# Statistics

Statistics is the platform for my continuous training of statistics and R programming.

What do you think? Comment, criticize, add, ask, answer. Thanks for your feedback.

From this page **I will soon be uploading statistical exercises and cases** with worked step-by-step solutions all linking to their respective theory in ‘My notes on statistics’.

Below, you will find the directory for ‘My notes on statistics’. **Thanks for leaving me your feedback** and questionsin the comment modules.

## My notes on statistics

### Probability

- Sample space, events and probabilities
- Complement of an event
- Independent events
- Dependent events
- Mutually exclusive events
- Mutually inclusive events
- Permutations
- Combinations
- Conditional probability
- Law of total probability
- Bayes’ Theorem

### Summarizing quantitative data

- Mean, median and mode
- Interquartile range (IQR)
- Variance and standard deviation of a population
- Variance and standard deviation of a sample

### Discrete Probability Distribution

- Discrete vs. continuous random variables
- Discrete probability distributions
- Mean, variance and standard deviation
- Mean of sum & difference
- The binomial distribution
- Poisson distribution
- The geometric distribution
- Hypergeometric distribution

### Modelling data distributions

- Continuous vs. discrete data
- Density curves
- Significance level
- Critical value
- Z-score
- The p-value
- The Central Limit Theorem
- Skewness and kurtosis

### The Normal Distribution

### Study design

Confidence intervals

### Hypothesis Testing

- Hypothesis testing
- One-tailed tests
- Two-tailed tests
- Proportion hypothesis testing
- Hypothesis test for a mean
- Statistical power
- Power of test calculation
- Chi-square Goodness of Fit Test

### Simple linear regression, fundamentals

- Scatter plots
- Correlation coefficient
- Regression line
- Squared errors of line
- Coefficient of determination, r2

### Simple linear regression, Inference

- Inference about regression
- The LINER model
- Residual plots
- Standard error of the slope
- Confidence interval for the slope
- Hypothesis test for the slope
- Mean and single response intervals
- Influential points
- Precautions in simple linear regression
- Transformation of data

### Two-sample inference for the dif. between groups

### ANOVA and the F-distribution

#### Carsten Grube

Statistical Data Analysis

Freelance Consultant

##### Normal distribution

##### Confidence intervals

##### Simple linear regression, fundamentals

##### Two-sample inference

##### ANOVA & the F-distribution

+34 616 71 29 85

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Spain: Ctra. 404, km 2, 29100 Coín, Malaga

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**About me**

Learning statistics. Doing statistics. Freelance since 2005. Dane. Living in Spain. With my Spanish wife and two children.

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