This bundle contains a full summary for the book "Statistics, the art and science of learning from data by A. Agresti (third edition". It contains the following chapters:
1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15.
USING DATA TO ANSWER STATISTICAL QUESTIONS
The information we gather with experiments and surveys is collectively called data. Statistics is the art and science of learning from data. Statistical problem solving consists of four things:
The three main components of
........Read moreDIFFERENT TYPES OF DATA
A variable is any characteristic observed in a study. The data values that we observe for a variable are called observations. A variable can be categorical and quantitative.
THE ASSOCIATION BETWEEN TWO CATEGORICAL VARIABLES
When analysing data the first step is to distinguish between the response variable and the explanatory variable. The response variable is the outcome variable on which comparisons are made. If the explanatory variable is categorical, it defines the groups to be compared with respect to values for the response variable. If
HOW PROBABILITY QUANTIFIES RANDOMNESS
Probability is the way we quantify uncertainness. It measures the chances of the possible outcomes for random phenomena. A random phenomenon is an everyday occurrence for which the outcome is uncertain. With random phenomena, the proportion of times that something happens is highly random and variable in the short run, but very predictable
SUMMARIZING POSSIBLE OUTCOMES AND THEIR PROBABILITIES
All possible outcomes and probabilities are summarized in a probability distribution. There is a normal and a binomial distribution. A random variable is a numerical measurement of the outcome of a random phenomenon. The probability distribution of a discrete random variable assigns a probability to each possible value. Numerical summaries of
HOW SAMPLE PROPORTIONS VARY AROUND THE POPULATION PROPORTION
The sample distribution of a statistic is the probability distribution that specifies probabilities for the possible values the statistic can take. The population distribution from which you take the sample. Values of its parameters are fixed, but usually unknown. Data distribution is the distribution of the sample data. It
POINT AND INTERVAL ESTIMATES OF POPULATION PARAMETERS
A point estimate is a single number that is our best guess for the parameter (e.g: 25% of all Dutch people are above 1,80m). An interval estimate is an interval of numbers within which the parameter value is believed to fall (e.g: between 20% and 30% of the Dutch people
STEPS FOR PERFORMING A SIGNIFICANCE TEST
A hypothesis is a statement about the population. A significance test is a method for using data to summarize the evidence about a hypothesis. The null hypothesis (H0) is a statement that the parameter takes a particular value (e.g: probability of getting a baby girl: p = 0.482). The alternative hypothesis
CATEGORICAL RESPONSE: COMPARING TWO PROPORTIONS:
Bivariate methods is the general category of statistical methods used when we have two variables. The outcome variable on which comparisons are made is called the response variable. The binary variable that specifies the groups is the explanatory variable. In an independent sample, observations in one sample are independent from observations in
INDEPENDENCE AND DEPENDENCE (ASSOCIATION)
Conditional percentages refer to a sample data distribution, conditional on a category. They form the conditional distribution. If the probabilities for two different categorical variables are the same in the same category, then these variables are independent. If the probabilities for two different categorical variables differ, then these variables are dependent. Dependence refers
MODEL HOW TWO VARIABLES ARE RELATED
A regression line is a straight line that predicts the value of a response variable ‘y’ from the value of an explanatory variable ‘x’. The correlation is a summary measure of association. The regression line uses the following formula:
The data
........Read moreONE-WAY ANOVE: COMPARING SEVERAL MEANS
The inferential method for comparing means of several groups is called analysis of variance, also called ANOVA. Categorical explanatory variables in multiple regression and in ANOVA are referred to as factors, also known as independent variables. An ANOVA with only one independent variable is called a one-way ANOVA.
Evidence against
........Read moreCOMPARE TWO GROUPS BY RANKING
Nonparametric statistical methods are inferential methods that do not assume a particular form of distribution (e.g: the assumption of a normal distribution) for the population distribution. The Wilcoxon test is the best known nonparametric method. Nonparametric methods are useful when the data are ranked and when the assumption of normality is inappropriate.
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