Statistics Chapter 1

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Statistics

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The sciences of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions. In addition, statistics is about providing a measure of confidence.

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Population

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entire group to be studies

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Individual

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a person or object that is a member of the population being studied

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Sample

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a subset of the population being studied.

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statistic

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a numerical summary of a sample

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descriptive statistics

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organizing and summarizing data

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inferential statistics

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uses methods that take a result from a sample and extend it to the population, and measure the reliability of the result

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paramater

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a numerical summary of the population

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The process of statistics

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1. Identify the research objective
2. Collect the data needed to answer the question
3. Describe the data
4. Perform inference

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qualitative or categorical variables

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allow for classification of individuals based on some attribute or characteristic.

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Quantitative variables

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provide numerical measures of individuals

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discrete variable

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a quantitive variable that has neither a finite number of possible values or a countable number of possible values. The term countable means that the value results from counting such as 0,1,2,3 and so on. A discrete variable can not take on every possible value between 2 possible values. E.g. people

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A continuous variable

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is a quantitive variable that has an infinite number of possible values that are not countable.

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nominal level of measurement

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a variable is at the nominal level of measurement if the values of the variable name, label, or categorize. In addition, the naming scheme does not allow for the values of the variable to be arranged or ranked in specific order. e.g. gender

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interval level of measurement

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A variable is at the interval level of measurement if it has the properties of the ordinal level of measurement and the differences in the values of the variable have meaning. A value of zero does not mean the absence of quantity. Arithmetic operations such addition and subtraction can be performed on values of this variable. e.g. temperature. (0F does not mean an absence of heat.)

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ratio level of measurement

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A variable is at the ratio level of measurement if it has the properties of the interval level of measurement and the ratios of the values of the variable have meaning. A value of zero means the absence of quantity. Arithmetic operation such as multiplication and division can be performed on the values of this variable. e.g. # of days someone studied.

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ordinal level of measurement

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if it has properties of the nominal level of measurement, however the naming scheme allows for the values of the variable to be arranged in ranked and specific order. e.g. grades A, B, C

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observational study

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measures the response variable without attempting to influence the value of either the response or the explanatory variables. That is, in an observational study, the research observes the behavior of the individuals without trying to influence the outcome of the study.

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designed experiment

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if a researcher assigns the individuals to a study to a certain group, intentionally changes the value of the explanatory variable, and then records the value of the response variable for each group the study is a designed experiment.

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confounding

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occurs when the effects of two or more explanatory variables are not separated. Therefore, any relation that may exist between a explanatory variable and the response variable may be due to some other variable or variables not accounted for in the study.

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lurking variable

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an explanatory variable that was not considered in a study, but that affects the value of the response variable in the study. In addition, lurking variables are typically related to explanatory variables considered in the study.

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3 types of observational studies

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Cross-sectional- collect info about individuals in a short amount of time.
Case control- are retrospective
Cohort Studies- observed over a long period of time. prospective. most powerful observational studies

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census

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a list of all individuals in a population with certain characteristics of each individual

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prospective study

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collects data over time

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response variable

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is the variable of interest to be measured in the study. The value of the response variable is affected by the explanatory variable.

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Random sampling

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the process of using chance to select individuals from a population to be included in the sample.

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simple random sampling

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a sample size of n from a population of N is obtained through simple random sampling if every possible sample of n has an equally likely chance of occurring.

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frame

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list of individuals in the population

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sample with replacement

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puts the person back in the population so there is a chance they will be picked a second time. Sample without replacement is more common

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seed

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the initial point for the generator to start creating random numbers

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stratified sampling

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provides more information about the population for less cost than simple random sampling.

obtained by separating the population in non overlapping groups called strata and then obtaining a simple random sample from each stratum. The individuals within each stratum should be homogenous or similar in some way. It can allow fewer individuals to be surveyed while obtaining the same or more info

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systematic sample

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Does not need a frame. It is obtained by selecting every kth individual in the population. The individual selected corresponds to a random number between 1 and k.
e.g. k=8th then pick between 1 and 8, say 5. So 5 would be sampled then every 8... 13, 21 etc.

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cluster sampling

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obtained by selecting all individuals within a randomly selected collection of group of individuals. e.g. sampling all of a random 10 classes in a school

if the cluster is heterogenous you want fewer clusters with more individuals in each cluster.

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convenience sample

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a sample which the individuals are obtained and not based on randomness.

e.g. people with clipboards at the mall
the most common type is voluntary response

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3 sources of bias

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sampling bias- tends to favor one part of the population over the other, also results due to undercoverage of a certain part of the population
nonresponse bias- occurs when those that don't respond to the survey have different opinions than those who do respond.
response bias- exists when the answers on the survey do not reflect the true feelings of the respondent. It can happen in a number of ways.

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Ways response bias occurs

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interviewer error- e.g. car dealer ship stating 90% like them
misrepresented answers - e.g. salaries inflated
wording of questions- must be balanced with yes/no stated
ordering of questions or words-
data entry error

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non sampling errors

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result from undercoverage, nonresponse bias, response bias, or data entry error. Such errors could also be present in a complete census of the population.

Sampling error results from using a sample to estimate information about a population.

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experiment

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a controlled study conducted to determine the effect varying one or more explanatory variables or factors has on a response variable. Any combination of the values of the factors is called a treatment.

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control group

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serves as a baseline treatment that can be used to compare to other treatments.

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blinding

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refers to nondisclosure of the treatment an experiment unit is receiving. there are 2 types single and double blinding
single blind- the subject doesn't know
double blind- neither the subject nor the researcher knows.

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a completely randomized design

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one in which each experimental unit is randomly assigned a treatment

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matched-pairs design

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one matched individual will receive one treatment and the other receives a different treatment. The matched pair is randomly assigned to the treatment using a coin flip or random-number generator. One common type of matched pair design is to measure before and after and the individual is matched against itself. Aka before-after or pretest-posttest experiments

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blocking

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grouping together similar (homogenous) experimental units within each group to a treatment is called blocking. e.g. the soccer scrimmage with 8,9,&10 year olds blocked by age

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confounding

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confounding occurs when the effect of two factors (explanatory variables) on the response cannot be distinguished.

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randomized block design

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used when the experiment units are divided into homogeneous groups called blocks. Within each block, the experimental units are randomly assigned to treatments.

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replication

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is using treatments on many experimental units. using more than one experimental unit ensures the effect of a treatment is not due to some characteristic in a single experimental unit.

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inferential statistics

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a process in which generalizations about the population are made on the basis of results obtained from a sample.