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    Choice Assistance with summaries of Statistical Methods for the Social Sciences - Agresti - 5th edition

    Choice Assistance with summaries of Statistical Methods for the Social Sciences - Agresti - 5th edition

    Summaries & ExamTests with Statistical Methods for the Social Sciences - Agresti

     

    Booksummaries to be used with the 5th edition of Statistical Methods for the Social Sciences

     Online: summary in chapters

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    Content Prints of summaries with Statistical Methods for the Social Sciences

    Booksummary: list of contents for the printed summaries

    • The printed Dutch booksummary contains the following chapters:
      • Wat zijn statistische methoden? – Chapter 1
      • Welke soorten steekproeven en variabelen zijn er? – Chapter 2
      • Hoe werkt beschrijvende statistiek? - Chapter 3
      • Hoe gebruik je kansverdelingen voor statistische inferentie? - Chapter 4
      • Hoe maak je schattingen voor statistische inferentie? – Chapter 5
      • Hoe gebruik je significantietoetsen? – Chapter 6
      • Hoe vergelijk je twee groepen met elkaar in de statistiek? – Chapter 7
      • Hoe kun je het verband tussen categorische variabelen analyseren? – Chapter 8
      • Hoe werken lineaire regressie en correlatie? – Chapter 9
      • Welke vormen hebben multivariate verbanden? – Chapter 10
      • Hoe analyseer je multipele regressie? – Chapter 11
      • Hoe werkt ANOVA? – Chapter 12
      • Hoe werkt multipele regressie met zowel kwantitatieve als categorische predictoren? – Chapter 13
      • Hoe construeer je een model voor multipele regressie van extreme of sterk gecorreleerde data? – Chapter 14
      • Hoe werkt logistische regressie? – Chapter 15
    • The printed English booksummary contains the following chapters:
      • What are statistical methods? – Chapter 1
      • What kinds of samples and variables are possible? – Chapter 2
      • Wat are the main measures and graphs of descriptive statistics? - Chapter 3
      • What role do probability distributions play in statistical inference? – Chapter 4
      • How can you make estimates for statistical inference? – Chapter 5
      • How do you perform significance tests? – Chapter 6
      • How do you compare two groups in statistics? - Chapter 7
      • How do you analyze the association between categorical variables? – Chapter 8
      • How do linear regression and correlation work? – Chapter 9
      • Which types of multivariate relationships exist? – Chapter 10
      • What is multiple regression? – Chapter 11
      • What is ANOVA? – Chapter 12
      • How does multiple regression with both quantitative and categorical predictors work? – Chapter 13
      • How do you make a multiple regression model for extreme or strongly correlating data? – Chapter 14
      • What is logistic regression? – Chapter 15

    Booksummary with former editions

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    Key differences: between the 5th and 4th edition of the book

    • In the 5th edition, the book also focuses on software packages R and Stata in addition to SPSS and SAS
    • New examples are used in the 5th edition to explain the material
    • In the 5th edition, chapters 5, 13 and 14 are supplemented with new topics
    • In the 5th edition, chapter 16 has been dropped

    Related summaries & other materials with Statistical Methods for the Social Sciences

     Alternatives: booksummaries & related summaries

    Knowledge & Study pages: summaries per field of study

    What are statistical methods? – Chapter 1

    What are statistical methods? – Chapter 1


    What is statistics and how can you learn it?

    Statistics is used more and more often to study the behavior of people, not only by the social sciences but also by companies. Everyone can learn how to use statistics, even without much knowledge of mathematics and even with fear of statistics. Most important are logical thinking and perseverance.

    To first step to using statistical methods is to collect data. Data are collected observations of characteristics of interest. For instance the opinion of 1000 people on whether marihuana should be legal. Data can be obtained through questionnaires, experiments, observations or existing databases.

    But statistics aren't only numbers obtained from data. A broader definition of statistics entails all methods to obtain and analyze data.

    What is the difference between descriptive and inferential statistics?

    Before being able to analyze data, a design is made on how to obtain the data. Next there are two sorts of statistical analyses; descriptive statistics and inferential statistics. Descriptive statistics summarizes the information obtained from a collection of data, so the data is easier to interpret. Inferential statistics makes predictions with the help of data. Which kind of statistics is used, depends on the goal of the research (summarize or predict).

    To understand the differences better, a number of basic terms are important. The subjects are the entities that are observed in a research study, most often people but sometimes families, schools, cities etc. The population is the whole of subjects that you want to study (for instance foreign students). The sample is a limited number of selected subjects on which you will collect data (for instance 100 foreign students from several universities). The ultimate goal is to learn about the population, but because it's impossible to research the entire population, a sample is made.

    Descriptive statistics can be used both in case data is available for the entire population and only for the sample. Inferential statistics is only applicable to samples, because predictions for a yet unknown future are made. Hence the definition of inferential statistics is making predictions about a population, based on data gathered from a sample.

    The goal of statistics is to learn more about the parameter. The parameter is the numerical summary of the population, or the unknown value that can tell something about the ultimate conditions of the whole. So it's not about the sample but about the population. This is why an important part of inferential statistics is measuring and crediting how representative a sample is.

    A population can be real (for instance foreign students) or conceptual (for instance the foreign students that will pass their statistics course this year).

    What part does software play in statistics?

    Software enables an easy application of complex methods. The most used software for statistics are SPSS, R, SAS and Stata.

    What kind of samples and variables are possible? – Chapter 2

    What kind of samples and variables are possible? – Chapter 2

    All characteristics of a subject that can be measured are variables. These characteristics can vary between different subjects within a sample or within a population (like income, sex, opinion). The use of variables is to indicate the variability of a value. As as example, the number of beers consumed per week by students. The values of a variable constitute the measurement scale. Several measurement scales, or ways to differ variables, are possible.

    The most important divide is that between quantitative and categorical variables. Quantitative variables are measured in numerical values, such as age, numbers of brothers and sisters, or income. Categorical variables (also called qualitative variables) are measured in categories, such as sex, marital status, or religion. The measurement scales are tied to statistical analyses: for quantitative variables it is possible to calculate the mean (i.e. the average age), but for categorical variables this isn't possible (i.e. there is no average sex).

    What are the main measures and graphs of descriptive statistics? - Chapter 3

    What are the main measures and graphs of descriptive statistics? - Chapter 3

    Descriptive statistics serve to create an overview or summary of data. There are two kinds of data, quantitative and categorical, each has different descriptive statistics.

    To create an overview of categorical data, it's easiest if the categories are in a list including the frequence for each category. To compare the categories, the relative frequencies are listed too. The relative frequency of a category shows how often a subject falls within this category compared to the sample. This can be calculated as a percentage or a proportion. The percentage is the total number of observations within a certain category, divided by the total number of observations * 100. Calculating a proportion works largely similar, but then the number isn't multiplied by 100. The sum of all proportions should be 1.00, the sum of all percentages should be 100.

    What role do probability distributions play in statistical inference? – Chapter 4

    What role do probability distributions play in statistical inference? – Chapter 4

    Randomization is important for collecting data, the idea that the possible observations are known but it's yet unknown which possibility will prevail. What will happen, depends on probability. The probability is the proportion of the number of times that a certain observation is prevalent in a long sequence of similar observations. The fact that the sequence is long, is important, because the longer the sequence, the more accurate the probability. Then the sample proportion becomes more like the population proportion. Probabilities can also be measured in percentages (such as 70%) instead of proportions (such as 0.7). A specific branch within statistics deals with subjective probabilities, called Bayesian statistics. However, most of statistics is about regular probabilities.

    How can estimates for statistical inference be made? – Chapter 5

    How can estimates for statistical inference be made? – Chapter 5

    Sample data is used for estimating parameters that give information about the population, such as proportions and means. For quantitative variables the population mean is estimated (like how much money on average is spent on medicine in a certain year). For categorical variables the population proportions are estimated for the categories (like how many people do and don't have medical insurance in a certain year).

    Two kinds of parameter estimates exist;

    1. A point estimate is a number that is the best prediction.
    2. An interval estimate is an interval surrounding a point estimate, which you think contains the population parameter.

    There is a difference between the estimator (the way that estimates are made) and the estimate point (the estimated number itself). For instance, a sample is an estimator for the population parameter and 0,73 is an estimate point of the population proportion that believes in love at first sight.

    How do you perform significance tests? – Chapter 6

    How do you perform significance tests? – Chapter 6

    A hypothesis is a prediction that a parameter within the population has a certain value or falls within a certain interval. A distinction can be made between two kinds of hypotheses. A null hypothesis (H0) is the assumption that a parameter will assume a certain value. Opposite is the alternative hypothesis (Ha), the assumption that the parameter falls in a range outside of that value. Usually the null hypothesis means no effect. A significance test (also called hypothesis test or test) finds if enough material exists to support the alternative hypothesis. A significance test compares point estimates of parameters with the expected values of the null hypothesis.

    How do you compare two groups in statistics? - Chapter 7

    How do you compare two groups in statistics? - Chapter 7

    In social science often two groups are compared. For quantitative variables means are compared, for categorical variables proportions. When comparing two groups, a binary variable is created: a variable with two categories (also called dichotomous). For instance for sex as a variable the results are men and women. This is an example of bivariate statistics.

    Two groups can be dependent or independent. They are dependent when the respondents naturally match with each other. An example is longitudinal research, where the same group is measured in two moments in time. For an independent sample the groups don't match, for instance in cross-sectional research, where people are randomly selected from the population.

    How do you analyze the association between categorical variables? – Chapter 8

    How do you analyze the association between categorical variables? – Chapter 8

    A contingency table contains the outcomes of all possible combinations of categorical data. A 4x5 contingency table has 4 rows and 5 columns. It often indicates percentages, this is called relative data.

    A conditional distribution means that the data is dependent on a certain condition and shown as percentages of a subtotal, like women that have a cold. A marginal distribution contains the separate numbers. A simultaneous distribution shows the percentages with respect to the entire sample.

    Two categorical variables are statistically independent when the probability that one occurs is unrelated to the probability that the other occurs. So this is when the probability distribution of one variable is not influenced by the outcome of the other variable. If this does happen, they are statistically dependent.

    How do linear regression and correlation work? – Chapter 9

    How do linear regression and correlation work? – Chapter 9

    Regression analysis is the process of researching associations between quantitative response variables and explanatory variables. It has three aspects: 1) investigating whether an association exists, 2) determining the strength of the association and 3) making a regression equation to predict the value of the response variable using the explanatory variable.

    What type of multivariate relationships exist? – Chapter 10

    What type of multivariate relationships exist? – Chapter 10

    Many scientifical studies research more than two variables, requiring multivariate methods. A lot of research is focussed on the causal relationship between variables, but finding proof of causality is difficult. A relationship that appears causal may be caused by another variable. Statistical control is the method of checking whether an association between variables changes or disappears when the influence of other variables is removed. In a causal relationship, x → y, the explanatory variable x causes the response variable y. This is asymmetrical, because y does not need to cause x.

    There are three criteria for a causal relationship:

    1. Association between the variables
    2. Appropriate time order
    3. Elimination of alternative explanations
    What is multiple regression? – Chapter 11

    What is multiple regression? – Chapter 11

    A multiple regression model has more than one explanatory variable and sometimes also (a) controle variable(s): E(y) = α + β1x1 + β2x2. The explanatory variables are numbered: x1, x2, etc. When an explanatory variable is added, then the equation is extended with β2x2. The parameters are α, β1 and β2. The y-axis is vertical, x1 is horizontal and x2 is perpendicular to x1. In this three-dimensional graph the multiple regression equation describes a flat surface, called a plane.

    A partial regression equation describes only part of the possible observations, only those with a certain value.

    What is ANOVA? – Chapter 12

    What is ANOVA? – Chapter 12

    For analyzing categorical variables without assigning a ranking, dummy variables are an option. This means that fake variables are created from observations:

    z1 = 1 and z2 = 0 : observations of category 1 (men)

    z1 = 0 and z2 = 1 : observations of category 2 (women)

    z1 = 0 and z2 = 0 : observations of category 3 (transgender and other identities)

    The model is: E(y) = α + β1z1 + β2z2. The means are deducted from the model: μ1 = α + β1 and μ2 = α + β2 and μ3 = α. Three categories only require two dummy variables, because what remains falls in category 3.

    A significance test using the F-distribution tests whether the means are the same. The null hypothesis H0 : μ1 = μ2 = μ3 = 0 is the same as H0 : β1 = β2 = 0. A small F means a big P and much evidence against the null hypothesis.

    The F-test is robust against small violations of normality and differences in the standard deviations. However, it can't handle very skewed data. This is why randomization is important.

    How does multiple regression with both quantitative and categorical predictors work? – Chapter 13

    How does multiple regression with both quantitative and categorical predictors work? – Chapter 13

    Multiple regression is also feasible for a combination of quantitative and categorical predictors. In a lot of research it makes sense to control for a quantitative variable. A quantitative control variable is called a covariate and it is studied using analysis of covariance (ANCOVA).

    A graph helps to research the effect of quantitative predictor x on the response y, while controlling for the categorical predictor z. For two categories, z can be the dummy variable, else more dummy variables are required (like z1 and z2). The values of z can be 1 ('agree') or 0 ('don't agree'). If there is no interaction, the lines that fit the data best are parallel and the slopes are the same. It's even possible that the regression lines are exactly the same. But if they aren't parallel, there is interaction.

    The predictor can be quantitative and the control variable can be categorial, but this can also be the other way around. Software compares the means. A regression model with three categories is: E(y) = α + βx + β1z1 + β2z2, in which β is the effect of x on y for all groups z. For every additional quantitative variable a βx is added. For every additional categorical variable a dummy variable is added (or several, depending on the number of categories). Cross-product terms are added in case of interaction.

    How do you make a multiple regression model for extreme or strongly correlating data? – Chapter 14

    How do you make a multiple regression model for extreme or strongly correlating data? – Chapter 14

    Three basic rules for selecting variables to add to a model are:

    1. Select variables that can answer the theoretical purpose (accepting/rejecting the null hypothesis), with sensible control variables and mediating variables
    2. Add enough variables for a good predictive power
    3. Keep the model simple

    The explanatory variables should be highly correlated to the response variable but not to each other. Software can test and select explanatory variables. Possible strategies are backward elimination, forward selection and stepwise regression. In backward elimination all possible variables are added, tested for their P-value and then only the significant variables are selected. Forward selection starts from scratch, adding variables with the lowest P-value. Another version of this is stepwise regression, this method removes redundant variables when new variables are added.

    What is logistic regression? – Chapter 15

    What is logistic regression? – Chapter 15

    A logistic regression model is a model with a binary response variable (like 'agree' or 'don't agree'). It's also possible for logistic regression models to have ordinal or nominal response variables. The mean is the proportion of responses that are 1. The linear probability model is P(y=1) = α + βx.

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