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# Statistics

### Vocabulary

Term | Definition |
---|---|

Statistics | the science of conducting studies to 1. collect, 2. organize, 3.summarize, 4.analyze, and 5. draw conclusions from data. |

How is statistics used in everyday life? (4 ways) | 1. Fields of human endeavor - sports, public health, and education. 2. Analyze results of a survey. 3. Tool in scientific research to make decisions based on controlled experiments. 4. Operations research, quality control estimation, and predictions |

Why do students study statistics? (3 reasons) | 1. To understand statistical studies. 2. To conduct research, design experiments, make predictions, and communicate results. 3. To become better consumers. |

What is Descriptive Statistics? | consists of the 1.collection, 2.organization, 3.summarization, and 4.presentation of data. |

What is Inferential Statistics? | consists of 1. generalizing from samples to populations, 2. performing estimations and hypothesis tests, 3. determining relationships among variables, and 4. making predictions. |

Variable | a characteristic or attribute that can assume different values. |

Data | the values the variables assume. |

Random Variables | variables whose values are determined by chance. |

Data Set | a collection of data values. |

Data Value (Datum) | each value of the data set. |

Probability | the chance of an event occurring. |

Population | all subjects that are being studied. |

Sample | a group of subjects selected from a population. |

Hypothesis Testing | a decision-making process for evaluating claims about a population based on information from samples. |

Qualitative Variables | Variables that can be placed into distinct characteristics (like a characteristic or attribute); NOT NUMBERS Examples: gender, color, religious preference, geographical location |

Quantitative Variable Discrete. | variables that assume values that can be counted Examples: # of children, # of students, # of calls received |

Quantitative Variable Continuous. | Variables that can assume an infinite number of values between any two specific values; they are obtained by measurement; often obtain fractions and decimals. Examples: weight measurement, length of time to answer a trivia question |

Nominal Measurements | Classifies data into mutually exclusive (non-overlapping) exhausting categories in which no order or ranking can be imposed on the data Examples: gender, zip code, eye color, nationality, marital status, religious affiliation |

Ordinal Measurements | Classifies data into categories that can be ranked, however, precise difference between the ranks do not exist; PRECISE MEASUREMENT DOES NOT EXIST Examples:ranking guest speakers, ranking floats, classifying a persons build, letter grades |

Interval Measurements | Ranks data and precise differences between units of measure do not exist, however, there is no meaningful (true) zero Examples: IQ tests, temperature, SAT scores |

Ratio Measurements | Possesses all the characteristics of interval measurements and there exists a true zero; true ratios exist when the same variable is measured on two different numbers of the population Examples: height, weight, area, time, salary, age |

Two purposes for collecting data. | 1. To describe situations or events 2. To help people make better decisions before acting |

Three ways to collect data. | 1. Surveys 2. Records 3. Observation |

Advantages/Disadvantages of Telephone Surveying | Adv. 1. Less costly 2. People can be more candid. 3. Not face to face Disadv. 1. Not everyone can be surveyed 2. May not be home 3. Unlisted & cellphones 4. Tone of interviewer may turn off person being called. |

Advantages/Disadvantages of Mailed Questionnaire | Adv. 1. Can cover wider geographical area 2. Less expensive 3. Responds can remain anonymous Disadv. 1. Low number of responses 2. Inappropriate answers on questions 3. May be hard to understand |

Advantages/Disadvantages to Personal Interviews | Adv. 1. Can obtain in depth responses Disadv. 1. Interviewers need to be trained. 2. More costly 3. Interviewer may be biased. 4. May not be a good sampling of people interviewed. |

Random Sampling | Selected by using chance methods or random numbers; numbering cards of generating random number by computer |

Systematic Sampling. | Obtained by numbering each subject of the population and then selecting every kth subject; need to be careful number the subjects. |

Stratified Sampling. | Obtained by dividing the population into groups (called strata) according to some characteristic important in the study, then get the sampling from each group |

Cluster Sampling. | Selected by dividing the population into intact groups (called clusters) that are representative of the population; some clusters are selected at random and all members of the selected clusters are the subjects; used when the population is very large. |

Independent Variable (Exploratory) | The variable that is being manipulated by the researcher. |

Dependent Variable (Outcome/Resultant) | The variable that is being studied to see if it changes due to the manipulation. |

Confounding Variable | A variable that influences the results of the dependent variable but cannot be separated from the independent variable. |

Hawthorne Effect | When the subject knows that they are participating purposely change their behavior in ways that if affects the results of the study. |

Control Group | the group that does not receive the treatment |

Treatment Group | the group that does not receive the treatment |

Margin of Error | When a random sample of size "n" is taken from a large population. + or - 1/ (square root of "n") |

Margin of Error Interval | percent of a sample + or - 1/(square root of "n") |

True Experimental Study | 1. Subjects should be assigned to groups randomly. 2. Treatments should be assigned to groups at random. |

Quasi-Experimental Study | When random assignments are not possible -- use an intact group. |

Observational Advantages (3): | 1. Occurs in natural setting. 2. Can be done in dangerous or unethical situations (suicide, rape, murder, etc.) 3. Can be done using variable that cannot be manipulated by the researcher. |

Observational Disadvantages (3): | 1. A definite cause and effect situation can't be determined since other factors have an effect on the results. 2. Can be expensive and time consuming. 3. May have inaccuracies in the measurements. |

Experimental Advantages (2): | 1. Researchers can decide how to select and group subjects. 2. Researchers can control and manipulate individual variable |

Experimental Disadvantages (3): | 1. May occur in unnatural settings (labs or classrooms) 2. Hawthorne Effect 3. Confounding variable |

Uses of Statistics (5) | 1. To describe data. 2. To compare two or more data sets. 3. To determine if variables are related. 4. To test hypothesis. 5. To make estimates about population variances. |

Misuses of Statistics (7) | 1. Suspect samples [too small, volunteer (optional poll), convenience sample] 2. Ambiguous Averages 3. Changing the Subject 4. Detached Statistics 5. Implied Connections 6. Misleading Graphs 7. Faulty Survey Questions |

Biased Question | a question worded in a way that a particular answer is favored over others. |

Unbiased Question | a question that is worded with no particular answer being favored. |

Sequential Sampling | Used in quality control - in which successive units are taken from the production line and sampled to ensure the product meets the standards |

Double Sampling | a large population is given a questionnaire to see who meets the requirements for the study. After reviewing the questionnaire a smaller population is defined and a sample is chosen from this population. |

Multistage Sampling | a sampling technique that uses a combination of sampling methods |

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ashtmcda