CAS MA 115 Lecture Notes - Lecture 1: Confidence Interval, Regional Policy Of The European Union, Simple Random Sample
1 May 2018
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CHAPTER 1 – DATA COLLECTION
Section 1.1 – Introduction to the Practice of Statistics
Objective 1: Define Statistics/Statistical Thinking
• Statistics – the collection, organization, summarization and analyzation of information in
order to draw conclusions/answer questions meant to provide a measure of confidence in
these conclusions
o Margin of Error and Confidence Interval are inversely related
o ex (of a confidence interval): 95% confidence interval means 95% of the time the
results will be positive while 5% of the time the results will be negative
▪ Large data set = smaller margin of error and larger confidence interval
▪ Small data set = larger margin of error and smaller confidence interval
• Data – the information used to draw conclusions, often describing characteristics
o Important to understand that data varies when measured within a sample and
within an individual
o ex (of variability): Measurement Error
Objective 2: Explain the Statistical Process
• Population – an entire group of objects/individuals to be studied
• Sample – a subset of the population that is being studied
o Questions: how to collect a sample & how large should a sample be?
o Answers: randomly & not too large or small (will affect the margin of
error/confidence interval)
• Individual – a person/object from the sample that is being studied (who must be a
member of the population)
• Descriptive Statistics – the process of organizing and summarizing data through
numerical summaries (mean, median, mode, etc.)/tables/graphs
• Inferential Statistics – the process of taking results from a sample and extending them to
fit a population, essentially measuring the reliability of the sample results
• Statistic – a numerical summary based on a sample
o ex: a sample of 250 students is obtained and from this sample we find that 86.4%
have a job
o ex: sample mean
• Parameter – a numerical summary based on a population
o ex: the percentage of all students on your campus who have a job is 84.9%
o ex: population mean
• The Process of Statistics
o 1. Identify the research objective. What is the question to answer?
▪ This can be an observational study or a designed study
o 2. Collect data needed to answer the question (from 1). This must be done
correctly or else the conclusions drawn will be meaningless.
▪ Determine the correct method of sampling that is fully representative
o 3. Describe the data. This will help narrow down the type of statistical methods
the researcher should use.
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o 4. Perform inference. Apply the right techniques to extend the results/conclusions
from the sample to a population and report reliability.
▪ ex: point estimate (least reliable), confidence interval (most reliable)
Objective 3: Distinguish Qualitative & Quantitative Variables
• Variables – characteristics of the individuals within a population
o ex: height, weight, age, etc.
o Important to understand that variables vary and that some factors influence the
variability
• Qualitative/Categorical – classification of individuals based on attributes/characteristics
o ex: nationality, level of education
• Quantitative – classification of individuals by some numerical measure (can be
added/subtracted)
o ex: number of children, household income, daily intake of whole grains
Objective 4: Distinguish Discrete & Continuous Variables
• Discrete – a quantitative variable that has a finite/countable number of possible values
o CANNOT take on every value between the number of possible values
o ex: 0, 1, 2, 3…
o ex: number of children
• Continuous – a quantitative variable that has an infinite number of possible values
o CAN take on every value between the number of possible values
o ex: 0, 0.1, 0.2, 0.3, 0.4, 0.5…
o ex: household income, daily intake of whole grains
• Data – the list of observations a variable can assume
• ex: gender = variable, data = male & female
o Qualitative Data – observations made from a qualitative variable
o Quantitative Data – observations made from a quantitative variable
▪ Discrete Data - observations corresponding to a discrete variable
▪ Continuous Data - observations corresponding to a continuous variable
Objective 5: What is the level of measurement a variable has?
• Nominal Level of Measurement – when a variable names/labels/categorizes but cannot be
arranged/ranked in a specific order
o ex: whether or not a school has a closed campus policy during lunch
• Ordinal Level of Measurement – when a variable has the properties of the previous level
and can be arranged/ranked in a specific order
o ex: class rank
• Interval Level of Measurement – when a variable has the properties of the previous level
and the differences in variable values have meaning (a value of zero not signifying an
absence of quantity), allowing them to be added/subtracted
o ex: values of military time
• Ratio Level of Measurement – when a variable has properties of the previous level and
the ratios of the variable values have meaning (a value of zero signifying an absence of
quantity), allowing them to be added/subtracted/multiplied/divided
o ex: number of vending machines in the school
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Document Summary
Section 1. 1 introduction to the practice of statistics. Individual a person/object from the sample that is being studied (who must be a member of the population: descriptive statistics the process of organizing and summarizing data through numerical summaries (mean, median, mode, etc. What is the question to answer: this can be an observational study or a designed study, 2. Collect data needed to answer the question (from 1). This must be done correctly or else the conclusions drawn will be meaningless: determine the correct method of sampling that is fully representative, 3. This will help narrow down the type of statistical methods the researcher should use: 4. Apply the right techniques to extend the results/conclusions from the sample to a population and report reliability: ex: point estimate (least reliable), confidence interval (most reliable) Section 1. 2 observational studies v. designed experiments. Obtain a frame that lists all individuals of interest and number them 1 to n: 2.
