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.

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.

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.

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.

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.

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.

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.

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.

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.