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

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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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