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Lecture 1

MAT 150 Lecture Notes - Lecture 1: 3I, Statistical Hypothesis Testing, Participation Bias


Department
Mathematics
Course Code
MAT 150
Professor
Li
Lecture
1

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Yuezhe Li, Notebook for MAT 150, as a material help fulfill GA duty
1 introduction to statistics
nominal: cannot define standard mathematical operations (addition, subtraction, etc.)
ordinal: data that represent categories that have some associated order; cannot define stan-
dard mathematical operations (addition, subtraction, etc.), thus many statistical analysis
(descriptive and inferential) are not appropriate;
interval: data that can be ordered and the arithmetic difference is meaningful;
ratio: similar to interval data, except that they have a meaningful zero point and ration of
two data point is meaningful.
qualitative data: nominal or ordinal;
quantitative data: interval or ration;
conducting a statistical study:
1. determine the design of the study:
state the question to be studies
determine the population (the particular group of interest) and variables (values that
can change amongst members of the population)
determine the sampling method
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2. collect data
(a) observational studies: observe data that already exist.
i. census: data collected from every member of the population
ii. representative sample: has same relevant characteristics as the population & does
not favor one group from the population over another
A. random sampling
B. simple random sampling
C. stratified sampling: divided into two or more subgroups (strata: share similar
characters), random sample fro each strata;
D. cluster sampling: dividing population into groups (clusters: similar to entire
population), then randomly select from each group
E. systematic sampling: one chosen by selecting every nth member of the pop-
ulation.
F. convenience sampling: convenient to select (for researchers): leads to mem-
bers of the sample all having similar characteristics, non-representative sam-
ples
iii. cross-sectional study: data are collected at single time point in time
iv. longitudinal study: data are gathered by following a particular group over a period
of time
v. meta-analysis: studies compiling information from precious studies, focus on one
variable affect several events
vi. case study: look at multiple variables affect a single event
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(b) experiments: generate data to help identify cause-and-effect relationships
treatment: some condition that applied to a group of people
i. response variables: variables in a treatment responding the treatment
ii. explanatory variables: variables in the treatment causing the change of re-
ponse variables.
subjects: people(participants)/ things being studied
principles for experiments design:
i. randomize the control group (no treatment group) and treatment group
(group of subjects applied the treatment)
ii. control for outside effects (confounding variables: factors other than treat-
ment that cause effect on subjects of experiment) on the response variables
iii. replicate the experiment a significant number of times to see meaningful
patterns
placebo effect: the placebo (substance that appears identical to the actual treat-
ment but contains no intrinsic beneficial elements) effect is a response to the
power of suggestion, rather than treatment itself, by the participant of experi-
ment
single-blind experiment: subject don’t know whether they are in the control
group or treatment group, but people who interacting in the experiment know
double-blind experiment: neither subject nor interacting people know in which
group each subject belongs
institutional review board: a group of people who review the design of a study
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