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Questions and Answers
What is the primary purpose of descriptive statistics?
What is the primary purpose of descriptive statistics?
What level of measurement is education level an example of?
What level of measurement is education level an example of?
What is the purpose of a null hypothesis?
What is the purpose of a null hypothesis?
What is the probability of obtaining a result as extreme or more extreme than the one observed?
What is the probability of obtaining a result as extreme or more extreme than the one observed?
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What is the consequence of a Type I Error?
What is the consequence of a Type I Error?
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What is the primary difference between correlation and causation?
What is the primary difference between correlation and causation?
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What is the purpose of regression analysis?
What is the purpose of regression analysis?
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What is the purpose of a t-test?
What is the purpose of a t-test?
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Study Notes
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.
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Description
Learn about the different types of statistical analysis, including descriptive and inferential statistics. Understand the levels of measurement, including nominal, ordinal, and interval data.
