Introduction to Basic Concepts in Statistics

**Biostatistics Module** **Unit 1: Introduction to Basic Concepts** **Statistics** - The term statistics, derived from the word state, was used to refer to a collection of facts of interest to the state. - **Statistics can be defined as**: - A way to get information from data. It...

**Biostatistics Module** **Unit 1: Introduction to Basic Concepts** **Statistics** - The term statistics, derived from the word state, was used to refer to a collection of facts of interest to the state. - **Statistics can be defined as**: - A way to get information from data. It is concerned with the collection of data, its subsequent description, and its analysis, which often leads to the drawing of conclusions. - It is a theory of decision making. **Branches of Statistics** 1. **Descriptive Statistics** - Deals with methods for organizing, summarizing, and presenting data in a convenient and usable form. - Uses graphical techniques to present data. - Uses numerical techniques such as measures of central location (mean, mode, median) and measures of variability (range, variance, standard deviation) to summarize data. - Steps: Collect data (e.g., Survey), Present data (e.g., Tables and graphs). 2. **Inferential Statistics** - Consists of methods for drawing conclusions about characteristics of a population based on information contained in a sample. - For conclusions to be correct, we build a measure of reliability into the statistical inference (confidence level and significance level). - Sample results can be used to make estimates and test hypotheses about population characteristics. **The Role of Probability** - In inferential statistics, we build a statistical model (margin of errors, confidence interval, level of significance) to provide a statement of quality. - Probability and sampling theory are gathered, then descriptive statistics are computed from which inferences will be based. **Why Statistics?** - To know how to properly present information. - To draw conclusions about populations based on sample information. - To improve processes. - To obtain reliable forecasts. - To provide input to study. - To measure performance of service or production process. - To evaluate conformance to standards. - To assist in formulating alternative courses of action. - To satisfy curiosity. **Key Definitions** - **Population**: The collection of things under consideration. - **Sample**: A portion of the population selected for analysis. - **Parameter**: A value that tells you something about a population. - **Statistic**: Tells you something about a small part of the population. - **Variable**: A characteristic of interest for the elements of a population or a sample. - **Data**: Observed values of a variable, collected, summarized, and interpreted. - **Time series data**: Data set containing observations on a single phenomenon observed over multiple successive points in time. - **Cross-sectional data**: Data set containing observations on multiple phenomena observed at a single point in time. **Data Sources** - **Census**: Complete enumeration of an entire population of statistical units. - **Advantages**: Provides the most reliable statistics if done professionally. - **Disadvantages**: Costly and timeliness is low. - **Surveys**: Based on a scientifically selected random sample from a population. - **Advantages**: More up-to-date, less time-consuming, and less costly than a census. - **Disadvantages**: Requires prompt data processing. - **Experimental Studies**: Identify variables of interest and control factors to obtain data. - **Observational (Non-experimental)**: Make no attempt to control or influence the variables of interest. - **Existing Sources**: Data might already exist within a firm or from government agencies. **Types of Data** - **Categorical (Qualitative)**: Labels or names used to identify an attribute of each element. - **Examples**: Gender, color, sex. - **Numerical (Quantitative)**: Require numeric values indicating how many or how much. - **Discrete Data**: Values that are isolated (e.g., number of children). - **Continuous Data**: No separation between possible values (e.g., test scores). **Measurement Scales of Data** - **Nominal Scale**: Data consist of labels or names without meaningful order. - **Examples**: Gender, religion. - **Ordinal Scale**: Exhibits properties of nominal data with meaningful order. - **Examples**: Education level, professional rank. - **Interval Scale**: Data have properties of ordinal data with meaningful intervals. - **Example**: Temperature. - **Ratio Scale**: Data have all properties of interval data with a meaningful zero point. - **Examples**: Distance, height, weight, time. **Exercises** 1. A psychologist has interviewed 250 out of 1507 school children throughout New York State and found that 80% spend at least 25 hours a week watching television. - a\) Identify the population and the sample. - b\) Identify the population parameter and the sample statistic of interest. 2. Determine whether the data type is quantitative, qualitative, or ranked. - a\) The weekly level of the prime interest rate during the past year. - b\) The name of the car driven by executives. - c\) The number of contacts made by each salesperson during a week. - d\) The rating (excellent, good, fair, or poor) given to performance evaluation.