Math 146

descriptive statistics

statistics that summarize the data collected in a study

inferential statistics

interpreting data and making a conclusion

population

all values of a variable from all member

sample

some values of a variable from some members (subgroup of a population)

parameter

The numerical value of a variable from a population. This is usually unknown.

statistic

The numerical value of a variable from a sample. We use it to estimate a parameter.

variable

A characteristic or measurement of each member

individual

A person or object that is being studied

probability

The chance (proportion) of a particular event happening

Quantitative

values that can be counted or measured (Discrete or Continuous)

(ex) Shoe sizes (Discrete), Time of sunset (Continuous)

qualitative data

Values that can be described or categorized

(ex) Majors in college, Ratings of a professor

nominal

Categories without any specific order

(ex) Student ID Number

ordinal

Categories with a specific order

(ex) Letter grade

interval

quantities that have a meaning in their difference, but not in their ratio

(ex) GPA (Grade Point Average)

ratio

Quantities that have a meaning in their difference as well as in their ratio

(ex) Exam score

simple random sampling (SRS)

Some members of a population are randomly selected to make a sample.  

(ex)  Choosing  lottery numbers

Systematic Sampling

A starting number is randomly selected, and we choose every kth member starting with the number selected.  

(ex) If "5" is selected as a starting number and if we use every 10th member, the sample would consist of 5th, 15th, 25th, 35th, etc.

Stratified Sampling

A population is divided into subgroups (called strata) and we do SRS from each subgroup to make a sample.  

(ex) All Green River students are first divided by their major, and 10 students are randomly chosen from each and every major to make a sample.

Cluster Sampling

A population is divided into subgroups (called clusters) and we randomly select some clusters and use all members in the selected clusters to make a sample.  (ex) All Green River students are first divided by their major, and 10 majors are randomly chosen.  We use all students in these 10 majors to make a sample.

Convenience Sampling

There is no randomization of any sort.  We make a sample from any members that are available. 

 (ex) Asking your classmates and relatives to be in your sample.

When choosing samplings, what should we do?

Follow ethics and avoid biases

Observational Study

Data are collected without any treatment.  

(ex) How long did you sleep last night?

Experiment

Data are collected with a treatment.  

(ex) How long did you sleep last night after taking the medicine?  The medicine is the treatment in this example.

Controlled Experiment

The independent variable is systematically manipulated while its effects on the dependent variable are measured with any extraneous variables controlled.

Blind Study

The objects do not know whether they are getting a treatment.

Double-Blind Study

Neither the objects nor the researchers know who is getting what.

Placebo

A fake treatment (like a sugar pill)

Placebo Effect

Some improvement is achieved, despite using a placebo, due to psychological factors.

Hidden Bias

Ordering or wording of a question affects an answer. 

(ex) "Good students study every day.  How many days a week do you study?"

Non-response

Not everyone is willing and available to answer.  The results of a low-rate survey are not valid.  

Voluntary response

Getting answers from people with strong opinions about a certain topic. 

(ex) Asking "how many cups of coffee do you drink a day?" in a coffee shop.

Overgeneralization

Applying a study on a certain group to all groups. 

(ex) A medicine works well with babies.  It should also work for seniors.

Frequency

The number of times data occur in a category or interval

Relative Frequency

The percentage of a frequency

Bar graph

Used for categorical data.  Have categories on one axis and their frequency on the other axis.  Draw rectangles (bars) with a height (or length) equal to the frequency.  The bars do not touch each other.

Pie chart

A circle graph with categories and their relative frequency

Stem Plot

Used for quantitative data.  Divide each number into two parts - stem and leaf.  List stems on the left and leaves on the right in the order.

Histogram

Used for quantitative data.  Have intervals (classes) with equal length on the horizontal axis and their frequency on the vertical axis.  Draw rectangles with a height equal to the frequency.  The rectangles touch each other so there is no gap in between, except the ones with zero frequency (no height).

Scatter Plot

Plot ordered pairs from two variables.