Applied Statistics Masterclass

Explore how to read and draw a scatter diagram to analyze correlation between independent and dependent variables, assess positive, negative, or no correlation, and interpret a best-fit line.

Explore covariance and the correlation coefficient to measure linear association between two variables, interpret positive and negative relationships, and apply formulas using standard deviations before regression.

Explore the unitless correlation coefficient r, its invariance to origin and scale, and interpret its magnitude and sign for X–Y relationships.

Explore Spearman's rank correlation coefficient for non-parametric data by ranking observations and computing rank differences, including corrections for ties.

Rank the scores, compute differences, and apply spearman's correlation formula to interpret the strength and direction of the monotonic relationship between two subject marks, via a worked example.

explains the coefficient of concurrent deviation, a simple sign-based method to assess correlation without measuring magnitude, by comparing successive x and y values and counting matching signs.

Explore the connection between correlation and regression, distinguishing simple and multiple linear regression from ordinal regression, and learn when to use historical data and normality checks to build predictive models.

Learn linear regression with the line y = a + b x, noting the intercept and slope for dependent and independent variables. Check correlation and assumptions to drop spurious variables.

Apply minimum least squares method to find the line of best fit by minimizing the sum of squared errors for five data points, with y = a + b x.

Ascombe's quartet illustrates the limitations of linear regression, showing how outliers and dataset shapes can mislead the best-fit line; visualize data and examine residuals to assess normality.

Learn to solve regression problems by using r with sx and sy to predict y from x and x from y, and interpret the sign of r for the slope.

Apply a simple linear regression to predict mom's height from daughter's height (and conversely), using X and Y variables, least-squares coefficients, and height data in centimeters.

Apply the probability method to a correlation problem: with r = 0.7 and n = 64, compute the probable error and bound rho between 0.657 and 0.743.

Explore how sample means estimate the population mean across multiple samples. The standard error measures the variability of the sample mean using the standard deviation divided by routine.

Explore why hypothesis testing matters by comparing the sample mean to population mean with standard error, and decide to reject the null hypothesis using p-values or critical values at 0.05.

Explore the difference between standard error and standard deviation, and how they relate to variation in the sample mean versus individual observations, with parametric versus non-parametric contexts.

Define type I and type II errors in hypothesis testing, clarifying alpha, beta, and power, with examples of false positives and false negatives when rejecting or not rejecting the null.

Form and distinguish null and alternate hypotheses using examples like house prices and YouTube age, setting mu equal to or not equal to a value and choosing the direction.

Explore how researchers choose significance levels and confidence, understand type I error and rejection regions, and why zero percent confidence is a bad idea.

Clarifies the chi-squared test as a nonparametric distribution test for independence, goodness of fit, and homogeneity, using observed and expected frequencies and degrees of freedom.

Explore the concept of analysis of variance (ANOVA) to compare means across three or more groups, distinguishing between-group and within-group variation and testing null and alternative hypotheses.

Compare the calculated value with the critical value in ANOVA to decide whether to reject or fail to reject the null hypothesis. Identify how this supports the alternative hypothesis.

Calculate the f cal value by partitioning variance into between group and within group components using sums of squares, degrees of freedom, and group means.

Solve a three-group ANOVA to assess teaching methodologies on student marks. Compute between- and within-group variance, derive F = 1.09, and conclude no difference at 95% level.

Explore one-way, two-way, and n-way ANOVA by comparing means of three or more groups across one or more independent variables, and illustrate dependent and independent variables in practical examples.

Learn to forecast monthly sales with additive and multiplicative models, incorporating cyclic, trend, and random fluctuation factors. The example yields 21000 under additive model and 21140 under multiplicative model.

Master graphical trend analysis by plotting data and drawing a freehand trend line to forecast future sales and profits using historical yearly data.

Apply the semi-average method to trend data by dividing chronological data into two parts, averaging each, and plotting the two midpoints to form a secular trend line.

Explore the weighted moving average method for trend analysis in time series, comparing it to simple moving averages, explaining lag and weighting, and applying a five-year window to produce predictions.