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Statistics Chapter 1

Statistics Chapter 1. Statistics, what is it? Statistics is the science of collecting, organizing, visualizing, summarizing and analyzing information to draw conclusions or answer questions. (Author adds: Statistics is also about providing a level of confidence in any conclusions.)

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Statistics Chapter 1

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  1. Statistics Chapter 1

  2. Statistics, what is it? • Statistics is the science of collecting, organizing, visualizing, summarizing and analyzing information to draw conclusions or answer questions. (Author adds: Statistics is also about providing a level of confidence in any conclusions.) • 2 TYPES DESCRIPTIVE AND INFERENTIAL • Descriptive Statistics: the collection, presentation and description of sample data. • Inferential Statistics: the technique of interpreting the values resulting from sample data to make decisions and draw conclusions about the population.

  3. 3 Major Reasons 1.To be an informed consumer: understand the information the media gives you. A) Interpret information in charts and graphs B) Understand numerical arguments C) Know the basics of how data should be gathered so it can be used correctly

  4. 2. Understanding and Decision making A) Decide whether existing information is adequate B) Collect more information in a reasonable way C) Summarize data in a useful and informative manner. D) Analyze the available data E) Draw a conclusion and access the risk of an incorrect decision

  5. 3. Evaluate the decisions that affect your life A) Was a decision made based on incorrect data or interpretation of the data? B) Were the correct techniques applied to make the decision? C) Was the correct decision made based on the data?

  6. Analysis of data is used to offset anecdotal claims (common beliefs such as cell phones cause cancer) • Variability of data. Do you watch the same amount of TV each day, eat the same amount of food. • Since data can vary the goal in statistics is to describe and understand this variability. • If the data is incorrectly obtained we can make incorrect conclusions such as (call ins) • Or there might be lurking variables. An hidden variable in a relationship that affects the characteristic of the other variables. Ex: The more firefighters on a seen the more damage there is to the home. What might be a lurking variable.

  7. Example: The TV show American Idol eliminates contestants based on the number of votes from viewers who send in their vote. A winner is declared as America’s Idol. What is wrong? Data is incorrectly obtain. Did we get a good sample of America or just those who watch? • Example: There is statistical data that shows a strong correlation between weight and reading ability, the more one weighs the better one reads. What is wrong? Lurking variables education and parenting

  8. Process of Statistics: Very much like the scientific method • Identify an objective. What question do you want to answer? This question must identify a population( a group you want to study) Individuals are member of the group to be studied. • Collect a sample of data. A sample is a subset of the data. • Organize ans summerize the information collected.(Descriptive statistics) • Draw a conclusion from the information. We hope the conclusion will reflect a generalization about the population of the study. (Inferential statistics)

  9. When a generalization is made about a population based on the sample data taken from the population we run the risk of an incorrect conclusion.This is known as a sampling error.

  10. Notes for Chapter 1 VOCABULARY: The entire collection of individuals or objects about which information is desired is called the of interest. It includes all of the subjects to be studied. A census is the collection of the data from the population. A sample is a of the, selected for study.

  11. Notes for Chapter 1 VOCABULARY: The entire collection of individuals or objects about which information is desired is called the Population of interest. It includes all of the subjects to be studied. A census is the collection of the data from the population. A sample is a of the, selected for study.

  12. Notes for Chapter 1 VOCABULARY: The entire collection of individuals or objects about which information is desired is called the Population of interest. It includes all of the subjects to be studied. A census is the collection of the data from everyonethe population. A sample is a of the, selected for study.

  13. Notes for Chapter 1 VOCABULARY: The entire collection of individuals or objects about which information is desired is called the Population of interest. It includes all of the subjects to be studied. A census is the collection of the data from everyonethe population. A sample is a subset of thePopulation, selected for study.

  14. Data are the observations that have been collected. A set of values collected from a population is know as a sample. • A is a numerical value describing some characteristic of a population.

  15. Data are the observations that have been collected. A set of values collected from a population is know as a sample. • A Parameter is a numerical value describing some characteristic of a population. • A is a numerical value describing some characteristic of a sample.

  16. Data are the observations that have been collected. A set of values collected from a population is know as a sample. • A Parameter is a numerical value describing some characteristic of a population. • A Statistic is a numerical value describing some characteristic of a sample. are the characteristics of an individual in a population.

  17. Data are the observations that have been collected. A set of values collected from a population is know as a sample. • A Parameter is a numerical value describing some characteristic of a population. • A Statistic is a numerical value describing some characteristic of a sample. Variables are the characteristics of an individual in a population.

  18. 2 types of variables. • Quantitative data consists of Numbers representing counts or measurements. • Temperature, weight, time, GPA

  19. 2 types of variables. • Quantitative data consists of Numbers representing counts or measurements. • Temperature, weight, time, GPA • Qualitative or Categorical data can be separated intoDifferent categories that are distinguished by some non-numerical characteristic. • Ethnicity, days of the week, eye color, type of car.

  20. 2 types of variables. • Quantitative data consists of Numbers representing counts or measurements. • Temperature, weight, time, GPA • Qualitative or Categorical data can be separated intoDifferent categories that are distinguished by some non-numerical characteristic. • Ethnicity, days of the week, eye color, type of car. • Math operations can be preformed on Quantitative data, but not on Qualitative

  21. A nominal level of measurement consists of names, label, or categories. An order can not be assigned to nominal data. ie. low to high • Hair color, sex, state, religion • A ordinal level of measurement can be arranged in some order or ranking. • Grades, Movie rankings, zip codes • Ordinal data allows for comparison but not difference in the data.

  22. Discrete data when the number of values for the data are countable. • Days of the week, number of students in a class, number of pages in a book • Continuous data has an infinite number of possible values for the data. The data could be any value along a line interval, including every possible value between two points. Usually a measurement. • Time, temperature, weight, height

  23. Interval level of measurement is like ordinal, with an additional property the differences between two data values is meaningful. There is no natural zero starting point in the data. (None of the quantity is not a meaningful value) Differences have meaning but ratios do not. Temperature, time in years • Ratio level of measurement is the interval level modified to include the natural zero starting point. (Zero indicates a value for the data) Differences and ratios are meaningful values. Weight, money

  24. The is the collection of all cars owned by all faculty at SCC.

  25. The Population is the collection of all cars owned by all faculty at SCC. • A is any subset of the population. The cars owned by the mathematics department.

  26. The Population is the collection of all cars owned by all faculty at SCC. • A Sample is any subset of the population. The cars owned by the mathematics department. • A is the characteristic of interest associated with the population. For example the dollar value of each car.

  27. The Population is the collection of all cars owned by all faculty at SCC. • A Sample is any subset of the population. The cars owned by the mathematics department. • A Variable is the characteristic of interest associated with the population. For example the dollar value of each car.

  28. The Population is the collection of all cars owned by all faculty at SCC. • A Sample is any subset of the population. The cars owned by the mathematics department. • A Variable is the characteristic of interest associated with the population. For example the dollar value of each car. • A data would be the dollar value of a particular car. Say $25,700.

  29. The Population is the collection of all cars owned by all faculty at SCC. • A Sample is any subset of the population. The cars owned by the mathematics department. • A Variable is the characteristic of interest associated with the population. For example the dollar value of each car. • A Single data would be the dollar value of a particular car. Say $25,700.

  30. The Population is the collection of all cars owned by all faculty at SCC. • A Sample is any subset of the population. The cars owned by the mathematics department. • A Variable is the characteristic of interest associated with the population. For example the dollar value of each car. • A Single data would be the dollar value of a particular car. Say $25,700.

  31. A Single data would be the dollar value of a particular car. Say $25,700. • The data would be the of values that correspond to the sample.

  32. A Single data (datum) would be the dollar value of a particular car. Say $25,700. • The data would be the Subset of values that correspond to the sample. • The that will be found is the average value of the cars in the sample.

  33. A Single data would be the dollar value of a particular car. Say $25,700. • The data would be the Subset of values that correspond to the sample. • The Statistic that will be found is the average value of the cars in the sample.

  34. A Single data would be the dollar value of a particular car. Say $25,700. • The data would be the Subset of values that correspond to the sample. • The statistic that will be found is the average value of the cars in the sample. • The which we are seeking is the average value of all the cars in the population.

  35. A Single data would be the dollar value of a particular car. Say $25,700. • The data would be the Subset of values that correspond to the sample. • The statistic that will be found is the average value of the cars in the sample. • TheParameter which we are seeking is the average value of all the cars in the population.

  36. HOW DO WE OBTAIN DATA? • A census, use existing sources, Survey samplingDesigned experiments • OBSERVATION STUDY- Observes the individuals but does not manipulate or influence the variable interest. • EXPERIMENT- A treatment is applied an we observe the effect of the treatment as a response variable.

  37. Recall the is any characteristic whose value may change from one individual to another in a population, sample, or experiment.

  38. Recall the Variable is any characteristic whose value may change from one individual to another in a population, sample, or experiment. (Lurking Variable) • CONFOUNDING VARIABLE: IS ONE THAT EFFECTS THE RESULTS OF DATA OF THE DESIGN OF THE SURVEY OR EXPERIMENT. When two different variables affect the response variable.

  39. Recall the Variable is any characteristic whose value may change from one individual to another in a population, sample, or experiment. • CONFOUNDING VARIABLE: IS ONE THAT EFFECTS THE RESULTS OF DATA OutsideOF THE DESIGN OF THE SURVEY OR EXPERIMENT. When two different variables affect the response variable.

  40. Recall the Variable is any characteristic whose value may change from one individual to another in a population, sample, or experiment. • CONFOUNDING VARIABLE: IS ONE THAT EFFECTS THE RESULTS OF DATA OutsideOF THE DESIGN OF THE SURVEY OR EXPERIMENT. When two different variables affect the response variable. • When the effects of two or more variables ________________ be determined confounding has occurred.

  41. Recall the Variable is any characteristic whose value may change from one individual to another in a population, sample, or experiment. • CONFOUNDING VARIABLE: IS ONE THAT EFFECTS THE RESULTS OF DATA OutsideOF THE DESIGN OF THE SURVEY OR EXPERIMENT. When two different variables affect the response variable. • When the effects of two or more variables __Can not___________ be determined confounding has occurred.

  42. When the effects of two or more variables can not be determined confounding has occurred. A effects the outcome of the response variable but is not part of the design of the experiment. They will often cause confounding

  43. When the effects of two or more variables can not be determined confounding has occurred. A _Lurking Variable_ effects the outcome of the response variable but is not part of the design of the experiment. They will often cause confounding • CONCEPT OF RANDOMNESS: ALL MEMBERS OF POPULATION HAVE AN CHANCE OF BEING SELECTED.

  44. When the effects of two or more variables can not be determined confounding has occurred. A _Lurking Variable_ effects the outcome of the response variable but is not part of the design of the experiment. They will often cause confounding. • CONCEPT OF RANDOMNESS: ALL MEMBERS OF POPULATION HAVE AN EQUAL CHANCE OF BEING SELECTED.

  45. CONCEPT OF RANDOMNESS: ALL MEMBERS OF POPULATION HAVE AN Equal CHANCE OF BEING SELECTED. • OBSERVATIONAL STUDY:OBSERVE AND MEASURE SPECIFIC CHARACTERISTICS, • BUT MODIFY

  46. CONCEPT OF RANDOMNESS: ALL MEMBERS OF POPULATION HAVE AN Equal CHANCE OF BEING SELECTED. • OBSERVATIONAL STUDY:OBSERVE AND MEASURE SPECIFIC CHARACTERISTICS, • BUT DO NOTMODIFY

  47. CONCEPT OF RANDOMNESS: ALL MEMBERS OF POPULATION HAVE AN Equal CHANCE OF BEING SELECTED. OBSERVATIONAL STUDY:OBSERVE AND MEASURE SPECIFIC CHARACTERISTICS, BUT DO NOTMODIFY Cross-sectional studies collect data from a specific point in time. Retrospective studies collect data from the past. Prospective studies collect data over time.

  48. OBSERVATIONAL STUDY:OBSERVE AND MEASURE SPECIFIC CHARACTERISTICS, BUT Do not modify. • Cross-sectional studies collect data from a specific point in time. • Retrospective studies collect data from the past. • Prospective studies collect data over time. • A FRAME IS THE OF ALL INDIVIDUALS IN THE POPULATION.

  49. Retrospective studies collect data from the past. • Prospective studies collect data over time. • A FRAME IS THE List OF ALL INDIVIDUALS IN THE POPULATION. • EXPERIMENT: TO APPLY SOME _ AND THEN OBSERVE THE EFFECTS

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