Introduction to Statistics
- Statistics- the science of learning from data in the presence of variability
- Three main reasons for studying statistics:
- Being informed
- Making good decisions
- Evaluating decisions that affect you
- How does statistics vary from mathematics:
- Role of context
- In statistics, context provides meaning
- Logic of statistical inference
- Use “what if” reasoning that includes consideration of uncertainty and variability
- Population- the total set of all “individuals” of interest
- Sample- a subset of “individuals” selected from the population
- Parameter- numerical characteristic of a population, a fixed quantity
- Statistic- numerical characteristic of a sample, a variable quantity (changes from sample to sample)
- Statistical questions
- A question that can be answered by collecting data that varies
- many possible vantage points; no single answer
- Identify
- the population
- the variable
- the variation
- Statistical problem solving process
- Formulate a statistical research question
- Collect data
- Analyze data
- Interpret results
- Three main components of statistics
- Describing data
- Summarizing and analyzing
- Producing data
- Plan how to obtain data needed to answer the question
- Drawing conclusions from data
- Using inferential procedures to make decisions and predictions
- Descriptive statistics- methods for organizing and summarizing information
- Inferential statistics- methods for drawing conclusions about a population
- Based on information obtained from a sample
- Can only be used with sample data
- Categorical variable- non-numerical variable with different categories
- Quantitative variable- numerical value
- Discrete variable- its possible values form a set of separate numbers (something that can be counted)
- Continuous variable- its possible values form a continuum of values over the real number line (something that can be measured)