Mastering the basics of statistics with python

Explore the four data levels—nominal, ordinal, interval, and ratio—and learn how they enable classification, ranking, meaningful differences, and the choice between parametric and non-parametric tests.

Learn to calculate the mode as a central tendency measure, for simple and grouped data, alongside mean and median, using a formula and Python inbuilt functions with examples.

Compute the median for ungrouped data by locating the middle value, or averaging the two central values for even samples, then apply the grouped-data formula to locate the median interval.

Identify mean as the third measure of central tendency and learn to calculate it for ungrouped and grouped data using simple examples.

Learn to compute measures of central tendency in Python using the statistics library for descriptive statistics, with practical examples of mode, median, and mean, and explore NumPy and pandas.

Compare mean, median, and mode using the salaries of nine employees to illustrate central tendency and when averages can mislead.

Explore how measures of dispersion reveal data spread by calculating variance, comparing sample and population variance, and applying the Bessel correction in descriptive statistics.

Learn to calculate sample variance and population variance in python using the statistics library, then compute the population standard deviation and relate it to variance; percentile is covered next.

Understand standard deviation as the square root of variance, distinguish population variance from sample variance, and apply the population standard deviation formula to compute the spread.

Compute the coefficient of variation, sigma by mu times 100, to compare relative variability; product A has CV 14.53% and product B 14.38%, so A shows greater variability.

Explore variance as a measure of dispersion, including sample and population variance, standard deviation, coefficient of variation, and Chebyshev's theorem.

Explore the empirical rule for standard deviation, using mu and sigma to locate 68% between mu plus or minus sigma, and apply Chebyshev's theorem 1 minus 1 over k squared.

Introduce mean absolute deviation as a second dispersion measure after variance, calculating it from the mean’s absolute deviations and obtaining 4.8 to compare with the standard deviation.

Compute the 30th percentile by ordering data and interpolating with a quartile-based formula, showing how exact and approximate percentiles differ in exams, including the 90th and 99th percentiles.

Calculate percentiles in python using numpy, without a statistics library, by sorting data and applying np.percentile to obtain the 25th, 30th, 50th, and 75th percentiles.

Master quartiles as a dispersion measure with a k n plus one over fourk method to locate Q1, Q2, Q3, and apply the interquartile range for box and whisker plots.

Explore quartiles with Python using numpy to compute Q1, Q2, Q3 and the interquartile range, then visualize with a box-and-whisker plot to identify outliers.

Discover how the range serves as a measure of dispersion, showing how spread the data is, with examples like one, two, three, two, four yielding a range of three.

Explore measures of shape in descriptive statistics by examining skewness, symmetry, and the mean, median, and the mode relationship through income distributions and the normal distribution.

Calculate skewness with S = 3*(mu - MD)/sigma, where MD is the median and sigma the standard deviation; negatives indicate left skew, zeros indicate symmetry, positives indicate right skew.

Learn to compute skewness with Python using scipy.stats, visualize with a box-and-whisker plot, and interpret how data distribution and outliers affect skewness.

Explore kurtosis as a measure of shape by comparing leptokurtic, mesokurtic, and platykurtic distributions and their relation to the normal distribution and outliers, using Python.

Explore how to draw and interpret a box and whisker plot, with Q1, Q3, minimum, maximum, and outliers. See how skewness—positively skewed, negatively skewed, and normal data—shifts the mean.

Explore descriptive statistics with a practical Python example using pandas to compute mean, median, mode, dispersion, quartiles, box plots, skewness, and kurtosis on a student performance dataset from Kaggle.

Explore distributions in statistics, from normal to uniform, and how they enable inference and prediction with real examples like height data and dice outcomes.

Explore the binomial distribution through a quality-control example, learn its discrete probability formula p(x)=C(n,k)p^k(1-p)^{n-k}, and distinguish it from continuous distributions.

The lecture introduces the Poisson distribution as an extension of the binomial, using a bakery example with an average of three orders per hour to estimate five arrivals.

Explore the normal distribution as the most common data pattern, with mean 175 cm and sd 10 cm for male heights, and compute probabilities using standard formula and Python tools.

Explore inferential statistics, covering population and statistic, hypothesis testing, parametric and nonparametric tests, and regression models such as linear and logistic.

Understand the difference between population and statistic, how samples support inferential statistics, and key ideas such as mu, x bar, sigma, s, and the parameter vs statistic distinction.

Demonstrate the central limit theorem with Python by sampling from exponential and Poisson distributions, showing sample means form a normal distribution around the population mean as n grows.

Convert raw scores to z scores using z = (x - mu)/sigma, explore the standard normal distribution and z-table, and apply these concepts to probability and hypothesis testing in Python.

Master z score calculation in statistics with Python to apply core concepts from the course.

Formulate the null and alternative hypotheses, and identify two-tailed versus one-tailed tests; apply hypothesis testing steps with the z score and central limit theorem to sample means.

Formulate a hypothesis and evaluate it by measuring sample means, computing the z-score, and applying a significance level to test if the mean differs from 500 grams.

Learn to build confidence intervals using z-values and probabilities, with examples from bulb lifetimes and test scores to estimate population means.

Explore p value in hypothesis testing by comparing observed z scores to a significance level, and learn how Python-based tests report p values to decide on rejecting the null hypothesis.

Learn to read the z-table for probabilities of z values, e.g., 1.4 or 1.45, and find critical z for one- and two-tailed tests at 0.05 significance.

Learn to compute z values in Python using SciPy's scipy.stats.norm, derive critical z for two-tailed and one-tailed tests with ppf and cdf, and interpret p-values.

Explore the t distribution for unknown population standard deviation and small samples, compute the t statistic, and use the t table with degrees of freedom n-1.

Use python and scipy.stats to compute t values, p-values, and critical values with t.cdf and t.ppf, using degrees of freedom n-1 and alpha 0.05.

Perform a one-sample mean z-test with known sigma to assess if mean bottle content is below 500 ml at 5% significance, using n=40 and x̄=496 ml.

Visualize mean testing in Python by analyzing a sample mean with a one-tailed test, interpreting z values, p values, and the significance level to decide the null hypothesis.

Compare two delivery services using a two-sample t-test with unknown population stdevs, applying both pooled variance and Welch's methods to test mu_a = mu_b at 5% significance.

Use Python and statsmodels to perform a one-sample proportion z test against p0=0.8, compute the z statistic and p-value, and reject the null at 0.05 for a left-tailed alternative.

Perform a one-sample proportion test to evaluate p against 0.8, using a z-test with 150 observations (108 on time) at alpha 0.05, and reject the null.

Apply finite population proportion testing with the correction factor. Case with N=500, p0=0.6, and a sample of 80 (42 defect-free) yields fail to reject the null in a one-tailed test.

Explore the chi square distribution and its relation to the normal distribution, focusing on degrees of freedom, alpha and critical values, and simulations of how the curve changes.

Conduct a chi-square test for population variance using sample variance s^2 and n, with degrees of freedom n minus one, at a 5% significance level.

Explore parametric hypothesis testing by moving from one-sample tests to two-sample tests, comparing means, proportions, and variances for independent and dependent samples.

Use a two-sample t test with unknown population standard deviations to compare two services, applying pooled variance and Welch tests at 5% to assess mu_a vs mu_b.

Compare the means of two independent samples with a hypothesis test using delivery times from service A and service B. Evaluate equal and unequal variance and compute the t statistic.

compare two independent samples using two-sample t tests with unknown population standard deviations, applying pooled variance and Welch's approaches to test mu_a = mu_b at 5% significance.

Learn how the Welch t test handles two-sample comparisons with unequal variances, compute the standard error as s_a^2/n_a + s_b^2/n_b, and note that degrees of freedom are calculated differently.

Compare means of two independent populations using a two-sample z test when variances are known; compute z = (x̄1 − x̄2)/√(σ1^2/n1 + σ2^2/n2) without pooling.

perform a paired t-test for dependent samples to compare productivity before and after training, calculating d bar, s_d, and t, then determine significance at 0.05.

Explain the pooled and unpooled two-sample population proportion test, using a click-through example to show when to use each approach and the null p one equals p two.

Compare two proportions using a two-sample pooled proportion test, compute p1, p2, and pooled proportion, and reject the null with a z-statistic near -1.96, concluding p2 is greater than p1.

Master the 2-sample pooled proportion test in python using statsmodels, comparing 65/500 and 84/480 with alpha 0.05; the two-sided test yields p=0.0498, rejecting the null.

Evaluate whether drug A improves seven-day recovery by at least five percentage points using an unpooled proportion test, computing p1, p2, standard error, and z with Python.

Perform a two-sample unpooled proportion test in Python with statsmodels, comparing 92/600 vs 125/650, testing p1-p2>0.05; results: z=-0.514, p=0.696, fail to reject.

use the f test to compare variances by computing f = s1^2/s2^2 and f distribution with n1-1 and n2-1 degrees of freedom to test the null that sigma1^2 equals sigma2^2.

Learn to use anova to compare three or more sample means, including one-way and two-way designs with fertilizer yield examples, and post hoc tests to identify which means differ.

Examine the steps of two-way ANOVA testing, formulating null and alternative hypotheses, calculating group and grand means, and computing between, within, and total sum of squares.

Explore the steps of an anova test, including total, within and between sum of squares, degrees of freedom, mean sum of squares, the f-test, and p-values.

Identify significant differences among fertilizer groups with ANOVA, then apply Tukey post hoc testing to compare A, B, and C at 0.05, concluding C > B > A.

Learn to perform a one-way ANOVA in Python using statsmodels, build a dataframe with fertilizer groups, interpret the ANOVA table, and run a Tukey post-hoc test to identify differences.

Learn how to perform a two-way ANOVA to evaluate the effects of fertilizer and irrigation on yields, test for main effects and interaction, and formulate corresponding null and alternative hypotheses.

Explore the two-way ANOVA with fertilizer and irrigation and their effects on yields. Formulate null and alternative hypotheses for fertilizer effects, irrigation effects, and their interaction.

compute the grand mean from all sample values, then compute marginal means for each factor (fertilizer and irrigation) and the cell means for treatment combinations, illustrating steps in two-way anova.

Master the steps to compute sum of squares in two-way ANOVA, including total, fertilizer, irrigation, and interaction, plus error, ensuring consistency with grand mean.

Compute degrees of freedom for fertilizer (2), irrigation (1), interaction (2), and error (6). Calculate mean squares and F at 0.05; irrigation and fertilizer significant; interaction not; post hoc test.

Learn to perform a two-way anova in Python using pandas and statsmodels, compare fertilizer and irrigation effects on yield, and run type 2 anova with tukey post hoc tests.

Explore regression as a statistical model to study and predict a dependent variable from one or more independent variables, with a focus on linear regression and its extensions.

Model the regression equation y = beta0 + beta1 x using study hours to predict exam scores, estimate beta1 and beta0 from x̄ and ȳ, and interpret intercept and slope.

Compute sum of squares in regression, derive predicted values from y_hat = beta0 + beta1 x using y_i and y_bar, and confirm SST equals SSR plus error sum of squares.

Analyze degrees of freedom in a six-sample regression, compute SST, SSR, SSE, and their mean sum of squares (MSR, MSE), and apply the ANOVA-style table steps.

Explain the coefficient of regression and the correlation coefficient r, including r's sign for linear relationships. Show that r squared is the coefficient of determination, with a 0.92 example.

Calculate the f statistic as MSR divided by MSE to test the null hypothesis of no relation between x and y; p value 0.0024 confirms significant regression.

From a six-sample regression, compute p-values and t statistics to test the intercept and slope in the equation 73.93 + 3.49x, confirming both parameters are highly significant.

Explore confidence intervals for regression parameters and mean responses, compare them with prediction intervals, and use Python to compute y hat, standard errors, and t statistics.

Learn to diagnose regression assumptions using residual analysis in Python, including linearity, homoscedasticity, normality of residuals, and independence, with residuals vs fitted plots and Shapiro-Wilk tests using built-in libraries.

Learn to perform linear regression in Python with NumPy and statsmodels, build a design matrix with a constant, fit an OLS model, and interpret the intercept, slope, R-squared, and p-values.