Statistics Basics

Types of Statistical Analysis

• Descriptive Statistics: summarizes and describes the basic features of a dataset
• Inferential Statistics: uses sample data to make inferences about a larger population

Levels of Measurement

• Nominal: categorical data with no inherent order (e.g. gender, ethnicity)
• Ordinal: categorical data with a natural order or ranking (e.g. education level)
• Interval: numerical data with equal intervals between consecutive values (e.g. temperature in Celsius)
• Ratio: numerical data with a true zero point (e.g. height, weight)

Hypothesis Testing

• Null Hypothesis (H0): a statement of no effect or no difference
• Alternative Hypothesis (H1): a statement of an effect or difference
• Test Statistic: a numerical value used to determine the significance of the results
• P-Value: the probability of obtaining a result as extreme or more extreme than the one observed, assuming the null hypothesis is true
• Significance Level (α): the maximum probability of rejecting the null hypothesis when it is true (typically 0.05)

Types of Errors

• Type I Error: rejecting the null hypothesis when it is true (α)
• Type II Error: failing to reject the null hypothesis when it is false (β)

Correlation and Causation

• Correlation: a statistical relationship between two variables
• Causation: a cause-and-effect relationship between two variables
• Note: correlation does not imply causation

Common Statistical Analysis Techniques

• Regression Analysis: modeling the relationship between a dependent variable and one or more independent variables
• t-Tests: comparing the means of two groups
• ANOVA (Analysis of Variance): comparing the means of three or more groups
• Chi-Square Tests: analyzing categorical data

Statistical Analysis

• Descriptive statistics summarize and describe the basic features of a dataset, providing a snapshot of the data.
• Inferential statistics use sample data to make inferences about a larger population, going beyond the data itself.

Measurement Levels

• Nominal data is categorical with no inherent order, such as gender or ethnicity.
• Ordinal data is categorical with a natural order or ranking, like education level.
• Interval data is numerical with equal intervals between consecutive values, such as temperature in Celsius.
• Ratio data is numerical with a true zero point, like height or weight.

Hypothesis Testing

• The null hypothesis (H0) states no effect or no difference, while the alternative hypothesis (H1) states an effect or difference.
• A test statistic is a numerical value used to determine the significance of the results.
• The p-value is the probability of obtaining a result as extreme or more extreme than the one observed, assuming the null hypothesis is true.
• The significance level (α) is the maximum probability of rejecting the null hypothesis when it is true, typically set at 0.05.

Errors

• A type I error occurs when the null hypothesis is rejected when it is true, with a probability of α.
• A type II error occurs when the null hypothesis is not rejected when it is false, with a probability of β.

Correlation and Causation

• Correlation refers to a statistical relationship between two variables, but does not imply causation.
• Causation implies a cause-and-effect relationship between two variables.

Statistical Techniques

• Regression analysis models the relationship between a dependent variable and one or more independent variables.
• t-Tests compare the means of two groups.
• ANOVA (Analysis of Variance) compares the means of three or more groups.
• Chi-Square tests analyze categorical data.