From Means to Medians: Tools for Statistical Decision Making

Download the three downloadable resources containing Excel templates, worksheets, examples, and samples to support the foundational topics in statistics for this course, and prepare to dive into the first section.

Explore the normal distribution as the foundation of parametric statistics, define mu and standard deviation, and compare mean, median, and mode across symmetric and skewed cases.

Explore nonparametric statistics and practical examples of nonnormal distributions such as Weibull, lognormal, exponential, and uniform, highlighting decisions when data deviate from normal.

Apply descriptive statistics in excel to analyze defects per unit, using the data analysis toolpak to compute mean and std dev and build bins and a histogram.

Explore how the normal (gaussian) distribution behaves as standard deviation changes and the center shifts, using z-scores and the 68–95–99.73% rules to illustrate how variability affects quality.

Assess statistical conclusion validity by ensuring adequate sampling, appropriate tests, and reliable measurements, and verify underlying distributions and test assumptions to support sound data-driven decisions.

Explore robustness in statistics, showing how t tests and ANOVA remain reliable under deviations from normality and outliers. Emphasize random sampling and the central limit theorem guiding sample size decisions.

illustrates the central limit theorem: as sample size increases, the distribution of averages becomes more normal, with reduced variability from sigma to sigma over sqrt(n) and same mean mu.

Explore how subgroup averages create a normal distribution from any parent distribution, illustrating the central limit theorem with a deck of cards and sample means.

Explore parametric statistics with a comprehensive Excel toolkit, including Anderson-Darling tests, t-test calculators, templates, and diagrams. Download the all-in-one Excel file to practice the parametric models across the course videos.

Apply the chi square goodness of fit test to determine if observed frequencies differ from expected under the null hypothesis, and assess whether the data fits the normal distribution.

Conduct a chi-square analysis to test whether post position affects outcomes in an eight-horse race and whether weight loss data follow a normal distribution.

Practice chi-square goodness-of-fit using a normal distribution with mean 85 and sd 4 for 103 students across ten categories, yielding chi-square 8.36 with df 9, leading to acceptance of the null at 0.05.

Apply the Anderson-Darling test to a 50-sample length dataset, interpreting the D statistic and significance levels to reject normality and switch to non-parametric methods when appropriate.

Analyze fill-rate data from high-speed can filling to determine distribution shape using the Anderson-Darling test and a control chart, revealing non-normality and range-driven variability in production.

Apply the Anderson-Darling test for normality to 100 data points using the SPC for Excel to compute the statistic and assess the normality of the data.

Review progress on hypothesis testing, normal distribution, robustness, and the central limit theorem, including the Anderson-Darling goodness-of-fit test. Preview upcoming parametric tests—t test, ANOVA, and Pearson's correlation—and their nonparametric parallels.

Compare means with the t test and anova to make rational, data-driven decisions against a standard or between groups, and understand when each method applies.

perform a one-tailed t test on washer thickness with n=100, x-bar=0.52, s=0.06 to test mu=0.5. reject the null since t=3.33 exceeds the critical value, indicating the machine needs an adjustment.

Explore an Excel TI calculator tab that computes the t statistic from population mean, sample standard deviation, and size, while showing t distribution, pdf, and cdf with degrees of freedom.

Use a one-tailed t test to assess whether mu declined from 50 minutes; with x-bar 47, s 11.9, n 35, t -1.491, df 34, 1.690, accept the null.

Conducts a one-tailed hypothesis test to determine if mild lead exposure lowers children's test scores, using 1% significance, and rejects the null hypothesis.

Use the t statistic calculator to compare the sample and population means, showing observed t value exceeds the critical value and rejects the null about lead exposure affecting children's intelligence.

Compare two independent sample means with a two-sample t test using pooled variance, compute the t statistic, and decide with df n1+n2-2, as in brand A and B example.

Practice t tests by evaluating whether bulb burn time exceeds 500‑hour standard, using 25 samples and a t statistic of 2.25 with df 24, leading to rejection of null.

Explore the binomial distribution as a binary population, illustrating how sample outcomes arise and how the quincunx shows the binomial distribution forming the normal curve.

Compute the probability of getting exactly two fours in five rolls of a fair six-sided die using the binomial distribution, with p=1/6, q=5/6, and the combination formula.

Explore how to compute the binomial distribution in Excel using the pdf and cdf, adjust n and p, and interpret probabilities for dice rolls.

Compute binomial probabilities for a sample of five bolts with a 20% defect rate, including zero, one, and five defects, using longhand and a binomial calculator.

Solve a binomial practice for a family of four to find probabilities of at least one boy and two, three, or four boys with p=0.5, using combinations and Excel calculator.

Apply analysis of variance (ANOVA) to test whether three wheat varieties yield equally on average, splitting variation into experimental error and variety effects, using f distribution in a one-way design.

Explore analysis of variance to compare multiple samples, testing whether thermometer readings differ under a one-way and two-way ANOVA, with coding, sums of squares, and error variation.

Explore the f distribution in analysis of variance by comparing mean square ratios from group data, using excel to interpret the anova table and f critical.

Demonstrate performing a one-way ANOVA in Excel using the data analysis toolpak, including input data, labels, alpha 0.05, and output range; interpret the F value and F critical.

Compare means across three samples with different sizes using anova, test the null hypothesis, and interpret f statistics, between groups, within groups, and a box and whisker chart.

Assess four thermocouples using anova at 5% significance to detect differences in readings, revealing a significant difference with f ratio 3.59 versus 3.10 and suggesting calibration accuracy concerns.

The lecture introduces Pearson's correlation coefficient as a measure of linear association between two variables, showing how r ranges from -1 to 1 and why scatter diagrams reveal non-linearity.

Explore using Pearson's r and r squared in Excel to assess relationships: a very strong link between plant height and weight, and a moderate link between midterm and final grades.

Explore Pearson correlation between stock and bond prices on the New York Stock Exchange in the 1950s, quantify with r=0.391 and r^2=0.15, using Excel for data analysis.

Explore the correlation between fuel tank leak rates for two production crews using Pearson's correlation, revealing a moderate linear relationship (r = 0.624, r^2 = 0.39) across days.

Explore nonparametric methods with practical Excel worksheets, including Mann-Whitney tests, Spearman's correlation, and Pearson's correlation coefficient, highlighting easier use and fewer assumptions than parametric models.

Transition from normality assumptions to distribution-free nonparametric tests, including sign, Wilcoxon, Mann-Whitney, Friedman, Wallis, and Spearman.

Apply the sign test to compare two bolt-producing machines using 12 days of data, evaluate with a binomial to z conversion and continuity correction, and assess 5% significance.

Apply the sign test to compare two machines' performance, compute np, adjust with a 0.5 correction, and conclude no difference in defective bolts per day using a two-tailed z test.

Conduct a one-tailed sign test to determine if battery life exceeds 250 hours. With 24 batteries (15 positives), z = 1.02, we fail to reject the null at 0.05.

The sign test uses 40 statewide math scores to test deterioration from a median of 66; removing ties yields z=1.14 at 5% level, not significant.

Apply a sign-test with a binomial-to-normal approximation to test a null hypothesis, showing 36 of 40 cases above the median and yielding z 4.90, thus rejecting the null.

Explore the Wilcoxon signed rank test as a nonparametric substitute for the repeated measures t test, for paired data. It assumes symmetry and tests whether the median difference is zero.

Compute the signed-rank w statistic from paired observations, use ranked absolute differences and 5% critical values to accept or reject H0, illustrated with hens and egg production.

Use a signed rank test on 12 twin sets to compare first-born and second-born twins on a personality measure, with W = 28.5 and critical value 13, concluding no difference.

Apply the Wilcoxon signed rank test to mood scores before and after exercise for 40 subjects, rank absolute differences, and conclude no significant difference.

Explore the Mann-Whitney U test, a nonparametric alternative to the t test for two independent groups on a continuous variable. Determine if central tendency differs using a two-tailed 5% test.

Demonstrates a Mann Whitney non-parametric test for two industrial wafer cleaning systems (11 samples each), using ranks, U statistic, and z to determine if the groups differ.

use the Mann-Whitney test to compare cable strengths from two alloys (n=8 and n=10), rank the data, compute U and Z, and conclude a significant difference at 5% two-tailed level.

Use the Mann–Whitney test to compare two shifts’ production performance, rank data, compute R1 and R2, and evaluate mean, variance, U, and Z for a one-tailed 5% test.

Using a Mann-Whitney nonparametric test on 12 farm and 36 town boys, rank fitness scores and compute U and Z for a one-tailed test at alpha 0.05, showing no difference.

Practice the Mann–Whitney test to determine if two cigarette brands have different nicotine levels, using a two-tailed 5% significance and a null hypothesis of equality.

Explore the Friedman test, a non-parametric method for comparing more than two related samples by ranking data, illustrated with athlete performance across quarters.

Demonstrate how the Friedman test, a nonparametric version of anova, compares four grass types by ranking options across 12 homeowners.

The Friedman test compares three serum-determination methods for pancreatitis across nine specimens, using ranked data to reject the null that the methods yield the same serum values at 5% significance.

Apply the Friedman test to a three-drug reaction-time study with ten subjects, ranking responses using the Raghavji function and handling ties. Conclude differences when 8.45 exceeds 5.99.

Apply the Kruskal-Wallis test to compare five machines using ranked data, compute the H statistic, and decide if all machines perform the same at alpha 0.05.

Learn how the Kruskal-Wallis test compares three samples of different sizes by ranking data and computing the H statistic to reject the null when H exceeds the chi-square value.

apply the Kruskal-Wallis test to compare newspaper teams A, B, and C using ranks to compute the h statistic, and reject the null at 5% because 6.75 exceeds 5.99.

Kruskal-Wallis analysis of five-week store data shows a significant difference in customers served per ten minutes at the 5% level. H statistic confirms the difference.

Understand Spearman's rank correlation test, a nonparametric measure of rank correlation that assesses monotonic relationships and can be used with ranked data, compared to Pearson's correlation.

Apply Spearman's rank correlation to father–son height data and contrast it with Pearson correlation, computing d^2 differences and assessing the strength of association.

analyze 12 twin sets to compare first-born and second-born test results using spearman's rank correlation and pearson's coefficient, ranking each pair, calculating d squared, and interpreting a high correlation.

Analyze Spearman's rank correlation and Pearson's correlation coefficient using presidents' inauguration age and death age. The study reports Spearman 0.6837 with 40 presidents and a Pearson 0.5662.

Summarizes hypothesis testing, normal distribution, robustness, and the central limit theorem, then compares parametric and nonparametric tests (t, ANOVA, Wilcoxon, Mann-Whitney, Spearman, Pearson) with practical references.

Explore tools for statistical decision making from means to medians and gain practical insights from real-world examples to advance in the workplace, pursue promotions, and tackle new projects.

Explore bonus resources and links to three Udemy courses—quality engineering statistics, reliability engineering statistics 2025 edition, and certified lean six sigma green belt 2025 edition—plus downloadable documents and coupons.