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[Important] Getting the most out of this course
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Statistics guessing game!
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Using the Q&A forum
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(optional) Entering time-stamped notes in the Udemy video player
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Should you memorize statistical formulas?
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Arithmetic and exponents
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Scientific notation
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Summation notation
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Absolute value
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Natural exponent and logarithm
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The logistic function
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Rank and tied-rank
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Is "data" singular or plural?!?!!?!
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Where do data come from and what do they mean?
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Types of data: categorical, numerical, etc
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Code: representing types of data on computers
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Sample vs. population data
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Samples, case reports, and anecdotes
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The ethics of making up data
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Bar plots
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Code: bar plots
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Box-and-whisker plots
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Code: box plots
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"Unsupervised learning": Boxplots of normal and uniform noise
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Histograms
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Code: histograms
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"Unsupervised learning": Histogram proportion
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Pie charts
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Code: pie charts
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When to use lines instead of bars
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Linear vs. logarithmic axis scaling
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Code: line plots
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"Unsupervised learning": log-scaled plots
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Descriptive vs. inferential statistics
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Accuracy, precision, resolution
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Data distributions
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Code: data from different distributions
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"Unsupervised learning": histograms of distributions
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The beauty and simplicity of Normal
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Measures of central tendency (mean)
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Measures of central tendency (median, mode)
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Code: computing central tendency
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"Unsupervised learning": central tendencies with outliers
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Measures of dispersion (variance, standard deviation)
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Code: Computing dispersion
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Interquartile range (IQR)
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Code: IQR
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QQ plots
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Code: QQ plots
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Statistical "moments"
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Histograms part 2: Number of bins
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Code: Histogram bins
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Violin plots
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Code: violin plots
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"Unsupervised learning": asymmetric violin plots
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Shannon entropy
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Code: entropy
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"Unsupervised learning": entropy and number of bins
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Garbage in, garbage out (GIGO)
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Z-score standardization
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Code: z-score
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Min-max scaling
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Code: min-max scaling
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"Unsupervised learning": Invert the min-max scaling
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What are outliers and why are they dangerous?
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Removing outliers: z-score method
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The modified z-score method
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Code: z-score for outlier removal
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"Unsupervised learning": z vs. modified-z
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Multivariate outlier detection
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Code: Euclidean distance for outlier removal
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Removing outliers by data trimming
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Code: Data trimming to remove outliers
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Non-parametric solutions to outliers
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An outlier lecture on personal accountability
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What is probability?
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Probability vs. proportion
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Computing probabilities
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Code: compute probabilities
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Probability and odds
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"Unsupervised learning": probabilities of odds-space
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Probability mass vs. density
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Code: compute probability mass functions
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Cumulative probability distributions
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Code: cdfs and pdfs
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"Unsupervised learning": cdf's for various distributions
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Creating sample estimate distributions
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Monte Carlo sampling
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Sampling variability, noise, and other annoyances
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Code: sampling variability
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Expected value
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Conditional probability
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Code: conditional probabilities
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Tree diagrams for conditional probabilities
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The Law of Large Numbers
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Code: Law of Large Numbers in action
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The Central Limit Theorem
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Code: the CLT in action
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"Unsupervised learning": Averaging pairs of numbers
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IVs, DVs, models, and other stats lingo
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What is an hypothesis and how do you specify one?
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Sample distributions under null and alternative hypotheses
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P-values: definition, tails, and misinterpretations
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P-z combinations that you should memorize
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Degrees of freedom
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Type 1 and Type 2 errors
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Parametric vs. non-parametric tests
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Multiple comparisons and Bonferroni correction
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Statistical vs. theoretical vs. clinical significance
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Cross-validation
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Statistical significance vs. classification accuracy
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Purpose and interpretation of the t-test
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One-sample t-test
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Code: One-sample t-test
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"Unsupervised learning": The role of variance
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Two-samples t-test
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Code: Two-samples t-test
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"Unsupervised learning": Importance of N for t-test
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Wilcoxon signed-rank (nonparametric t-test)
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Code: Signed-rank test
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Mann-Whitney U test (nonparametric t-test)
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Code: Mann-Whitney U test
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Permutation testing for t-test significance
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Code: permutation testing
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"Unsupervised learning": How many permutations?
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What are confidence intervals and why do we need them?
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Computing confidence intervals via formula
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Code: compute confidence intervals by formula
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Confidence intervals via bootstrapping (resampling)
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Code: bootstrapping confidence intervals
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"Unsupervised learning:" Confidence intervals for variance
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Motivation and description of correlation
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Covariance and correlation: formulas
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Code: correlation coefficient
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Code: Simulate data with specified correlation
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Correlation matrix
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Code: correlation matrix
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"Unsupervised learning": average correlation matrices
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"Unsupervised learning": correlation to covariance matrix
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Partial correlation
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Code: partial correlation
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The problem with Pearson
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Nonparametric correlation: Spearman rank
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Fisher-Z transformation for correlations
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Code: Spearman correlation and Fisher-Z
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"Unsupervised learning": Spearman correlation
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"Unsupervised learning": confidence interval on correlation
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Kendall's correlation for ordinal data
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Code: Kendall correlation
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"Unsupervised learning": Does Kendall vs. Pearson matter?
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Cosine similarity
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Code: Cosine similarity vs. Pearson correlation
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ANOVA intro, part1
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ANOVA intro, part 2
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Sum of squares
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The F-test and the ANOVA table
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The omnibus F-test and post-hoc comparisons
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The two-way ANOVA
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One-way ANOVA example
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Code: One-way ANOVA (independent samples)
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Code: One-way repeated-measures ANOVA
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Two-way ANOVA example
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Code: Two-way mixed ANOVA
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Introduction to GLM / regression
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Least-squares solution to the GLM
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Evaluating regression models: R2 and F
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Simple regression
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Code: simple regression
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"Unsupervised learning": Compute R2 and F
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Multiple regression
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Standardizing regression coefficients
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Code: Multiple regression
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Polynomial regression models
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Code: polynomial modeling
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"Unsupervised learning": Polynomial design matrix
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Logistic regression
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Code: Logistic regression
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Under- and over-fitting
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"Unsupervised learning": Overfit data
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Comparing "nested" models
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What to do about missing data
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What is statistical power and why is it important?
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Estimating statistical power and sample size
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Compute power and sample size using G*Power
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K-means clustering
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Code: k-means clustering
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"Unsupervised learning:" K-means and normalization
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"Unsupervised learning:" K-means on a Gauss blur
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Clustering via dbscan
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Code: dbscan
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"Unsupervised learning": dbscan vs. k-means
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K-nearest neighbor classification
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Code: KNN
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Principal components analysis (PCA)
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Code: PCA
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"Unsupervised learning:" K-means on PC data
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Independent components analysis (ICA)
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Code: ICA
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The two perspectives of the world
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d-prime
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Code: d-prime
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Response bias
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Code: Response bias
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