Categorical Data Analysis: Proportions and Chi-Square Tests
Nonparametric Tests for Group Comparisons
Errors, p-Values, and Statistical Power
Correlation Analysis
Linear Regression Modeling
Exact Tests, Counting Methods, and Test Selection
Course Description
Build a solid foundation in statistics with this free online course designed for beginners and curious learners in Basic Education. You will learn how to summarize data clearly, interpret variability, and understand how samples relate to populations so you can make sense of real-world datasets with confidence.
Move from descriptive statistics into statistical inference by developing intuition for the normal distribution, the central limit theorem, standard error, confidence intervals, and the logic behind hypothesis testing. You will also learn how p-values, degrees of freedom, and Type I and Type II errors connect to decision-making, and how power and sample size influence the strength of your conclusions.
The course guides you through widely used tests for comparing groups and proportions, including t-tests, one-way and repeated-measures ANOVA, chi-square procedures, and nonparametric alternatives such as Mann–Whitney and Wilcoxon tests. You will gain practical insight into when each method is appropriate and how to interpret results in context.
To round out your toolkit, you will explore correlation and regression, from basic concepts through assumptions, residual analysis, and multiple regression. Along the way, you will strengthen probability skills with combinations, permutations, and exact methods, helping you choose suitable statistical tests and communicate findings more effectively.
Course content
Video class: Population vs Sample06m
Exercise: Which notation correctly matches a sample statistic with its corresponding population parameter for the mean?
Video class: Mean, median and mode09m
Exercise: For a skewed distribution with extreme values (outliers), which measure of central tendency is generally the most appropriate?
Video class: Range, interquartile range (IQR) and box plots08m
Exercise: How is the interquartile range (IQR) defined?
Video class: Standard deviation | how to calculate the SD and variance08m
Exercise: Why is the sample variance (and sample standard deviation) calculated using n − 1 in the denominator instead of n?
Video class: Why do we divide by n-1 and not n? | shown with a simple example | variance and sd10m
Exercise: Why do we divide by n−1 (instead of n) when computing the sample variance using the sample mean?
Video class: The normal distribution | how to interpret and use it15m
Exercise: What does standardizing a value x from a normal distribution (with mean μ and standard deviation σ) produce?
Video class: The central limit theorem | Explained with a simple example09m
Video class: The standard error of the mean (SEM)| how to calculate and interpret | SE vs SD09m
Exercise: Which statement best describes the standard error of the mean (SEM)?
Video class: Confidence intervals - simply explained12m
Exercise: How do you construct a 95% confidence interval for a population mean when the population standard deviation is known (or the sample is large)?
Video class: The t-distribution - why we need it | explained with confidence intervals15m
Exercise: When the population standard deviation is unknown and the sample size is small, what should be used to build a 95% confidence interval for the mean?
Video class: The one-sample t-test and p-values10m
Exercise: In a one-sample t-test, what does the p-value represent (under the assumption of no real effect)?
Video class: t-test VS confidence intervals11m
Exercise: How do a 95% confidence interval and a two-tailed one-sample t-test (α = 0.05) lead to the same decision about a hypothesized mean μ0?
Video class: The degrees of freedom - explained with a simple example02m
Exercise: In many basic statistical calculations, what is the simplified interpretation of degrees of freedom when estimating one parameter?
Video class: The basic steps of hypothesis testing08m
Exercise: In hypothesis testing, when do you reject the null hypothesis (H0) using a significance level α?
Video class: The unpaired t-test | Independent samples t-test16m
Exercise: In an unpaired (independent two-sample) t-test, what is the null hypothesis typically stating?
Video class: The paired t-test | explained with a simple example11m
Exercise: Which key assumption is most important for a paired t-test when the sample size is small?
Video class: Paired vs unpaired t-test05m
Exercise: In a study measuring the same individuals’ body weight before and after a diet, which t-test is appropriate and why?
Video class: One-way ANOVA: the basics14m
Exercise: What does the F statistic (F ratio) in a one-way ANOVA represent?
Video class: One-way ANOVA: the calculations - step-by-step13m
Video class: The repeated-measures ANOVA | explained with a simple example13m
Video class: The geometric mean07m
Exercise: Why is the geometric mean preferred over the arithmetic mean for averaging yearly percentage changes (growth rates)?
Video class: Variables and scales in statistics05m
Exercise: Which statement best describes the difference between a variable and a parameter?
Video class: One-proportion Z-test and the corresponding confidence interval12m
Exercise: In a one-proportion z-test, what does the denominator of the z-statistic represent?
Video class: The Chi-square goodness of fit test | and the difference to the one-proportion Z-test10m
Exercise: In a chi-square goodness-of-fit test, how are the degrees of freedom determined?
Video class: The two proportion z-test and the Chi-square test of homogeneity12m
Exercise: In a two-proportion z-test, why does a 95% confidence interval for (p1 − p2) that includes 0 lead to the same conclusion as a two-sided p-value greater than 0.05?
Video class: The Chi-square test of independence VS homogeneity and goodness of fit06m
Exercise: What is the key feature of a chi-square test of independence compared with a chi-square test of homogeneity?
Video class: The McNemar test04m
Exercise: What part of the 2×2 table is used to compute the McNemar test statistic?
Video class: The Mann Whitney U test (Wilcoxon Mann Whitney test) part 1/212m
Exercise: What does the Wilcoxon Mann–Whitney test primarily assess when comparing two independent groups?
Video class: The Mann Whitney U test (Wilcoxon Mann Whitney test) part 2/2 | exact p-value10m
Exercise: In the Wilcoxon–Mann–Whitney test, what does the U statistic represent in terms of comparisons between two groups?
Video class: The Wilcoxon signed-rank test10m
Exercise: In the Wilcoxon signed-rank test, what is used as the test statistic?
Video class: The basics of type 1 and 2 errors | explained with a simple example12m
Exercise: Which situation is a Type I error in hypothesis testing?
Video class: The probability of making a type 1 error06m
Exercise: When the null hypothesis is true, what does the significance level (alpha) represent?
Video class: The probability of making a type 2 error | explained with a simple example (part 1/2)14m
Exercise: In a one-sided left-tailed z-test (α = 0.05) for whether a diet reduces mean weight, what does the probability of a Type II error (β) represent?
Video class: The probability of making a type 2 error | explained with a simple example (part 2/2)08m
Exercise: In a two-sided hypothesis test, what does the probability of a Type II error (β) correspond to?
Video class: Statistical power and sample size calculations15m
Exercise: How is statistical power related to the Type II error probability (β)?
Video class: p-values - a deeper understanding | alpha | t-statistics13m
Video class: Correlation - the basics | Pearson correlation12m
Exercise: What does a Pearson correlation coefficient close to 0 indicate?
Video class: Correlation | hypothesis testing | assumptions07m
Exercise: When testing whether a Pearson correlation is significantly different from zero, what degrees of freedom are used for the t-test?
Video class: Spearman's rank correlation | Pearson VS Spearman08m
Exercise: Which statement best describes how Spearman’s rank correlation differs from Pearson’s correlation?
Video class: Linear regression | the basics - for beginners14m
Exercise: In simple linear regression for predicting used car price from age, which variable should be placed on the y-axis?
Video class: Least squares - explained with a simple numeric example11m
Exercise: In the method of least squares for simple linear regression, which line is considered the best fit to the data?
Video class: Linear regression | hypothesis testing09m
Exercise: In simple linear regression, what t-test is typically used to test whether the explanatory variable has a significant linear effect on the response?
Video class: Linear regression | the R-squared value08m
Exercise: What does the R-squared (coefficient of determination) represent in a linear regression model?
Video class: Assumptions in Linear Regression - explained | residual analysis16m
Video class: Multiple linear regression - explained with two simple examples15m
Exercise: In multiple linear regression with predictors age and mileage for car price, how should the coefficient for age be interpreted when mileage is included in the model?
Video class: Permutations Combinations and the Hypergeometric distribution13m
Video class: Fisher's test and how to calculate the exact p-value13m
Exercise: When is Fisher’s exact test typically preferred over the chi-square test for a 2×2 table?
Video class: How to choose an appropriate statistical test18m
Exercise: Which test is the non-parametric alternative to a one-way ANOVA when comparing more than two independent groups?
