Statistics

Find curated lessons and exercises on statistics, probability and research methods. Part of the materials have been made available under Creative Commons license.


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Below you find a list of all the lessons and exercises on statistics, probability and research methods, that are open or will be released with an open license. These materials have been created by Grasple over the past five years in collaboration with different universities. All of these will be released with an open Creative Commons license in the coming months. To access materials that are not yet CC licensed, you can create a free teacher account.

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  •   Indicates whether a lesson/explanation is available per subject
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  •   Content has an open Creative Commons license
  • cc  Content will be released with an open Creative Commons license in the near future

Inferential Statistics

  • 5 cc Sampling Distribution
  • 11 cc The Three Distributions
  • 5 cc Standard Deviation of a Sample
  • 16 cc Standard Error
  • 11 cc Normal Distribution
  • 12 cc Central Limit Theorem

Statistical Estimation

  • 8 cc Point Versus Interval Estimates
  • 10 cc Confidence Intervals for the Mean (conceptual)
  • 10 cc Student's t-Distribution (conceptual)
  • 5 cc t-Distribution

Hypothesis Testing

  • 9 cc Hypothesis Testing (conceptual)
  • 7 cc Type-I and Type-II Errors
  • 9 cc P-Value (conceptual)
  • 12 cc P-Value and Calculations
  • 11 cc Power
  • 9 cc Choosing a Suitable Statistical Test

Statistical Tests

  • 9 cc t-Test 1 Sample
  • 12 cc t-Test 2 Samples
  • 11 cc F-Test
  • 5 cc t-Test 2 Samples: Equal Variances
  • 6 cc t-Test 2 Samples: Unequal Variances
  • 6 cc t-Test 2 Samples: Paired Samples
  • 6 cc ANOVA
  • 14 cc ANOVA Calculations
  • 10 cc F-Table

Z-Score

  • 19 cc Z-Score
  • 14 cc Value to Probability
  • 14 cc Probability to Value
  • 11 cc Z-Table
  • 6 cc Probability Intervals

Z-Test

  • 5 cc Z-score to Z-test
  • 8 cc Z-test
  • 27 cc Calculate confidence Intervals using Z-distribution

Relations (interval/ratio)

  • 7 cc Relations
  • 7 cc Pearson's r
  • 6 cc Correlation vs Causation
  • 10 cc Covariance
  • 8 cc Testing Pearson's r

Relations (nominal/ordinal)

  • 11 cc Chi-Squared GOF
  • 10 cc Chi-Squared for Independence
  • 12 cc Cramer's V

Regression

  • 13 cc Linear Regression
  • 12 cc Regression Equation
  • 12 cc Testing Regression Coefficients
  • 9 cc Regression Confidence Interval

SPSS

  • 16 cc Intro SPSS
  • 12 cc SPSS: First Visualizations
  • 10 cc Manual Data Entry in SPSS
  • 13 cc Importing Data in SPSS
  • 10 cc More Visualisations in SPSS
  • 10 cc Frequency Tables in SPSS
  • 15 cc Descriptive Statistics in SPSS
  • 21 cc Chi-Squared for Independence in SPSS
  • 10 cc Coding in SPSS
  • 10 cc Recoding in SPSS

Evidential Statistics

  • 8 cc Effect Size
  • 9 cc Cohen's d
  • 7 cc Forest Plot

Clinical Measures

  • 4 cc Minimal Detectable Change (MDC)
  • 3 cc Minimal Clinically Important Difference (MCID)
  • 7 cc Odds Ratio

Other

  • 4 cc Kolmogorov-Smirnov Test
  • 6 cc Given Power, Calculate Sample Size
  • 4 cc Prediction Intervals versus Confidence Intervals
  • 18 cc NHST Procedure
  • 7 cc Hypotheses
  • 5 cc Statistical Significance

Probability

  • 9 cc Probability Trees
  • 4 cc Conditional Probability
  • 4 cc Take With or Without Replacement
  • 5 cc Expected Value
  • 6 cc Rules for Repetition

Probability Basics

  • 6 cc Conceptual Understanding of Random Variables
  • 7 cc Conceptual Understanding of Probabilities
  • 7 cc Conceptual Understanding of Sample Space
  • 7 cc Conceptual Understanding of (Probability) Distributions
  • 7 cc Conceptual Understanding of Discrete vs Continuous Distributions
  • 7 cc Conceptual Understanding of Probability Density Functions and Cumulative Density Functions

Probability Calculations & Rules

  • 7 cc Conceptual Understanding of Marginal Probabilities
  • 7 cc Conceptual Understanding of Joint Probabilities
  • 7 cc Conceptual Understanding of Conditional Probabilities
  • 7 cc Notation of Probabilities
  • 7 cc Conceptual Understanding of Dependent and Independent Events
  • 7 cc Conceptual Understanding of Probability Rules
  • 4 cc Computing Probabilities Using Probability Rules

Counting and Expected Values

  • 7 cc Conceptual Understanding of Expected Values
  • 6 cc Computing Expected Values
  • 7 cc Conceptual Understanding of Combinations
  • 7 cc Conceptual understanding of Permutations
  • 6 cc Computing Combinations
  • 3 cc Computing Permutations

The Normal Distribution

  • 5 cc Notation of Normal Distribution and Parameters
  • 7 cc Conceptual Understanding of Standard Normal Distribution
  • 3 cc Conceptual Understanding of Combining of Several Normally Distributed Variables
  • 5 cc Computing Parameters of Combined Normally Distributed Variables

Binomial Distribution

  • 12 cc Conceptual Understanding of Binomial Distribution
  • 5 cc Notation of Binomial Distribution and Parameters
  • 8 cc Properties of Binomial Distributions
  • 3 cc Computing with Binomial Distributions

Poisson Distribution

  • 7 cc Conceptual Understanding of Poisson Distribution
  • 7 cc Notation of Poisson Distribution and Parameters
  • 5 cc Properties of the Poisson Distribution
  • 4 cc Computing with Poisson Distributions
  • 12 cc Central Limit Theorem

t-distribution

  • 10 cc Student's t-Distribution (conceptual)
  • 5 cc t-Distribution

Random Variables

  • 2 cc Population and Sample - Conceptual explanation
  • 3 cc Experiments - Conceptual Explanation
  • 2 cc Random Variables - Conceptual Explanation
  • 3 cc Realizations of Random Variables - Conceptual Explanation
  • 3 cc Continuous versus Discrete Random Variables - Conceptual Explanation
  • 2 cc Notation of Probabilities - Conceptual Explanation

Distribution Functions

  • 2 cc Probability Distribution - Conceptual Explanation
  • 2 cc Distribution Functions - Conceptual Explanation
  • 3 cc Probability Density Functions - Conceptual Explanation
  • 2 cc Probability Calculations Using Probability Density Functions
  • 2 cc Probability Mass Functions - Conceptual Explanation
  • 2 cc Probability Calculations Using Probability Mass Functions

Distribution Functions

  • 3 cc Cumulative Distribution Functions - Conceptual Explanation
  • 2 cc Probability Calculations Using Cumulative Distribution Functions
  • 2 cc Relation and Difference Between Mass, Density and Cumulative Functions - Conceptual Explanation
  • 2 cc Finding Probability Density Function Using the Cumulative Distribution Function

Well known distribution functions

  • 1 cc Well Known Continuous Distribution Functions (List)

Center and Spread of Distributions

  • 4 cc Expected Value - Conceptual Explanation
  • 4 cc Calculating the Expected Value for Continuous Random Variables
  • 4 cc Second Moment - Conceptual Explanation
  • 4 cc Calculating the Second Moment for Continuous Random Variables
  • 4 cc Variance - Conceptual Explanation
  • 4 cc Calculating the Variance of a Random Variable

Conditional Probability

  • 2 cc Conditional Probability - Conceptual Explanation
  • 2 cc Conditional Distribution Functions - Conceptual Explanation
  • 5 cc Calculations with Conditional Distribution Functions

Estimation

  • 2 cc Statistic versus Parameter - Conceptual Explanation
  • 3 cc Statistical Models and Estimation - Conceptual Explanation
  • 3 cc Regression Analysis - Conceptual Explanation
  • 2 cc Finding Parameters of Linear Model Using Regression Analysis
  • 2 cc Maximum Likelihood - Conceptual Explanation
  • 5 cc Estimate Parameters of Distributions Using Maximum Likelihood Estimation

Research Cycle

  • 17 cc Research Cycle
  • 10 cc Phase 1: Problem analysis
  • 10 cc Phase 2: Research design
  • 10 cc Phase 5: Reporting
  • 13 cc Analysis Schema

Qualitative research

  • 1 cc Literature and APA referencing
  • 3 cc Select sampling methods
  • 15 cc Recognise select sampling methods
  • 21 cc SPI(C)E Acronym
  • 9 cc Triangulation
  • 20 cc Coding

Correlational research

  • 35 cc Measurement levels
  • 7 cc Operationalisation
  • 13 cc More on Measurement levels and Operatinialisation
  • 17 cc Aselect sampling methods
  • 18 cc Validity and Reliability
  • 6 cc Correlation vs Causation
  • 23 cc Population and Sample
  • 3 cc Correlation
  • 10 cc Descriptive Statistics
  • 5 cc Correlations in samples

Experimental research

  • 20 cc Forming hypotheses
  • 10 cc Randomisation

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