Applied Statistics Masterclass

Explore the concept of correlation analysis, learn how two variables relate, and apply Pearson and Spearman methods to assess strength, direction, and limitations.

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 Culberson's product moment coefficient, aka Pearson's correlation, using two formulas to relate X and Y via deviations from their means and their product sums.

Compute the correlation coefficient R ≈ 0.8831 for economics and accountancy, and interpret it as a fairly high positive, not perfect, relationship.

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.

Learn how the coefficient of determination (R-squared) measures how much variation in Y is explained by X, while the coefficient of non determination captures the rest, including spurious correlations.

The lecture introduces hypothesis testing, defining null and alternative hypotheses, rejection regions, and significance level alpha, using an example where a claim of 150 is tested against sample averages.

Clarify the burden of proof in hypothesis testing by contrasting population mean and sample mean, and explain that the null hypothesis is assumed true until disproven.

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.

Identify null and alternative hypotheses and classify tests as lower-tailed, upper-tailed, or two-tailed, then determine rejection regions with practical examples.

Learn how to set up null and alternative hypotheses, identify the rejection region and cutoff, and determine whether data provide evidence against the null hypothesis.

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.

Apply chi-square tests to assess independence in categorical data, form null and alternative hypotheses, compare observed and expected proportions, and determine significance with alpha and degrees of freedom.

Demonstrates a chi-square goodness-of-fit test to compare old and new policy acceptance across four regions, computing expected counts and concluding with a significant policy effect.

Assess bias in 18 coin flips using a chi-square test. Conclude whether to reject the null, referencing degrees of freedom and the critical value for the alternative hypothesis.

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.

Explore the degree of freedom concept in ANOVA, calculating rows, columns, and total degrees of freedom, and using numerator and denominator df to determine the critical values.

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.

Learn how to calculate the f critical value using numerator and denominator degrees of freedom, total sample size, and the 95 percent confidence level.

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.

Explore time series analysis for forecasting by decomposing data into trend, seasonal variance, cyclical variance, and random variance, using additive and multiplicative models on chronologically collected data.

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.

Apply moving average analysis to trend data using three-year and five-year windows, calculating the arithmetic mean over fixed periods to smooth yearwise values and reveal underlying trends.

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.