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# Prob & Stats

### Chapter 1 & 14

Statistics The science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data.
How are statistics used in everyday life? 1. In fields of human endeavor - sports, public health & edu. 2. To analyze the results of a survey 3. As a tool in scientific research to make decisions based on controlled experiments. 4. Operations research, quality control estimation, and predictions
Reasons to study statistics. 1. To be able to understand statistical studies. 2. To be able to conduct research, design experiments, make predictions, and communicate results. 3. To become better consumers.
Variable A characteristic or attribute that can assume different values.
Data The values the variable assume
Random Variables Variable 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 Consists of all subjects that are being studied
Sample A group of subjects selected from a population
Descriptive Statistics Consists of the collection, organization, summarization, and presentation of data.
Inferential Statistics Consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables,and making predictions.
Quantitative Variables Numerical and can be ordered and ranked Ex: age, height, weight, body temp.
Continuous Variables Variables that can assume an infinite amount of values between any two specific values. (Usually obtained by measuring - fractions or decimals) Ex: time, distance
Find the boundaries: .43 sec .425 - .435 seconds
Nominal Level of Measurement Classifies data into mutually exclusive (non-overlapping) exhausting categories in which no order or ranking can be imposed on the data. Ex: gender, zip code, political party, marital status, eye color, nationality, subjects taught by professors
Ordinal Level of Measurement Classifies data into categories that can be ranked; however, precise differences between the ranks do exist. Ex: Ranking guest speakers (poor, good, excellent), letter grades (A, B, C, D, F), ranking floats (1st, 2nd, 3rd)
Interval Level of Measurement Ranks data and precise differences between units of measure do exist;however, there is no meaningful. Ex: IQ test, Temp. ( 0 F does not mean no- it is a temp), SAT scores
Ratio Level of Measurement Possesses all the characteristics of the interval measurement and there exists a true zero. Ex: Height, Weight, Area, Number of pounds lifted (200, 100 lbs- 2:1 ratio), Time, Salary, Age, Number of phone calls received
What are the two purposes of data collection? 1. To describe situations or events 2. To help people make better decisions before acting
3 Ways to Collect Data Surveys, Mailed Questionnaire, Personal Interview
Telephone Surveys Advantage-Less costly,people can be more candid, not face to face. Disadvantages- Not all people can be surveyed, may not be home,unlisted, or cell phones.
Mailed Questionnaire Advantages - can cover a wider geographic area, less expensive to conduct, respondents can remain anonymous. Disadvantages - low number of responses
Personal Interview Advantages- can obtain in-depth response. Disadvantages- Interviewers need to be trained, more costly, interviewer may be biased, may not be a good sampling of people interviewed.
Random Sampling A sampling technique where you randomly select a group of subjects for study from a larger group. Ex: numbering cards, generating a random number by the computer
Systematic Sampling A sampling technique where you take a random sample of the population by using every kth variable. Ex:
Stratified Sampling A sampling technique where you take samples from each stratum or sub-group of a population.
Cluster Sampling A sampling technique where the entire population is divided into groups, or clusters, and a random sample of these clusters are selected.
Sequential Sampling used in quality control--successive units taken form the production line and sampled to ensure the product meets the standards
Double Sampling reviewing the questionnaire a smaller population is defined and a sample is chosen from this population.
Things that make a survey question bad 1. Asking biased questions 2. Using confusing words 3. Asking double barreled questions 4. Using double negatives in a question 5. Ordering questions improperly
Qualitative Variables Variables that can be placed into distinct categories(characteristics not numbers) Ex: gender, color, religious preference, geographical location
Discrete Variables Variables that assume values that can be counted. Ex: # of children, # of students, # of calls received
Descriptive Statistics consists of the collection, organization, summarization, and presentation of data.
Inferential Statistics consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions.
Telephone Surveys: Advantages less costly, people can be more candid, not face to face
Telephone Surveys: Disadvantages not all people can be surveyed, may not be home, unlisted & cell phones, tone of interviewer may turn off person being called
Mailed Questionnaire: Advantages can cover a wider geographic area, less expensive to conduct, respondents can remain anonymous
Mailed Questionnaire: Disadvatages low number of responses, inappropriate answers on questions, may be hard to understand
Personal Interview: Advantages can obtain in-depth responses
Personal Interview: Disadvantages interviewers need to be trained, more costly, interviewer may be biased, may not be a good sampling of people being interviewed
Observation Study The researcher merely observes what is happening or what has happened in the past and tries to draw conclusions based on these observations Ex: age of motorcycle owners
Experimental Study The researcher manipulates one of the variables and tries to determine how the manipulation influences other variables Ex: types of instruction affects the number of sit-ups done
True experimental study 1. subjects should be assigned to the groups randomly 2. treatments should be assigned to the groups at random
Quasi- Experimental Study when random assignments are not possible- use an intact group Ex: in education, use certain schools or classrooms
Advantages of Experimental Studies 1. Researchers can decide how to select and group subjects 2. Researchers can control or manipulate individual variables
Disadvantages of Experimental Studies 1. May occur in unnatural studies (labs/classrooms) 2. Hawthorne Effect 3. Confounding Variable
Advantages of Observational Studies 1. occurs in a natural setting 2. can be done in dangerous or unethical situations (suicide, rape, murder, etc.) 3. can be done using variables that cannot be manipulated by the researcher Ex: drug users vs. non drug users, right-handed vs. left-handed
Disadvantages of Obsevational Studies 1. definite cause and effect situation cannot be determined since other factors have had effect on the results 2. can be expensive and time consuming 3. may have inaccuracies in the measurements Ex: records from the 1800's or before
Independent Variable ( explanatory variable) The one that is being manipulated by the researcher Ex: type of instruction
Dependent Variable (outcome variable, resultant variable) The variable that is being studies to see if it changes due to manipulation Ex: Number of sit-ups
Confounding Variable is one that influences the results of the dependent variable but cannot be separated from the independent variable Ex: subject on a special diet who also exercises, heredity
Hawthorne Effect The subject knows that they are participating purposely change their behavior in ways that it affects the results of the study
Control Group The group that does not receive the treatment Ex: no instructions about the sit-ups; called the placebo
Treatment Group The group that receives the specific treatment Ex: the group that gets the specific instruction about sit-ups
Margin of Error When a random sample of size n is taken from a large population, the margin of sampling error is +/- (1/square root of n)
Margin of Error Interval If p is a percent of a sample responding in a certain way, then the percent of the population that would respond that way is P +/- (1/ square root of n)
sequential sampling used in quality control- successive units taken from the production line and sampled to ensure the product meets the standards
double sampling A large pop. is given a questionnaire to see who meets the requirements for the study. After reviewing the questionnaire a smaller pop. is defined & a sample is chosen from this pop.
Created by: eknight