Comprehensive class notes in the Introduction to Statistics course, covering key mathematical concepts and principles. It includes detailed explanations and visual aids such as graphs and charts. These notes serve as a valuable resource for understanding the fundamental tools and methods used in st...
Math
Descriptive or univariate
What is statistics?
The practise of collecting and analyzing data
What is data?
The factual information collected from a survey or other...
Define numerical data
Data are numbers
Population: entire group of objects or individual considered for a survey
Sample: part of a group being surveyed
Numerical description of a population → parameter
Branches of statistics
Descriptive: involves the organization, summarization, and display of data
Inferential: involves using a sample to draw conclusions about a population
Statistics are numbers used to: describe and draw conclusions about data
Data: collection of observations (measurements…)
,Statistics: science of planning studies and experiments, obtaining data,
and then organizing, summarizing, presenting, analyzing, interpreting, and
drawing conclusions based on the data
Population: the complete collection of all individuals to be studied; the
collection is complete in the sense that it includes all of the individual to be
studied
Census: collection of data from every member of a population
Sample: sub-collection of members selected from a population
Sampling method:
Does the method chosen greatly influence the validity of the conclusion?
Voluntary response (or self-selected) samples often have bias (those with
special interest are more likely to participate). These samples' results are no
necessarily valid.
Other methods are more likely to produce good results
Conclusions:
Make statements that are clear to those without an understanding to
statistics and its terminology
Avoid making statements not justified by the statistical analysis
, Or generalizations
Practical implications:
State practical implications of the results
There may exist some statistical significance yet there may be no practical
significance.
Common sense might suggest that the finding does not make enough of a
difference to justify its use or to be practical.
The subject of statistics is largely about using sample data to make
inferences about on entire population.
Parameter: a numerical measurement describing some characteristic of
a population
Statistic: a numerical measurement describing some characteristic of a
sample
2 types of data: quantitative and qualitative data
Quantitative data: consists of numbers representing counts or
measurements.
Qualitative data: consists of names or labels (representing categories)
Quantitative data can further be described by distinguishing between
discrete and continuous types
, Discrete data: result when the number of possible values is either a
finite number or a “countable”number
Continuous data: result from infinitely many possible values that
correspond to some continuous scale that covers a range of values
without gaps, interruptions, etc..
Data
Quantitative Qualitative
Numerical Descriptive
Discrete Continuous
Usually counted Usually measured
Levels of measurement:
Nominal: classification
Characterized by data that consists of names, labels, or categories only,
and data cannot be arranged in an ordering scheme
Ordinal: classification and order
Implies statement of greater than and less than
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