doi.org/10.1017/9781108894319.015","url":null,"abstract":"","PeriodicalId":334587,"journal":{"name":"Statistics for the Social Sciences","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133225602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}