ExamTickets with Statistical Methods for the Social Sciences by Agresti - 6th edition

General ExamTickets with the book

• Keep a separate list for yourself with test statistics and the situations in which they are used. For example, you could create a table listing statistics like t-tests, chi-squared tests, and ANOVA, along with when they are used (e.g., comparing two means, testing for independence, comparing means across multiple groups).
• In principle, the entire book is an important foundation for working with statistics. If you only have time for four chapters, study chapters 3, 5, 6, and 9. These chapters cover essential topics like descriptive statistics, probability, hypothesis testing, and correlation.
• If you have an exam on the book, make sure you are familiar with the formula sheet (at the back), what's on it, and what's not. This will help you quickly reference important formulas during the exam.
• Mathematics is like a language, but with symbols instead of letters. Carefully reading each part of a formula is the first step towards understanding what the formula calculates. Imagine a formula for calculating the area of a circle: A = πr². Here, "A" represents the area, "π" is a constant, and "r" is the radius. By breaking down the formula, you can see how it relates the radius of a circle to its area.
• If you're overwhelmed by all the symbols, distinguish between the regular symbol (the absolute value y), the symbol with a bar above it (the mean ȳ), and the symbol with a hat above it (the estimate ŷ). These different symbols carry specific meanings in statistical notation. For instance, in a regression analysis, ŷ represents the predicted value of the dependent variable for a given value of the independent variable.
• This book doesn't explain statistics in the easiest possible way (unfortunately). The author has chosen to strive for completeness and accuracy in his wording. Try to understand why concepts are explained in a certain way, why they are important, and why they haven't been simplified. This will help you understand the book better (just like summaries).
• If you choose to skip a few chapters, you could leave out chapters 10 and 13. Chapter 13, in particular, is less substantial than other chapters

What are statistical methods? - ExamTickets 1

• Anyone can learn statistics, even if you're not great at math or find it a bit intimidating. The key is to think logically and be persistent.
• To understand why statistics is useful, think about the goal of a survey: to gather data that can tell us something about a larger group. For example, if a company wants to know how satisfied its customers are, they might conduct a customer satisfaction survey. The results from this survey can be used to make inferences about the satisfaction levels of all their customers.
• It can be tricky to differentiate between descriptive and inferential statistics. Descriptive statistics summarize data, while inferential statistics use data to make predictions or inferences about a larger population. For instance, if you're studying the heights of basketball players, descriptive statistics might tell you the average height and the range of heights. Inferential statistics could be used to determine if the average height of NBA players is significantly different from the average height of college basketball players.

What types of samples and variables are there? - ExamTickets 2

• There are many different types of samples and variables. For example, if you're studying the effects of a new drug, you might randomly select a group of people to receive the drug (the treatment group) and another group to receive a placebo (the control group). Variables in this study could include age, gender, and whether or not the participant experienced side effects.
• It's easy to get overwhelmed by all the different types of variables. To make things simpler, think about a study you're interested in, like how much makeup people wear. You could use categorical variables like "yes" or "no" to indicate whether someone wears makeup, or you could use an ordinal variable with categories like "never," "sometimes," and "always." You could also use quantitative variables like the number of milligrams of makeup used per day.
• A parameter is a numerical characteristic of a population. For example, the average height of all adults in a country is a population parameter. If you're unsure about parameters, think about them as the "true value" you're trying to estimate based on your sample data.
• The margin of error is a common term in statistics. It tells you how accurate your results are likely to be. For example, if a poll reports that 55% of voters support a particular candidate, with a margin of error of 3%, you can be reasonably confident that the true percentage of voters who support the candidate is between 52% and 58%.
• While simple random sampling is the most common method, there are other sampling techniques like stratified sampling (dividing the population into groups and then sampling from each group) and cluster sampling (dividing the population into clusters and then randomly selecting clusters).

How does descriptive statistics work? - ExamTickets 3

• When choosing between the mean, median, and mode, consider the characteristics of your data. If you have a few extreme values, the median might be a better choice than the mean. For example, if you're calculating the average income of a group of people and there are a few billionaires, the mean will be skewed upward by these high values.
• The best way to learn statistics is through practice. Calculate the mean, median, and mode for different datasets.
• Don't be intimidated by formulas. If you find formulas challenging, like the one for standard deviation, try breaking them down into simpler terms. For instance, the sum of squares, ∑ (yi – ȳ)², might look complex, but it's really just adding up the squared differences between each data point (yi) and the mean (ȳ).
• The standard deviation is a measure of how spread out your data is. A small standard deviation means that the data points are clustered closely around the mean, while a large standard deviation means that the data points are more spread out. For example, if you're measuring the heights of a group of people, a small standard deviation would indicate that most people are about the same height, while a large standard deviation would indicate that there is a wide range of heights.

How do you use probability distributions for statistical inference? - ExamTickets 4

• When conducting statistical inference, it's crucial to distinguish between the sample (e.g., 100 students surveyed at a university) and the population (e.g., all students at the university). Imagine two normal distributions: one for the sample and one for the population. Symbols like ȳ (sample mean) and µ (population mean) help differentiate between the two.
• For characteristics like age, weight, or income, we can analyze their probability distributions using measures like the sample mean (ȳ) and standard deviation (s). These measures themselves can be considered variables and analyzed further. It's like Russian nesting dolls; each layer reveals more detail.
• The distinction between the sampling distribution (the distribution of sample means) and the distribution of the sample data (the data from a specific sample) is important. For instance, if you repeatedly sample 100 students and calculate the mean height for each sample, the distribution of these means is the sampling distribution.
• When tackling a statistical problem, start by identifying the necessary information. To calculate a z-score, you'll need the standard deviation.
• Bootstrap methods are a relatively new technique used to estimate the sampling distribution. Imagine you have a sample of 100 students. You can create many new samples by randomly sampling with replacement from the original sample. This can help estimate the variability of a statistic like the mean.
• The population proportion (π) is a parameter that represents the proportion of a certain characteristic in the population. For example, if 60% of the population prefers a certain brand of soda, π = 0.6.
• To save time calculating confidence intervals, remember these z-scores: 1.96 for 95% confidence and 2.58 for 99% confidence.

How do you make estimates for statistical inference? - ExamTickets 5

• Bootstrap methods are a relatively new addition to statistics textbooks. Whether or not your professor will include them on exams depends on how up-to-date they want to be.
• Imagine you have a small sample of student test scores. To estimate the variability of the sample mean, you could repeatedly resample (with replacement) from your original sample and calculate the mean for each resample. This gives you a distribution of sample means, which can be used to construct confidence intervals.
• The population proportion is denoted by π (not to be confused with pi). For example, if you want to know the proportion of people in a city who own a dog, π would represent this proportion in the entire population.
• To save time calculating confidence intervals, remember these common z-scores: 1.96 for 95% confidence intervals and 2.58 for 99% confidence intervals. For instance, if you calculate a 95% confidence interval for the mean height of a population, you would add and subtract 1.96 standard errors from the sample mean.

How do you use significance tests? - ExamTickets 6

• Practice conducting hypothesis tests to get comfortable with the concept of a p-value. For example, you might test the hypothesis that the average height of men is greater than the average height of women. The p-value tells you the probability of observing your data (or more extreme data) if the null hypothesis (e.g., there is no difference in height between men and women) is true.
• Pay attention to the specific information you need for each statistical test. For example, the binomial distribution is less commonly used. If you're flipping a coin 10 times, you might use the binomial distribution to calculate the probability of getting exactly 5 heads.
• There are many ways to calculate effect size. Cohen's d is a common measure. If you're comparing the mean heights of two groups, Cohen's d tells you how large the difference in means is relative to the variability within each group.

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

• Hypothesis tests come in many forms. The general formula for a test statistic (like a z-score or t-score) is: (observed value - hypothesized value) / standard error. For example, if you're testing whether a coin is fair, you might calculate a z-score to determine how many standard errors the observed proportion of heads is from the expected proportion (0.5).
• Software can automate many statistical tests. For complex or nonparametric tests, it's often sufficient to know which test to use in a given situation. If you need to compare the medians of two groups, you might use a Mann-Whitney U test, and software can calculate the test statistic and p-value for you.

How can you analyze the connection between categorical variables? - ExamTickets 8

• A contingency table or crosstab might seem simple, but mistakes can easily creep into calculations. Make sure you've practiced the chi-squared test, odds ratio, residuals, and gamma a few times. You can find practice problems in statistics textbooks or online.

How do linear regression and correlation work? - ExamTickets 9

• Even statistics textbooks advise that anyone doing serious regression analysis should use software. Apps can also perform many calculations. The most important thing for linear relationships is not memorizing formulas or being able to work out the most complex situations, but understanding what analysis tools are available, when to use them, and how to interpret the results.
• Linear regression is not an easy topic. You can work your way through it without understanding it by memorizing the properties, relationships, and interpretations of all the parameters. But if you understand what the equations are calculating, even partially, you'll have less trouble with multiple regression.
• Although the population residual is not often used in statistics, philosophically it offers interesting possibilities. They can represent the unique, unpredictable aspects of individuals that are not captured by statistical models, highlighting the limits of deterministic explanations and the role of chance in shaping outcomes.

What forms have multivariate connections? - ExamTickets 10

• The real skill isn't knowing the names of different types of multivariate relationships, but being able to apply them to real-world situations. Practicing exercises definitely has a causal relationship with improving your statistics skills.
• The term 'control' is used differently in statistics than in everyday language. When dealing with statistical problems, consider whether the usual meaning of 'control' (checking if something is correct) or the purely statistical meaning (eliminating the effect of a third variable) is intended.
• A concept that hasn't been explicitly mentioned yet is a moderator. A moderator is a variable that changes the relationship between two other variables. For example, let's say we're studying the relationship between hours of study and exam scores. Age might be a moderator: for younger students, there might be a stronger correlation between study hours and exam scores compared to older students.
• You might wonder if multivariate relationships can be treated as a separate topic, or if they should be grouped together with multiple regression. In any case, multiple regression is (more than) complicated enough, so it's better to approach it in steps.

How do you analyze multiple regression? - ExamTickets 11

• If you want to save time and effort understanding and memorizing complex methods, consider which statistics can be directly obtained from SPSS or other programs.
• SSE, TSS, correlation, coefficient of determination: In multiple regression, there are many terms involved. Take a moment to review what they represent so that the calculations become more meaningful. For example, the sum of squared errors (SSE) measures how well your regression model fits the data, while the total sum of squares (TSS) represents the total variation in the dependent variable.
• If you don't understand the multiple correlation coefficient and the multiple coefficient of determination, study the (simple) correlation and (simple) coefficient of determination. These concepts are similar for multiple regression, but applied to multiple variables. To illustrate, the simple correlation coefficient measures the strength and direction of the linear relationship between two variables, while the multiple correlation coefficient measures the strength of the linear relationship between one dependent variable and multiple independent variables.
• Most statistics textbooks cover linear regression first and multiple regression later. However, bivariate linear regression is actually a special case of regression. An alternative approach would be to start with multiple regression, with a footnote stating that bivariate linear regression is a particularly simple case that can also occur.

How does Anova work? - ExamTickets 12

• As a rule, you'll usually choose a confidence interval over a significance test. This even applies to a complex problem like comparing the variance within groups. This is because a confidence interval provides more precise information.
• If you've done anything in SPSS, there's a good chance you've already used ANOVA without realizing it.
• If you're wondering who invented certain parts of ANOVA, R.A. Fisher is a good guess. We owe a lot of statistical methods to this statistician.
• To practice with dummy variables, think of a research question you find interesting, with two categorical explanatory variables and a quantitative response variable, which you can analyze using two-way ANOVA. For example, you could investigate the effects of different teaching methods (online vs. in-person) and student gender on exam scores.
• Sphericity is a statistical assumption in repeated measures ANOVA, which assumes that the variances of the differences between repeated measures are equal. If you understand sphericity, you don't have to worry much about your ability to understand statistics. If you don't understand sphericity, don't worry either, it's a complex and rare topic.

How does multiple regression work with both quantitative and categorical predictors? - ExamTickets 13

• Interpreting graphs is crucial for gaining a deeper understanding of what a model represents and how variables influence each other.
• Textbooks will brings together insights on various topics: significance tests, least squares lines, interaction, cross-products, coefficients of determination, and so on. If you can follow this easily, you can quickly go through it. If you don't immediately understand what the terms mean, it's a good reason to study the explanations of the individual topics in more detail.
• If you understand how regression works with both categorical and quantitative variables, you understand how most research in the social sciences works!
• An unstructured correlation sounds paradoxical and it's hard to give examples of it, but it can occur. For instance, in a complex social network, the relationships between individuals might not follow a clear pattern, making it difficult to identify a specific correlation.

How do you construct a model for multiple regression of extreme or highly correlated data? - ExamTickets 14

1. Try saying "heteroscedasticity" ten times - fast.
2. Robust variance and recent developments in nonparametric regression have only recently been added to the statistician's toolkit. Whether these developments are welcomed or viewed with skepticism will vary from researcher to researcher.

How does logistic regression work? - ExamTickets 15

• If you were good at logarithms in high school, it will work to your advantage. However, if that wasn't your favorite subject, don't worry; the primary tasks of researchers are finding suitable models and explaining the results. The calculations are almost always done by software.
• If you find the hierarchy of five measures of association complicated, take three colors and draw circles for variables x, y, and z to visualize the ways they can overlap. For example, if x represents height, y represents weight, and z represents age, you could draw overlapping circles to show how these variables might be related. Overlap between the height and weight circles might indicate a positive correlation (taller people tend to weigh more), while the overlap between age and height could show a more complex relationship, with height increasing during childhood and then stabilizing in adulthood.