Statistics: Quiz 1
What kind of experiment is the following: researchers observe subjects and measure variables interest without assigning treatments to the subject
Observational study: no attempt to influence outcomes
Identify the population and sample: During the Super Bowl game, a marketing company emails a survey to 6000 randomly selected households about effectiveness of the commercials. 4000 individuals respond, some indicating they did not watch the Super Bowl.
Population: all house holds with access to super bowl Sample: 4000 individuals responded
Identify the following variables as quantitative (measurement) or qualitative (categorical). If quantitative, identify as discrete or continuous. Student identification numbers (S0#s at SEMO)
Qualitative
Social Security Number
Qualitative, nominal
What kind of experiment is the following: Researchers randomly apply treatments to experimental units (people, animals, plots of land, etc.) and then proceed to observe the effects of the treatment on the experimental units.
Randomized Experiment -randomly divide into 2 groups 1.) treatment 2.) no treatment treatment: medicine, training program
sample frame
-A list of individuals or items from which the sample is taken. -Ideally the individuals or items in the sampling frame are the same as the individuals or items in the population. -If the population is all students enrolled in a course at Southeast, it's possible to compile a list of all Southeast students for the sampling frame. -If the population is all hunters in Missouri, it's possible to compile a list of all individuals with a Missouri hunting permit. Landowners do not need a permit to hunt on their own property, so they may not have a hunting permit. In this case the sampling frame may not be identical to the intended population.
Voluntary response sampling
-post a survey and allow respondents to choose whether or not they respond
types of sample
-simple random sample -stratified sample -cluster sample -systematic sample -convenience sample
stratified random sample
1.Divide the population into groups of similar individuals, called strata. In practice, the strata are chosen from the sampling frame. Ideally the sampling frame is the same, or very close to being the same, as the population. 2.Choose a separate simple random sample in each stratum. 3.Combine these simple random samples to form the full sample.
Find relative frequency of sale price/item: Frequency no of items: $1-5 8 $6-10 6 $11-15 4 Total: 32
8/32=.25=25%
Sampling Bias
A sample is collected from a population and some members of the population are not as likely to be chosen as other members. -undercoverage: leave out groups of people
Bias
A statistic is biased if it is calculated in such a way that it systematically under estimates or over estimates the population parameter
Systematic sampling
A systematic sample is obtained by selecting every k th individual from the population. The first individual selected is a random number between 1 and k.
Cluster Sampling
Cluster sampling involves the selection of all members in randomly selected groups, or clusters. 1.Divide the population into clusters. 2.Randomly choose clusters. 3.All subjects in the chosen clusters make up the sample.
Quantitative or Measurement Variable
Numeric value that represents count or measurement, height, weight, GPA
What sample is this: Example: Undergraduate college students are divided by credit hours completed—at most 30 hours, 31-60 hours, 61 to 90 hours, at least 90 hours. 50 students in each group are randomly selected and given a survey about relevant issues. It's okay if strata are of unequal size. If more freshmen (at most 30 hours) are enrolled, you may want that strata to be larger than the other three strata.
Stratified random Sample
what kind of sampling is: Example: Every 200th product coming off an assembly line is pulled and weighed to see if the products are the correct weight.
Systematic sampling
inferential statistics
Use descriptive statistics from sample to reach conclusions about populations
cumalative frequency
add right side till you get down the the number they asked about on the left
Is convenience sampling likely to be a representative sample?
almost never
paramter
calculation from a population mean of population, M (but curvy M)
Statistic
calculation from a sample, (X with line above it)
Qualitative or
categorical data
what kind of sample is this: Example—The clusters could be the ER in each hospital in a city. Randomly choose 5 hospitals and survey all the ER triage nurses in the 5 hospitals about certain practices
cluster sampling
what kind of sample is: Example: Stand outside a store and ask recent customers about a product just purchased.
convenience sampling
what kind of sample is: Example: Suppose as a freshman, you are unhappy with the method of registration at Southeast and decide to issue a formal complaint. To gather support, you ask the opinions of students that live on your floor that are also freshmen.
convenience sampling
discrete data
countable data
Discrete variable
countable usually whole number
response variable
dependent variable: changes as result of explanatory variable
Convenience Sampling
do whats easy to collect data
Population
entire group being studied
What are the two variables
explanatory and response
How do you find relative frequency
freq/total
Frequency table to histogram: what side does relative frequency label go on and ranges
frequency on left side and ranges on bottom
explanatory variable
independent variable: causing the change
Interval or ratio: (temp) C and F
interval
A quantitative variable may be
interval or ratio
nominal variable
just a label, name only, gender, ethnicity, etc.
ordinal variable
label with a clear order; good, ok, bad
Descriptive statistics
look at sample, draw graph, look at table, do calculations
quantitative or
measurement data
interval variable
no true 0 starting point, find differences (subtract), temp in F or C
A qualitative variable may be
nominal or ordinal
Continuous variable
not countable, between any 2 values is another value weight
What kind of experiment is the following: -find 100 women age 30 of which 50 have been smoking a pack a day for 10 years when the other 50 have been smoke free for 10 years -measure lung capacity for each of the 100 women -analyze, interpret, and draw conclusions from data
observational study: explanatory- smoking or not smoking response variable- lung capacity
Statistic or parameter: 20% of college As students are women
parameter
Identify if the following data represents a parameter or statistic. 42% of the governors of the 50 United States are Democrats.
paramter
Non response bias and how can we improve this?
people dont respond, represent certain groups we can do call backs or have incentives
Identify the population and sample: A political scientist randomly selects 25 of the 100 senators currently serving in Congress, then finds the lengths of time that they have served.
population: 100 senators sample: 25 selected senators
Identify the following variables as quantitative (measurement) or qualitative (categorical). If quantitative, identify as discrete or continuous. Eye color
qualitative
Grades in a course: A, B, C, D, F
qualitative, ordinal
variable
quality or quantity being studied
what can be discrete or continuous
quantitative
Whats discrete or continuous
quantitative variable
Identify the following variables as quantitative (measurement) or qualitative (categorical). If quantitative, identify as discrete or continuous. High temperature in Cape Girardeau for each day in July
quantitative, continuous
Identify the following variables as quantitative (measurement) or qualitative (categorical). If quantitative, identify as discrete or continuous. Weight of all football players on roster at Southeast
quantitative, continuous
temperature of an August day in degrees Fahrenheit
quantitative, continuous, interval
weight of football players on SEMO roster
quantitative, continuous, ratio
Identify the following variables as quantitative (measurement) or qualitative (categorical). If quantitative, identify as discrete or continuous. The years of cicada emergence: 1936, 1953, 1970, 1987, 2004
quantitative, discrete
Year of graduation from high school of all students currently at Southeast
quantitative, discrete, interval
Yearly salary of employees at Southeast
quantitative, discrete, ratio
interval or ratio: age in years
ratio
interval or ratio: weight in pounds
ratio
Qualitative or Categorical Variables
represents quality or characteristic, label, gender, ethnicity, grade level
Qualitative
result of categorizing or describing attributes of a population
quantitative
result of counting or measuring attributes of a population always numerical data
continuous data
result of measuring as long as measuring device is precise; between two values is another value
Voluntary response sample
sample members are self-selected and likely to be a biased sample
what kind of sample is: Given a population of size N, each sample of size n has an equally likely chance of being chosen.
simple random sample: like drawing names from a hat
Identify if the following data represents a parameter or statistic. A news source reports the average amount of time watching television is 4.6 hours per day.
statistic
Identify if the following data represents a parameter or statistic. A sample of households is selected and the average (mean) number of people per household is 2.58. (U.S. Census Bureau)
statistic
sample
subset of population
ratio variable
true 0 starting point, compare with ratios (percents), also subtract weight of newborn
Why use stratified sampling?
•Also find individual estimates for each stratum. •If the variables are more consistent within each stratum than within the population, stratified sample produces more accurate estimates of the population variables. •Depending on location of strata, stratified sampling may be cheaper. •Allows use of different interviewers in each strata.
Advantages of Cluster Sampling
•Only a list of clusters in needed, not a list of each individual or item. •Cheaper to survey everyone in several locations than a few people in many locations.