-
Data
- Consist of information coming from
- observations, counts, measurements, or responses. ex “People who eat three daily servings of whole grains have been
- shown to reduce their risk of…stroke by 37%.”
-
Statistics
- The
- science of collecting, organizing, analyzing, and interpreting data in order to
- make decisions.
-
Data Sets
- Population
- The collection of all outcomes, responses,
- measurements, or counts that are of interest.
- Sample
A subset of the population.
-
Sample
A subset of the population.
-
Population
- The collection of all outcomes, responses,
- measurements, or counts that are of interest.
-
Parameter
- A number
- that describes a
population characteristic. - Average age of all people in the United States
-
Statistic
- A number
- that describes a
sample- characteristic.
- Average age of people
- from a sample of three states
-
Branches of Statistics
Descriptive Statistics Inferential Statistics
-
Descriptive Statistics
- Involves
- organizing, summarizing, and displaying data.
- e.g. Tables, charts, averages
-
Inferential Statistics
Involves using sample data to draw conclusions about a population.
-
-
Qualitative Data
- Consists
- of attributes, labels, or
nonnumerical entries.
-
Quantitative data
Numerical measurements or counts
-
Designing a Statistical Study
- Identify
- the variable(s) of interest (the focus) and the population of the study.
- Develop a
- detailed plan for collecting data. If you use a sample, make sure the sample is
- representative of the population.
- Collect
- the data.
- Describe
- the data using descriptive statistics techniques.
- Interpret
- the data and make decisions about the population using inferential statistics.
- Identify
- any possible errors.
-
Observational study
- •A
- researcher observes and measures characteristics of interest of part of a
- population.
- •Researchers
- observed and recorded the mouthing behavior on nonfood objects of children up
- to three years old.
(Source: Pediatric- Magazine)
-
Experiment
- •A
- treatment is applied to part of a population and responses are observed.
-
Simulation
- •Uses a
- mathematical or physical model to reproduce the conditions of a situation or
- process.
- •Often
- involves the use of computers.
- •Automobile
- manufacturers use simulations with dummies to study the effects of crashes on
- humans.
-
Control
- for effects other than the one being
- measured.
-
•Confounding variables
- §Occurs
- when an experimenter cannot tell the difference between the effects of
- different factors on a variable.
- §A coffee
- shop owner remodels her shop at the same time a nearby mall has its grand
- opening. If business at the coffee shop increases, it cannot be determined
- whether it is because of the remodeling or the new mall.
-
•Placebo effect
- §A subject
- reacts favorably to a placebo when in fact he or she has been given no medical
- treatment at all.
- §Blinding is a technique where the subject does
- not know whether he or she is receiving a treatment or a placebo.
- §Double-blind experiment neither the subject nor the
- experimenter knows if the subject is receiving a treatment or a placebo.
-
Simple Random Sample
- Every
- possible sample of the same size has the same chance of being selected.
-
Stratified Sample
- •Divide a
- population into groups (strata) and select a random sample from each group.
-
Cluster Sample
- •Divide
- the population into groups (clusters) and select all of the members in one or
- more, but not all, of the clusters.
-
Systematic Sample
- •Choose a
- starting value at random. Then choose every
kth member of the population.
-
nominal level of measurement
- A
- variable is at the
nominal level of measurement if the- values of the variable name, label, or categorize. In addition, the naming scheme does not allow
- for the values of the variable to be arranged in a ranked, or specific, order.
-
ordinal level of measurement
- A
- variable is at the
ordinal level of measurement if it- has the properties of the nominal level of measurement and the naming scheme
- allows for the values of the variable to be arranged in a ranked, or specific,
- order.
-
interval level of measurement
- A
- variable is at the
interval level of measurement if it- has the properties of the ordinal level of measurement and the differences in
- the values of the variable have meaning. A value of zero in the interval level of measurement does not mean the
- absence of the quantity. Arithmetic
- operations such as addition and subtraction can be performed on values of the
- variable.
-
ratio level of measurement
- A
- variable is at the
ratio level of measurement if it- has the properties of the interval level of measurement and the ratios of the
- values of the variable have meaning. A
- value of zero in the ratio level of measurement means the absence of the
- quantity. Arithmetic operations such as
- multiplication and division can be performed on the values of the variable.
-
Confounding
- in a study occurs when the effects of two or more
- explanatory variables are not separated. Therefore, any relation that may exist between an explanatory variable
- and the response variable may be due to some other variable or variables not
- accounted for in the study.
-
lurking variable
- A lurking variable is an explanatory
- variable that was not considered in a study, but that affect the value of the
- response variable in the study. In
- addition, lurking variables are typically related to any explanatory variables
- considered in the study.
-
Cross-sectional
Studies
- Observational studies that collect information about
- individuals at a specific point in time, or over a very short period of time.
-
Case-control Studies
- These studies are retrospective,
- meaning that they require individuals to look back in time or require the
- researcher to look at existing records. In case-control studies, individuals that have certain characteristics
- are matched with those that do not.
-
Cohort Studies
- A cohort study first identifies a group of individuals
- to participate in the study (cohort). The cohort is then observed over a period of time. Over this time
- period, characteristics about the individuals are recorded. Because the data is collected over time,
- cohort studies are
prospective.
-
census
- A census is a
- list of all individuals in a population along with certain characteristics of
- each individual.
-
Random sampling
- is the process of using chance to select individuals
- from a population to be included in the sample.
-
simple random sampling
- A sample of size n from a
- population of size
N is obtained through simple random sampling if every possible- sample of size
n has an equally- likely chance of occurring. The sample
- is then called a
simple random sample.
-
The 110th Congress of the United States had 435 members
in the House of Representatives. Explain how to conduct a simple random sample
of 5 members to attend a Presidential luncheon.
Then obtain the sample.
Put the members in alphabetical order. Number the members from 1 - 435.
-
stratified sample
- A stratified sample is one
- obtained by separating the population into homogeneous, non-overlapping groups
- called
strata, and then obtaining- a simple random sample from each stratum.
-
A systematic sample
- A systematic sample is
- obtained by selecting every
kth individual from the population. The first individual- selected is a random number between 1 and
k.
-
cluster sample
- A cluster sample is
- obtained by selecting all individuals within a randomly selected collection or
- group of individuals.
-
convenience sample
- A convenience sample is one
- in which the individuals in the sample are easily obtained.
- Any studies that use this type of
- sampling generally have results that are suspect. Results should be looked upon with extreme
- skepticism.
-
Bias
- If the
- results of the sample are not representative of the population, then the sample
- has
bias. - Three Sources of Bias
1.Sampling Bias
2.Nonresponse Bias
3.Response Bias
-
Sampling bias
- means that the technique used to obtain the individuals
- to be in the sample tend to favor one part of the population over another.
-
Undercoverage
- Undercoverage is a
- type of sampling bias.
Undercoverage occurs when the proportion of one segment of the- population is lower in a sample than it is in the population.
-
Nonresponse bias
- Nonresponse bias exists when
- individuals selected to be in the sample who do not respond to the survey have
- different opinions from those who do.
-
Response bias
- exists when the answers on a survey do not reflect the
- true feelings of the respondent.
- Types of Response Bias
- Interviewer error
- Misrepresented answers
- Words used in survey question
- Order of the questions or words within the question
-
Nonsampling errors
- are errors that result from sampling bias, nonresponse bias,
- response bias, or data-entry error. Such
- errors could also be present in a complete census of the population.
-
Sampling error
- is error that results from using a sample to estimate
- information about a population. This type of error occurs because a sample
- gives incomplete information about a population.
-
raw data
- When data is collected from a survey or designed
- experiment, they must be organized into a manageable form. Data that is not organized is referred to as
raw data.
-
frequency distribution
- A frequency distribution lists
- each category of data and the number of occurrences for each category of data.
-
relative frequency
- The relative frequency is the
- proportion (or percent) of observations within a category and is found using
- the formula:
-
- A relative frequency distribution lists the
- relative frequency of each category of data.
-
bar graph
- A bar graph is constructed by labeling each category of data on
- either the horizontal or vertical axis and the frequency or relative frequency
- of the category on the other axis.
-
Pareto chart
- A Pareto chart is a bar graph where
- the bars are drawn in decreasing order of frequency or relative frequency
-
Difference between discrete and continuos data
- The first step in
- summarizing quantitative data is to determine whether the data is discrete or
- continuous. If the data is discrete and
- there are relatively few different values of the variable, the categories of data
- will be the observations (as in qualitative data). If the data is discrete, but
- there are many different values of the variable, or if the data is continuous,
- the categories of data (called
classes)- must be created using intervals of numbers.
-
histogram
- A histogram is constructed by
- drawing rectangles for each class of data whose height is the frequency or
- relative frequency of the class. The
- width of each rectangle should be the same and they should touch each other.
-
stem-and-leaf plot
- A stem-and-leaf
- plot
uses digits to the- left of the rightmost digit to form the
stem. Each rightmost digit- forms a
leaf. - For example, a data
- value of 147 would have 14 as the stem and 7 as the leaf.
-
dot plot
- A dot
- plot
is drawn by placing- each observation horizontally in increasing order and placing a dot above the
- observation each time it is observed.
-
class midpoint
- The class
- midpoint
is found by adding- consecutive lower class limits and dividing the result by 2.
-
frequency polygon
- A frequency
- polygon
is drawn by plotting- a point above each class midpoint on a horizontal axis at a height equal to the
- frequency of the class. After the points
- for each class are plotted, draw straight lines between consecutive points.
-
cumulative frequency distribution
- A cumulative
- frequency distribution
displays- the aggregate frequency of the category. In other words, for discrete data, it displays the total number of
- observations less than or equal to the category. For continuous data, it displays the total
- number of observations less than or equal to the upper class limit of a class.
-
cumulative relative frequency distribution
- A cumulative
- relative frequency distribution
- displays the aggregate proportion (or percent) of observations less than or
- equal to the category.
-
ogive
- An ogive (read as “oh jive”)
- is a graph that represents the cumulative frequency or cumulative relative
- frequency for the class. It is
- constructed by plotting points whose
x-coordinates are the upper class limits and whose y-coordinates are the- cumulative frequencies or cumulative relative frequencies. After the points for each class are plotted,
- draw straight lines between consecutive points. An additional line segment is drawn connecting the upper limit of the
- class that would
preceed the first class (if- it existed).
-
time series data.
- If the value of a
- variable is measured at different points in time, the data is referred to as
time- series data
.
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