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Section 1.1 An Overview of Statistics What Is Statistics? Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions. Ch1 Larson/Farber 2 Important Terms Population The collection of all responses, measurements, or counts that are of interest. Sample A portion or subset of the population. Ch1 Larson/Farber 3 Important Terms Parameter A number that describes a population characteristic. Example: Average gross income of all people in the United States in 2002. Statistic A number that describes a sample characteristic. Example: Average gross income of people from three states in 2002. Ch1 Larson/Farber 4 Two Branches of Statistics Descriptive Statistics Involves organizing, summarizing, and displaying data. Inferential Statistics Involves using sample data to draw conclusions about a population. Ch1 Larson/Farber 5 Section 1.2 Data Classification Types of Data Qualitative Data -consist of attributes, labels or qualities Quantitative Data -consist of measurements, counts or quantities Ch1 Larson/Farber 7 Levels of Measurement A data set can be classified according to the highest level of measurement that applies. The four levels of measurement, listed from lowest to highest are: 1. Nominal 2. Ordinal 3. Interval 4. Ratio Ch1 Larson/Farber 8 Levels of Measurement 1. Nominal: Categories, names, labels, or qualities. Cannot perform mathematical operations on this data. Ex: type of car you drive, your major, zip code 2. Ordinal: Data can be arranged in order. You can say one data entry is greater than another. Show rank or position Ex: movie ratings, condition of patient in hospital Ch1 Larson/Farber 9 Levels of Measurement 3. Interval: Data can be ordered and differences between 2 entries can be calculated. There is no inherent zero (a zero that means none). Ex: Temperature, year of birth 4. Ratio: There is an inherent zero. Data can be ordered, differences can be found, and a ratio can be formed so you can say one data value is a multiple of another. Ex: Height, weight, age Ch1 Larson/Farber 10 Section 1.3 Experimental Design Data Collection Observational Study: Observe and record what the group is doing. Experiment: Apply a treatment to a part of the group. Simulation: Use a mathematical model (often with a computer) to reproduce condition. Ch1 Larson/Farber 12 Data Collection Survey: Asking people questions by interview, mail or telephone Census: A count or measure of the entire population. Sampling: A count or measure of part of the population. Ch1 Larson/Farber 13 Sampling Techniques (Simple) Random Sample: Each member of the population has an equal chance of being selected. Assign a number to each member of the population. Random numbers can be generated by a random number table, computer program or a calculator. Data from members of the population that correspond to these numbers become members of the sample. Ch1 Larson/Farber 14 Sampling Techniques Stratified Sample: when it is important to have members from each segment of the population Ex. Income, race, education Divide the population into groups (strata) and select a random sample from each group. Ch1 Larson/Farber 15 Sampling Techniques Cluster Sample: when the population falls into naturally occurring subgroups Ex. Zip codes, class Divide the population into clusters and randomly select one or more clusters. The sample consists of all members from selected cluster(s). Ch1 Larson/Farber 16 Sampling Techniques Systematic Sample: each member is assigned a number and every kth member is chosen Choose a starting value at random. Then choose sample members at regular intervals. If k = 5, every 5th member of the population is selected. Random.org Ch1 Larson/Farber 17 Sampling Techniques Convenience Sample: Choose readily available members of the population for your sample. This often leads to biased results so it is not used very often. Ch1 Larson/Farber 18 Bias Biased sample: the sample does not represent the entire population Ex: a sample of 18-22 year old college students does not represent the population of 18-22 year olds Ch1 Larson/Farber 19 Bias Biased question: using a survey question that encourages people to answer a certain way Ex: Do people have the right to possess loaded guns in their homes to protect themselves and their families? Or: Do people have the right to possess loaded guns in their homes? Ch1 Larson/Farber 20