Applied Statistics - Midterms

statistics

the science of collecting, organizing, analyzing, interpreting, and presenting data

variable

a characteristic or attribute that can assume different values

data

- values (measurements or observations that the variables can assume

- consists of information coming from observations, counts, measurements, or responses

descriptive and inferential

two types of statistics

descriptive statistics

describes features in a data set; does not allow us to make any conclusions beyond the given data

inferential statistics

making inferences or conclusions about data; determining relationship among variables and makes predictions

population (N)

entire collection of objects/outcomes which data are collected.

physical population

well defined population, often finite and available at the time the sample is collected

conceptual population

population consisting all the values that might possibly have been observed from a population

sample (n)

a subset of the population containing the observed objects or outcomes of resulting data

summary measure

single numeric feature which describes a particular feature of the data

statistic (from sample data)

parameter (from population data)

types of summary measure

qualitative variables

variables that can be placed into distinct categories, according to some characteristic or attribute

quantitative variables

variables that can be counted or measured

dependent variables

The outcome factor; the variable that may change in response to manipulations of the independent variable.

independent variable

The experimental factor that is manipulated; the variable whose effect is being studied.

nominal scale

a scale in which objects or individuals are assigned to categories that have no numerical properties

e.g. gender, nationality, civil status, student number

ordinal scale

a scale of measurement in which the measurement categories form a rank order along a continuum

e.g. scale ratings, education level, economic status

interval scale

A quantitative measurement scale that has no "true zero," and in which the numerals represent equal intervals (distances) between levels

e.g. temperature, scores, hours, IQ level, years

ratio scale

a quantitative scale of measurement in which the numerals have equal intervals and the value of zero truly means "nothing"; starts from absolute or true zero point

e.g. height, weight, area

primary

types of data according to nature of collection

survey study

systematic method of gathering information from the characteristics of a population

direct / interview method

researcher has direct contact with interviewee; asks questions to obtain needed information

indirect / questionnaire method

researcher distributes questionnaire to respondents and expect them to answer the questions

registration method

method of collecting data gathered by laws (e.g. birth and death rates, number of registered voters)

retrospective study

studies primary data collected by another source

observational study

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

experimental design

used to find out cause and effect relationships; often used by scientists

simulation study

process of collecting data from a simulation, which is a computer model of a system that mimics its behavior

observation unit

basic unit of observation; object which a measurement is taken

target population

complete collection of observations we want to study

sampled population

the collection of all possible observation units that might have been chosen in a sample; the population from which the sample was taken

sampling unit

unit that can be selected for a sample

sampling frame

a list of sampling units in the population from which a sample may be selected

selection bias

occurs when some part of the target population is not in the sampled population; when some population units are sampled at a different rate than intended by the investigator

measurement error

when a response in the survey differs from the true value; happens when people lie / forget / give different answers / impress the interviewer / misinterpret the question

sampling error

error that results from taking one sample instead of examining the whole population

non-sample error

errors that cannot be attributed to the sample-to-sample variability; examples include selection bias and measurement error

simple random sample

systematic random sample

stratified random sample

cluster sample

types of simple probability samples

simple random sampling

every member/unit of the population has an equal probability of being selected for the sample

simple random sampling with replacement

one unit is randomly selected from the population to be the first sampled unit, with probability 1/N

simple random sampling without replacement

every possible subset of n distinct units in the population has the same probability of being selected as the sample, with probability n/N

Yamane or Slovin's formula

use this formula in simple random sampling technique if the population is known and finite

n = N/1+Ne^2

n - sample size; N - population size, e - margin of error (percentage)

Yamane or Slovin's formula

Cochran's Sample Size Formula

use this formula in simple random sampling technique if the population size is unknown but infinite

n = p(1-p)z^2 / e^2

n - sample size, p - population proportion, e - acceptable margin of error, z - z-score at significance level

Cochran's Sample Size Formula

90%: z = 1.645

95%: z = 1.96

99%: z = 2.576

z-score at confidence level

systematic sampling

sampling technique: select some starting point and then select every kth element in the population

stratified random sampling

a random sampling technique in which the researcher identifies particular demographic categories of interest (called "strata") and then randomly selects individuals within each category.

n_sample = n * (stratum / total)

n - computed sample size

(always round up the strata size)

stratified random sampling formula

cluster sampling

clusters of participants within the population of interest are selected at random, followed by data collection from all individuals in each cluster.

non-probability sampling

method of selecting sampling units from a target population using a subjective or non-random method

convenience sampling

choosing individuals who are easiest to reach (e.g. interviewing people passing by)

purposive sampling

researchers deliberately choose qualified participants to take the study

quota sampling

based on certain quotas or predetermined criteria; forces the inclusion of members of different subpopulations

snowball sampling

selection of participants through referrals from earlier participants; used if the population of interest is hard to find (people with certain disabilities, victims of specific crimes, drug users)

30 to 500

30 for each category

preferred sample size for most research

primary data

data collected specifically for a desired analysis (e.g. surveys)

secondary data

data that is already collected and are available for statistical analysis

raw data

information obtained by observing values of a variable

discrete data

data obtained by observing values of a qualitative variable

continuous data

data obtained by observing values of a qualitative variable

ungrouped data

data that are not organized, or could only be numerically organized

grouped data

data that are organized and arranged into different classes or categories

tabular, textual, graphical

methods of presenting data

frequency distribution

organization of raw data in table form, using classes and frequencies

frequency distribution table (FDT)

A statistical table showing the frequency or number of observations contained in each of the defined classes or categories

relative frequency

obtained by dividing frequency by the sum of all frequencies; expressed as percentages

class limit

endpoints of a class interval

class boundaries

the numbers used to separate the classes so that there are no gaps in the frequency distribution; ends in .5

lower limit - 0.5

lower boundary

upper limit + 0.5

upper boundary

class width (i)

difference between boundaries for any class

class mark

midpoint of a class interval