NCSU ST 311 Terms

Population

The entire group of items/individuals (units) that we want information about, about which inferences are to be made (ex: all NCSU undergrads)

Sample

The smaller group, the part of the population we actually examine in order to gather information.

Sample Size

The number of people in a sample (ex: 100 people selected from a list of all NCSU undergrads)

n

Notation used to denote sample size

Census

Special case when every unit in the population is measure or surveyed (ex: All NCSU undergrads)

Variable

The characteristic of the units that we want to learn about (ex: GPA of NCSU undergrads)

Parameter

a numerical summary of a variable for the entire population (ex: average GPA for all NCSU undergrads)

Statistic

a numerical summary of a variable for a sample (ex: average GPA for 100 students selected from all NCSU undergrads)

Sampling Frame

the list of units from which a sample is selected (ex: a list of all NCSU undergrads)

Voluntary Response Sample

Bad Sampling Method; only those people who volunteer to participate are included in the sample (ex: online polls)

Convenience Sample

Bad Sampling Method; most convenient (readily available) group is considered as the sample (asking people walking by)

Simple Random Sample (SRS)

Good Sampling Method; every different possible sample of the desired size has the same chance of being selected; requires sampling frame of everyone in the population (ex: Using random number generator to select 100 students from all NCSU undergrads)

Stratified Random Sample

Good Sampling Method; population is first divided into nonoverlapping groups, called Strata, and a simple random sample is selected from each group. Within a stratum, every person has the same chance of being selected; all groups are represented in the sample (ex: Dividing all NCSU undergrads into strata by year [Freshman, Sophomore, Junior, Senior], then using random number generator to selected 25 students from each strata)

Strata

nonoverlapping groups used in a stratified random sample

Cluster Sample

population is divided into nonoverlapping groups, called clusters, a simple random sample of clusters is selected, and all individuals in the selected clusters are included in the sample. Every cluster has the same chance of being selected. Some groups are represented in the sample. (ex: Dividing all NCSU undergrads into clusters by major [Biology, Chemistry, etc.], then using a random number generator to select clusters)

Clusters

nonoverlapping groups used in a Cluster sample

Systematic Sample

population is a list divided into consecutive segments. One individual is randomly selected from the first segment and the same position is selected from each of the remaining segments. (Select every kth unit from random starting point) (ex: Dividing all NCSU undergrads into 100 segments. Use random number generator to select a student from the first segment. Then select that same number from each segment)

Undercoverage

Tendency for a sample to differ from the corresponding population because the sampling frame excludes some parts of the population

Nonresponse bias

Tendency for a sample to differ from the corresponding population because a subset of the sample cannot be contacted or does not respond

Response bias

Tendency for a sample to differ from the corresponding population because participants respond differently from how they truly feel

Categorical variable

places a unit into one of several groups or categories
(ex: major, car color, letter grades)

Quantitative variable

takes numeric values for which arithmetic operations such as adding and averaging make sense (ex: height, age (in years), exam score (points)

Graphs to summarize categorical data

Pie charts and Bar Charts

Graphs to summarize quantitative data

Histograms, Dot Plots, and Box Plots

Distribution

overall pattern of how often the different possible values occur; drawn as a curve

Symmetric Distribution

No significant tail to either side

Right Skewed

Tail to the right

Left Skewed

Tail to the left

Uni-modal

One hump

Bi-modal

two humps

Multi-modal

3 or more humps

Outliers

Unusual points that are not consistent with the rest of the data

Range

Maximum - Minimum

Interquartile Range (IQR)

Q3 - Q1

How to find IQR

1. Order Data
2. Find median = Q2
3. Find middle value of both sides of median

Addition, Subtraction, Multiplication, and Division

affects measures of center (mean, median) or location (quartiles)

Multiplying and Dividing

Measures of spread (standard deviation, range, IQR)