Math Exam 1

stratified sampling

a variation of random sampling; the population is divided into subgroups and weighted based on demographic characteristics of the national population

double-blind experiment

an experiment in which neither the participants nor any experimenters know who belongs to the treatment group and who belongs to the control group

single-blind experiment

an experiment in which the participants are unaware of which participants received the treatment

Population

any kind of group-people, animals, things

population parameter

characteristics of the population

continuous data (quantitative)

if they can take on any value in a given interval ex. a persons weight can be anything between a few pounds and a few hundred people, so data that consists of weight are continuous, measurements of the time it takes to walk a mile

Discrete Data (Quantitative)

if they can take on only particular values and not other values in between Ex. the number of students in your class is discrete because it must be a whole number, and shoe sizes are discrete because they take on only integer and half-integer values, such as 7, 71/2, 8, 81/2 (foot lengths are continuous but shoe sizes are discrete), ex 2, the numbers of calendar years

control group

in an experiment is the group of subjects who do not receive the treatment being tested In an experiment, the group that is not exposed to the treatment; contrasts with the experimental group and serves as a comparison for evaluating the effect of the treatment.

treatment group

in an experiment is the group of subjects who receive the treatment being tested the participants in an experiment who are exposed to the level of the independent variable that involves a medication, therapy, or intervention

systematic error

the same value or proportion for every measurement.

random sampling

we chose a sample of items in such a way that every sample of the same size has an equal chase of being selected a sample that fairly represents a population because each member has an equal chance of inclusion.

cluster sampling

we first divide the population into groups, or clusters, and select some of these clusters at random, we then obtain the sample by choosing all the members within each of the selected clusters. a sampling technique in which clusters of participants that represent the population are used

stratified sampling

we use this method when we are concerned about differences among subgroups, or strata, within a population. We first identify the strata and then draw a random sample within each stratum. The total sample consists of all the samples from the individual strata. A type of probability sampling in which the population is divided into groups with a common attribute and a random sample is chosen within each group

relative change

(new value - reference value)/reference value x 100%

5 basic steps in a statistical study

1. State the goals of your study precisely. That is, determine the population you want to study and exactly what you'd like to learn about it 2. Choose a representative sample from the population 3. Collect raw data from the sample and summarize these data by finding sample statistics of interest 4. Use the sample statistics to make inferences about the population 5. Draw conclusions: determine what you learned and whether you achieved your goal

Frequency Table (Relative Frequency Table)

A frequency table lists the categories in a categorical variable and gives the count (or percentage) of observations for each category

Histogram (relative frequency histogram)

A histogram uses adjacent bars to show the distribution of a quantitative variable. Each bar represents the frequency (or relative frequency) of values falling in each bin.

cluster sampling

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

response variable

A variable that measures an outcome of a study.

A principal orders t-shirts and wants to check some of them to make sure they were printed properly. She randomly selects 2 of the 10 boxes of shirts and checks every shirt in those 2 boxes. What type of sample is this?

Cluster random sampling Groups being used

quantitative data

Have numerical values representing counts or measurements. Ex. the time of runners, incomes of college graduates

qualitative data

Have values that can be placed into non-numerical categories Ex. eye color, flavors of ice cream, names of employers, genders of animals

systematic sampling

We use a sample that happens to be convenient to select. A procedure in which the selected sampling units are spaced regularly throughout the population; that is, every n'th unit is selected.

How to determine if a sample is likely to be representative of a population

Your sample will need to contain individuals who resemble the whole population by including all demographic groups (gender, rural, urban, income levels, etc.) and have them in the same proportions as the whole population. For example, it's not truly representative if you have too many rural participants, or males, etc.

Pareto Chart

a bar graph whose bars are drawn in decreasing order of frequency or relative frequency

pie chart

a chart that shows the relationship of a part to a whole

explanatory variable

a variable that we think explains or causes changes in the response variable

Sample statistic

numbers describing characteristics of the sample found by consolidating/summarizing the raw data

participation bias

occurs any time participation in a study is voluntary

random error

occurs because of random and inherently unpredictable events in the measurement process

selection bias

occurs whenever researchers select their sample in a biased way

time series graph

represents data that occur over a specific period of time

stack plot

shows different data sets in a vertical stack

Each student at a school has a student identification number. Counselors have a computer generate 50 random identification numbers and those students are asked to take a survey.

simple random sampling Everyone has the same chance of being selected

A school chooses 4 randomly selected athletes from each of its sports teams to participate in a survey about athletics at the school. What type of sampling strategy was used?

stratified random sampling Groups being used

Sample

subset of the population from which data are actually obtained

While students are lined up for school pictures, a teacher passes out a survey to every 10th student

systematic random sampling Picks every nth student