Dr Nelson's Statistics Semester One, And Beyond

Explore the idea of variable types and typology, distinguishing categorical and quantitative data and seeing examples like colors, weights, and test scores to guide initial data analysis.

Classify data as categorical or quantitative to determine suitable analysis methods, with nominal and ordinal subtypes for categorical data, and discrete and continuous for quantitative data, including binary variables.

Identify variable types by classifying act score as quantitative and continuous, place of birth and favorite candy as categorical and nominal, grade as ordinal, and scholarship award as quantitative.

Explore how statistics uncover relationships between variables, using study hours and exam scores as an example. Learn to chart data, see upward trends, and discuss prediction and error in models.

Explore how statistics reveal relationships between variables in program evaluation, using binary participation and continuous outcomes like acceptance rates and scholarships to judge meaningful differences.

Explore how binary variables like race and program participation reveal relationships, and how statistics judge whether observed differences reflect chance, bias, or implicit racism.

Dr Nelson explains how to analyze survey data with categorical and ordinal variables, showing why averages don't apply, and how to use frequencies and most frequent responses to interpret surveys.

Create a continuous composite from related categorical survey items to quantify certainty about graduating college, enabling average, correlation, and regression analyses.

Explore core statistical notations such as X, X bar, the sum symbol, and the sum of errors and squared errors, and learn to interpret and apply them in data analysis.

Explore the sum of errors and the sum of squared errors for the age variable X, using five observations and a mean of twenty.

Explore measures of variation and dispersion, including variance, standard deviation, range, and inter quartile range, with sample and population formulas using sum of squared errors and n or n-1 denominators.

Compute the range by subtracting the lowest observation from the highest; for example, X range is 14, time spent studying 14 hours, and exam scores 33 points.

Compute the interquartile range by hand from the sorted x data, determine the first quartile, the median, and the third quartile, then subtract the first quartile from the third quartile.

Compute the sample variance for the X variable by summing squared errors from the mean. Divide the sum of squared errors, 168, by seven to obtain the variance, 24.

Calculate the standard deviation by hand from data by squaring errors, summing them to form the sample variance with n-1, then take the square root to obtain 4.89 hours.

Demonstrate calculating variation measures in Stata using hours studied and exam scores, including standard deviation, variance, quartiles and the cortile range, and how to interpret outliers.

Explore measures of dispersion in Python with pandas, revealing mean, standard deviation, variance, range, quartiles, and interquartile range via df.describe().transpose(), with notes on percentile differences.

Learn how standard deviation highlights meaningful differences between groups, using Stata to compare mean weights of domestic and foreign cars, and express differences as effect sizes such as Cohen's d.

Apply the standard normal distribution to interpret data with mean zero and sd one, estimate proportions within standard deviations, and compare observations using z-scores.

Explore the standard error, a controversial statistic with multiple calculation methods, and compare different approaches used in tools, videos, and textbooks.

Prepare the room amount data from the integrated post-secondary education data system in Excel, creating a working copy and removing missing values to illustrate the standard error.

This lecture demonstrates how to randomly shuffle data, select 400 observations, and compute the average and standard deviation, then derive the standard error as the estimate of the sampling distribution.

Estimate the standard error from sampling results using the sample mean and standard deviation. Use this standard error to infer the population and support confidence intervals and t tests later.

Link standard deviation and standard error using the room amount data from the integrated post-secondary education data system, with mean 5,616 and standard deviation 2,111 to infer population.

Understand standard errors in small samples by using the simple formula standard deviation divided by the square root of n. Compare alternative methods and note variability across tools like Stata.

Explore statistical notation for the mean, errors, variance, and standard deviation, including x-bar, mu, s, sigma, and sample versus population concepts.

Generate a thousand random study hours observations in Stata, compute the mean and standard deviation, and visualize dispersion with histograms, adjusting bins to reveal central tendency and data spread.

Visualize dispersion and compare outcomes across groups using box and whisker plots in Stata, highlighting measures of central tendency and dispersion like mean, median, and interquartile range.

Visualize dispersion with box plots and violin plots, comparing age across union status and industry in Python on a Google Colab notebook using the end lsw 88 data.

Learn to create violin plots in Stata with the Violin Plot package, install and run via plot, build horizontal and wage-by-industry visuals, and adjust labels with the graph editor.

discover how to obtain summary statistics for income in Stata, including mean, standard error, median, min, max, and percentiles, and interpret the 95 percent confidence interval for the population mean.

Explore how confidence intervals bound the population mean using the auto data set and observe that the mean price lies within a 95 percent interval across samples.

Compute a 95% confidence interval for nine observations (small sample) using the t distribution and standard error, then compare hand calculations with STADA, cross-check results, and report consistently.

Learn to calculate confidence intervals by hand for a large sample using LSW 88 DTA dataset, focusing on the age variable and standard error, variance, and z-based margins in Stata.

Explain how confidence intervals around the mean compare Group A and Group B, using the automobile data to decide if the price difference is meaningful based on overlapping intervals.

Clarify how to identify independent and dependent variables with a theoretical framework, using ACT score, place of birth, and scholarship award, and note input equals independent and output equals dependent.

Frame a precise research question by identifying the independent variable (X) and dependent variable (Y), such as place of birth influencing ACT scores or ACT score influencing scholarship awards.

Convert research questions into null and alternative hypotheses, learn how evidence rejects the null and supports the alternative, with examples on ACT scores, place of birth, and scholarship awards.

Explore the research (analytical) process, from framing a research question and hypotheses through data collection, hypothesis testing, and reporting conclusions, noting its linear but often iterative nature.

Explore p values as a versatile statistic for assessing statistical significance, guiding null hypothesis rejection, and complementing with effect sizes, confidence intervals, and data visualization.

Navigate data types as a continuum, weighing quantitative, ordinal, and nominal options for birth order, age, and student counts, and defend practical discrete or continuous choices.

Evaluate the effect size to compare mean scores between program participants and nonparticipants. Analyze year one and year two data with standard deviation to interpret score differences.

Explore how to compute Cohen's d to compare program outcomes using means and pooled standard deviation, illustrated with year one and year two differences and a 0.7 effect size.

Practice calculating effect sizes across years to draw conclusions about program effectiveness, compare year-by-year results, and inform policymakers on funding and program design.

Visualize exam scores across years by comparing participants and nonparticipants in study and exam preparation programs using box plots to reveal central tendency and dispersion differences between groups.