STAT 201: CH 1

statistics

study of how best to collect, analyze, interpret, present and draw conclusions from data

data

any collection of numbers, characters, images, or other itens that provide info about something

descriptive statistics aka exploratory data analysis (EDA)

• organizing data

• summarizing data

• presenting data in an informative way

inferential statistics

• determining something about the group of interest (population) based on a sample

• methods for making decisions/predictions and drawing conclusions about population

objectives of statistical analysis

1. how best can we collect data?

2. how should we explore/present data?

3. what can we infer from the analysis?

4. how to quantify and explain the variability?

population

the entire group of interest

sample

part of the population selected to draw conclusions abou tthe entire population

individual (subject)

a person or any specific object in a population

variable

any characteristic of an individual

• can take different values for different individuals

• what do we ask each individual?

• qualitative or quantitative

qualitative (categorical) variable

• are you a sport fan

• favorite ice cream flavor

• year of school

quantitative variable

• how much do you spend daily

• how many pets do you have

• how many classes are you taking

proportions and percentages

summarize categorical/qualitative variables

means and medians

preferred measure of center of the distribution for quantitative

observational study

observes individuals and measures variables of interest but does not attempt to influence the values of the variables

• purpose is to describe some group or situation

• ex: samplings and surveys

why sample?

• difficult to find entire population

• limited resources

• measurements that require destroying the item

census

official count or survey of a population, typically recording various details of individuals; difficult to organize

samples are often used

to make inferences about the population, how you draw it will affect accuracy

chance error/sampling error

random samples can vary from what is expected, in any direction

• occurs when a sample is drawn from a population deviates from true population

• ex: sample too small for representation

bias or systematic error

systematic error in one direction

• ex: sample taken from members of costco when looking for a representative sample of cstat population

sampling frame

list from which the sample is drawn

representative sample

have the same characteristics as the population

convenience sample

individuals who are easily accessible are more likely to be included in the sample; will not be representative; not random

quota sample

first specify your desired breakdown of various subgroups, then reach those targets however you can

selection bias

systematically excluding/favoring particular groups

• avoid: examine sampling frame and the method of sampling

response bias

people don’t always respond truthfully

• avoid: examine nature of questions and method of surveying

nonresponse bias

people don’t always respond

• people decide to take part in the study (self selected)

• avoid: keep surveys short and be persistent

• people who don’t respond aren’t like the people who do

random/probability sample

• reduce bias

• estimate the bias and chance error

• quantify the uncertainty

for sample to be random:

• must be able to provide the chance that any specified set of individuals will be in the sample

• all ind in the pop do not need to have the same chance of being selected

• you will still be able to measure the errors because you know all the probabilities

• not all probability samples are necessarily good

sampling with replacement

once a member of the population is selected, that member is returned to the population for the selection of the next individual

sampling without replacement

member of the population may be chosen only once; not returned to population before next selection

if population is huge compared to sample

random sampling with and without replacement are pretty much the same

probabilities of sampling with replacement

much easier to compute

simple random sampling (SRS)

• every member in population has equal chance of being selected in sample; sample selected from list of every unit in population (often difficult)

• variation in samples: two or more samples form the same population, taken randomly, and having close to the same characteristics of the population will likely be diff from each other

systemic random sampling

list if members in population, pick random starting point, select every kth member of population

stratified sampling

• split population into like groups (strata)

• within each strata do random sampling

• good for making sure certain members of pop are in sample

cluster sampling

• split pop in different clusters (normally by proximity)

• perform simple random sample to select clusters

• within each cluster, sample every member in the cluster

• often used because it is cheaper and easier

non sampling errors

self funded samples: performed to support a certain claim

misleading use of data

in an observational study

we observe a population without applying treatment

in a randomized experiment

we randomly assign the subjects in the study to the treatment

response/dependent variable

measures outcome of study

explanatory/independent variable

may explain or influence changes in a response variable

lurking/confounding variable

not among the explanatory or response variables and is still associated with both explanatory and response variables

why not always use observational studies

cannot conclude cause-effect relationship or causal relationship

subjects/experimental units

individuals studied in an experiment, particularly when they are people

factors

explanatory variables in an experiment

treatment

any specific experimental condition applied to the subjects; if experiment has more than one factor, a treatment is a combination of specific values of each factor

the purpose of an experiment

to investigate a causal relationship between variables

how can we prove that the explanatory variable is causing a change in the response variable?

necessary to isolate the effect of the explanatory variable → randomized experiment

to counter power of suggestion

researchers set aside one treatment group as control group

control group

meant to serve as baseline with which the experimental group is compared; placebo provided

placebo

control treatment that is fake but otherwise indistinguishable from experimental treatment group

placebo effect

improvement in health due not to any treatment but only to the patient/doctor’s belief that he/she will improve

randomized comparative experiment

experiment that uses both comparison of two or more treatments and chance (random) assignment of subjects to treatments

the logic of randomized comparative experiment depends on

ability to treat all the subjects identically in every way except the actual treatments being compared

blinding

preserves power of suggestion

single: subjects don’t know who is receiving real treatment

double: researchers and subjects don’t know (gold standard); necessary when investigator evaluates experimental outcome

blocking

arranging of experimental units in groups (blocks) that are similar to one another; if variable could influence response, should block it