Introduction To Statistics Chapter 1
Levels of Measurement
-Nominal -Ordinal -Interval -Ratio
Data Two Main Sources of Data
-Observational Studies -Experiment
Sampling Methods
-Systematic Sampling -Stratified Sampling -Cluster Sampling
Variables
x and y are variables that contain information about the same characteristic of each individual. Variables are measured and all measurements are variable. Even if an experiment is exactly repeated the results will differ slightly or be variable.
Placebo
A harmless, unmedicated treatment, that is made to look like the real treatment.
Sample
A sub collection of members selected from a population is a subset, or part, of a population. Ex. Our Stats Class Note: Statistic and Sample
Experiment
Applies some treatment and then observes its effect on the subjects.
Experiment
Apply some treatment and then observe its effects on subjects.
Ratio Level of Measurment
Differences and a natural starting point.
Interval Level of Measurment
Differences but no natural starting point ex. years 1000, 2000, 1776, and 1492
Cluster Sampling
Divides the population into sections (or clusters), randomly selects some of those clusters, and samples all members in the selected clusters.
Distribution
Gives the possible values of a variable or relative frequency of the variable but context must be know in order to interpret
Experimental units
In many cases, subjects (sometimes called experimental units) in the control group are given a placebo or treatment.
Randomization
Is a process of randomly assigning subjects to different treatment groups. A technique that can be used to obtain unbiased results.
Blinding
Is a technique where the subjects do not know whether they are receiving a treatment or a placebo.
Observational Studies
Method of observing and measuring specific characteristics without attempting to modify the subjects being studied
Double-blind experiment
Neither the experimenter nor the subjects know if the subjects are receiving a treatment or a placebo. The experimenter is informed after all the data has been collected this type of experimental design is preferred by researchers.
Observational Studies
Observe and measure specific characteristics without attempting to modify the subjects being studied. Three types of observational studies: -Cross Sectional Study -Retrospective Study -Prospective Study
Placebo effect
Occurs when a subject reacts favorably to a placebo when in fact the subject has been given no medicated treatment at all.
Confounding variable
Occurs when an experimenter cannot tell the difference between the effects of different factors on a variable.
Nominal Level of Measurement
Qualitative Only. Categories only, should not be used in calculations. ex. eye color (blue, brown,hazel); movie production companies (disney, mgm, universal)
Ordinal Level of Measurment
Qualitative or Quantitative only. Categories with some order, usually should not be used for calculations. Used to provide information about relative comparisons but not the magnitude of the differences. ex. course grades A,B,C,D, or F
Data Table
Records the same information about a group of individuals in a structured layout
Simple Random Sample
Samples in a way that of η subjects selected, every possible sample of the same size η has the same chance of being chosen
Good Samples
Samples that produce reliable non bias results. Some examples of these are: -Random Samples -Simple Random Samples
Bad Samples
Samples that produce results that are not very reliable and lead to bias. Some examples of these types of samples are: -Reported Results -Convenience Sample -Voluntary Response Sample
Systematic Sampling
Selects some starting point and then selects every κth element in the population. ex. Selecting every 3rd student
Stratified Sampling
Subdivides the population into at least two different subgroups that share the same characteristics , then draws a sample from each subgroup (or strata) reducing variation in results compared to selecting a random sample from the general population. ex. gender, age bracket, political parties
Population
The collection of ALL outcomes, responses, measurements, or counts data that are being considered and that of interest. ex. All students at North Island College
Sampling Method
The system in which the data was obtained. ie voluntary or self-selected response? Or simple random sample?
Data
There are two types of data, Quantitative (or numerical) and Categorical (or qualitative)
Random Sample
Uses members from the population that are selecting in such a way that each individual member in the population has an equal chance of being selected
Retrospective Study
When data is collected from the past by going back in time through records and interviews
Prospective Study
When data is collected in the future from groups sharing common factors.
Cross Sectional Study
When data is observed, measured, and collected at one point in time.
Convenience Sample
When results that are easy to get are used rather than conducting a simple random sample
Reported Results Sample
When subjects are asked to report results rather than the surveyor taking measurements themselves
Voluntary Response Samples
When survey is open to public and subjects decided whether to respond or not
Parameter
a numerical description of a POPULATION characteristics. Numerical measurement describing some characteristic of a population ex. The average height of North Island College Students Note: Parameter and Population
Statistic
a statistic is: A numerical description of a SAMPLE characteristics. ex. average height of statistic students attending North Island College Statistic: is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions.
Qualitative data
consist of attributes, labels, or nonnumerical entries. the NAMES are nonnummerical entries. Test: Name each level of measurement for which data can be qualitative? Nominal Ordinal
Data
consists of information coming from observations, counts, measurements, or responses.
Categorical data
consists of names or labels that are not numbers representing counts or measurements such as shirt numbers on athletes which are substitutes for names
Quantitative data
consists of numbers representing counts or measurements. Always has a unit of measurement like age counts in years and salary counts in dollars. ex. suggested retail prices are numerical entries. There are two types of quantitative data -Discrete Data -Continuous Data
Survey
is an investigation of one or more characteristics of a population.
Descriptive Statistics
is the branch of statistics that involves all the organization, summarization, and display of data.
Inferential Statistics
is the branch of statistics that involves using a sample to draw conclusions about a population. A basic tool in the study of inferential statistics is probability.
Context
knowing who, what, when, where something was measured or observed and the purpose of the study, as well as the sampling method.
Control group
part of the population may be used as a control group, in which No treatment is applied.
Continuous Data
results from infinitely many possible quantitative values, where the collection of values is not countable. Ex: The heights of students in a math class
Discrete Data
results when the data values are quantitative and the number of values is finite or "countable" *Note If there are infinitely many values but the collection of values is countable and it is possible to count them individually, the data is still discrete (such as the number of tosses of a coin before getting tails).
Simulation
the use of a mathematical or physical model to reproduce the conditions of a situation or process. Collecting data often involves the use of computers. Simulations allow you to study situations that are impractical or even dangerous to create in real life, save time, and money.
Correlation does not equal Causation
when one variable seems linked or correlated to another variable we cannot conclude that therefore change in one variable will cause change in the other.
