Stats 107 FINAL

individual/unit

the objects described by a set of data, may be people but also be may animals or things

variable

any characteristic of an individual, can take different values for different individuals

categorical variable

places an individual into one of several groups or categories

numerical/quantitative variables

takes numerical values for which arithmetic operations such as adding and averaging make sense.

population

in a statistical study is the entire group of individuals about which we want information

sample

part of the population from which we actually collect information and is used to draw conclusions about the whole

sample survey

survey some group of individuals by studying only some of its members, selected not because they are of special interest but because they represent the larger group

kind of observational study

response variable

a variable that measures an outcome or result of a study

observational study

observes individuals and measures variables of interest but does not intervene the responses. purpose is to describe some group or situation

census

a sample survey that attempts to include the entire population in the sample

experiment

deliberately imposes some treatment on individuals in order to observe their response. purpose is to study whether the treatment causes a change in the the response

biased

systematically favors certian outcomes

convenience sampling

selection of whichever individuals are easiest to reach

voluntary response sample

chooses itself by responding to general appeal. write-in or call-in opinion polls are examples of this

convenience sampling and voluntary response sample are often…

biased

simple random sampling (SRS)

of size “n” consists of “n” individuals from the population chosen in such a way that every set of “n” individuals has an equal chance to be the sample actually selected

a SRS gives…

each individual an equal chance to be chosen (avoiding bias0 and every possible sample an equal chance to be chosen

what are the different ways to obtain a simple random sample?

names in a hat, random integer generator, table of random digits

what are two steps to obtain a simple random sample?

1) assign a numerical label to every individual in the population

2) use random digits to select labels at random

parameter

a number that describes the population. it is a fixed number, but in practice we don’t know the actual value of this number because we cannot access the entire population

statistic

a number that describes a sample. the value can be determined and is known once we have taken a sample, but its value can change from sample to sample. often used to estimate an unknown parameter

variability

describes how the values of the sample statistic will vary when we take many samples

what does large variabilty mean?

the result of the sampling is not repeatable

what does a good sampling method have?

both small bias and small variability

to reduce bias…

use random sampling

to reduce the variability of an SRS…

use a larger sample

large samples…

almost always give an estimate that is close to the truth

margin of error

represents the natural sampling variability

to cut the margin of error in half…

we must use a sample four times as large

confidence statement

has two parts: a margin of error and a level of confidence. the margin of error says how close the sample statistic lies to the population parameter. the level of confidence says what percentage of all possible samples satisfy the margin of error

the conclusion of a confidence statement…

always applies to the population, not to the sample

our conclusion about the population is…

never completely certain

a sample survey can choose…

to use a confidence level other than 95%

a smaller margin of error with the same confidence?

take a larger sample

the variability of a statistic from a random sample is essentially…

unaffected by the size of the population as long as the population is at least 20 times larger than the sample

confidence statement

to say how accurate our conclusions about the population are

sampling errors

errors caused by the act of taking a sample. they cause sample results to be different from the results of a census of the population

random sampling error

the variation due to chance in choosing a random sample. the margin of error in a confidence statement includes only random sampling error

nonsampling errors

errors not related to the act of selecting a sample from the population. they can be present even in a census

undercoverage

occurs when some groups in the population have no chance of being included in the sample

sampling frame

list of individuals from which we will draw our sample

nonresponse

the failure to obtain data from an individual selected for a sample. most happens because subjects can’t be contacted or because some subjects who are contacted refuse to cooperate

what is the most serious problem facing sample surveys?

nonresponse

processing errors

mistakes in mechanical tasks such as doing arithmetic or entering responses into a computer

multiple inclusions

occur if some population members appear multiple times in the sampling frame so that they have a higher chance of being sampled

erroneous inclusions

can occur if the frame includes units that are not in the population of interest so that the invalid units have a chance of being in the sample

probability sample

a sample chosen by chance. we must know what samples are possible and what chance, or probability, each possible sample has

frame errors

can occur because the sampling frame is not an accurate representation of the population

response errors

incorrect answers by respondents

what are examples of nonsampling errors?

processing errors, response errors,

explanatory variable

a variable that we think explains or causes changes in the response variable

subjects

individuals studied in an experiment

treatment

any specific experimental condition applied to the subjects

lurking variable

a variable that has an important effect on the relationship among the variables in a study but is not one of the explanatory variables

confounded

when two variables’ effects on a response cannot be distinguished from each other. may be explanatory variables or lurking variables

placebo

dummy treatment with no active ingredients

double-blind

an experiment in which neither the subjects nor the physicians recording the symptoms know which treatment was received

randomized comparitive experiment

one that compares just two treatments

control group

placebo group, comparing the treatment and control group allows us to control the effects of lurking variables

what are the basic principles of statistical design of experiments?

control the effects of lurking variables, randomize, and use enough subjects

statistically significant

an observed effect of a size that would rarely occur by chance

a good comparative study…

measures and adjusts for confounding variables

discrete data

data that is counted

continuous data

unit of measure

qualitative

descriptive

completely randomized experimental design

all the experimental subjects are allocated at random among all treatments

matched pairs design

compares just two treatment. choose pair of subjects that are as closely matched as possible. assign one of the treatments to each subject in a pair by tossing a coin or reading odd and even digits

block

group of experimental subjects that are known before the experiment to be similar in some way that is expected to affect the response to the treatments

block design

the random assignment of subjects to treatments is carried out separately within each block

Hawthorne Effect

the tendency of some people to work harder and perform better when they are participants in an experiment. individuals may change their behavior due to the attention they are receiving from researchers rather than because of any manipulation of independent variables

what is the most common weaknesss in experiments?

we can’t generalize the conclusions widely

measure

a property of a person or thing when we assign a value to represent the property

instrument

used to make a measurement

units

used to record the measurements

valid

measure of property if it is relevant or appropriate as a representation of that property

rate

(a fraction, proportion, or percentage) at which something occurs is a more valid measure than a simple count of occurrences

predictive validity

it can be used to predict success on tasks that are related to the property measured

reliable

if the random error is small

random error

repeated measurements on the same individual give different results

a reliable measurement process has what variance?

a small variance

the average of several repeated measurements of the same individual is more or less reliable?

more reliable (less variable) than a single measurement

what to look for when determining if the numbers make sense?

missing information, inconsistencies, incorrect arithmetic, implausible, too regular or agree too well, hidden agenda

distribution of a variable

tells us what values it takes and how often it takes these values

pie chart

show how a whole is divided into parts

bar graph

all bars are the same width and do not touch each other

can also compare the size of the categories that are not parts of one whole

what does the height of the bars in a bar graph represent?

amount of people in that category

pie charts and bar graphs show the distribution of?

categorical variables

pictogram

a bar graph in which pictures replace the bars

line graph

used to display how a quantitative variable changes over time

time on x-axis

trend

a long-term upward or downward movement over time

seasonal variation

a pattern that repeats itself at known regular intervals of time

seasonally adjusted

the expected seasonal variation is removed before the data are published

linear correlation coefficient

r, it measures the strength and direction of linear relationship between x and y

R squared

coefficient of determination, measures the explanatory ability of the line of best fit

skewed right

bump is on the left and it tapers off to the right

skewed left

bump is on the right and it tapers off to the left

symmetrical

peak in the middle

uniform

bars are the same height

to describe the overall pattern of a distribution:

describe the center and the variability and describe the shape of the histogram with a few words

histogram

bars touch each other, quantitative variables