Mindmap stats 2 - the basics
Chapter 1:
Introduction to statistics and its role in social sciences. Provides overview of the major statistical methods.
Descriptive statistics: covers the basic measures of central tendency (mean, median, and mode) and variability (range, interquartile range, variance, and standard deviation). It also discusses the graphical representation of data through histograms and box plots.
Inferential statistics: this section discusses the process of making inferences about a population based on a sample. It covers concepts such as hypothesis testing, confidence intervals, and p-values
Chapter 2: summarizing and graphing data
Frequency distributions and histograms: covers the construction of frequency distributions and histograms, which are graphical representations of data that shows the frequency of observations falling into certain intervals or bins.
Stem-and-Leaf Display: another graphical method of representing data
Measures of central tendency: mean, median, and mode
Measures of variability: range, interquartile range, variance, and SD
Boxplots: Boxplots as graphical representations of data that show the distribution of the data, including the median, quartiles, and outliers
Chapter 4: discrete probability distributions
Introduction: discrete probability and their applications
The different discrete probability distributions: (1) The binomial distribution, (2) the Poisson Distribution, (3) The Hypergeometric Distribution, (4) the Geometric distribution, (5) The negative Binomial Distribution
Chapter 5: continuous probability distributions
Continuous probability distributions: (1) The normal distribution, (2) The uniform distribution, (3) The exponential Distribution, (4) The Gamma Distribution, (5) The Beta distribution
Mindmap stats 2 - the basics part 2
Chapter 6 - Inference based on a single sample
Point estimate: "best guess" or "best estimate" of an unknown population parameter (for example, the population mean).
Interval estimation: the evaluation of a parameter—for example, the mean (average)—of a population by computing an interval, or range of values, within which the parameter is most likely to be located.
Inferences about a population Mean: The construction of Confidence Intervals and hypothesis tests for a population mean.
Inferences about a population proportion The construction of confidence intervals and hypothesis tests for a population proportion
Chapter 7 - Inferences based on 2 samples
Independent samples: Inference based on two independent samples, such as comparing the means or proportions of two populations
- The construction of confidence intervals, hypothesis tests, and the interpretation of results
Paired samples: Inferences based on paired samples, such as comparing the means of two related populations or testing the difference between two correlated proportions
- Assumptions necessary for inference, the construction of confidence intervals, hypothesis tests, and interpretation of results
Comparing two variances: Inferences based on comparing two variances of two populations
- Assumptions necessary for inference, construction of CI, hypothesis tests, and interpretation of results
Analysis of Variance (ANOVA): A statistical technique used to test the equality of means among three or more populations
- Assumptions necessary for ANOVA, the construction of F-tests, and the interpretation of results
Chapter 8 - Regression analysis
Introduction: Introduction to correlation and regression analysis and the concepts if the linear relationship and the scatterplot
Correlation: Correlation = measures the strength and direction of the linear relationship between two quantitative variables.
- Interpretation of the correlation coefficient, assumption necessary for inference, construction of CI, and hypothesis tests for the population correlation coefficient
Simple Linear Regression: Linear relationship = modeling the linear relationship between two quantitative variables using a straight line.
- Assumptions necessary for regression analysis, the interpretation of the slope and intercept coefficients, and the construction of CI, and hypothesis tests for the population slope coefficient
Inference in regression
Multiple Regression analysis: modeling the linear relationship between a response variable and two or more predictor variables.
Model selection and checking: Model selection and checking in regression analysis, including the use of residual plots to check the assumptions and the methods for selecting the best model
Chapter 9 - statistical methods for analyzing categorical data
Goodness of fit tests: = used to test the fit of a theoretical probability distribution to a set of observed categorical data.
- Chi-squared goodness of fit test
Logistic regression: = statistical technique used to model the relationship between a binary response variable and one or more predictor variables