Chapter 1: Introduction to Statistics
Statistics – consists of facts and figures / a general field of mathemagicks.
- Refers to a set of mathemagical procedures for organizing, summarizing, and
interpreting information.
Stats serve two general purposes:
1) They are used to organize and summarize the information = communication of results.
2) Assist the researcher to answer the questions that initiated the research.
Population: the set of all the individuals of interest in a particular study.
Sample: a set of individuals selected from a population, usually intended to represent the
population in a research study.
Variable: something that can change or have different values.
Datum: the measurement obtained for each individual.
- Also called: a score or raw score.
Data Set: the complete set of scores.
Data (plural) are measurements or observations. A data set is a collection of measurements
or observations. A datum (singular) is a single measurement or observation and is commonly
called a score or raw score.
A Parameter: a value – usually a numerical value – that describes a population.
- Usually derived from measurements of the individuals in the population.
A Statistic: a value – usually a numerical value – that describes a sample.
- Usually derived from measurements of the individuals in the sample.
Descriptive and Inferential Statistical Methods:
Descriptive Stats: are statistical procedures used to summarize, organize, and simplify data.
- Techniques that take raw scores and organize/summarize them in a form that is more
manageable.
- Scores are organized in a table or a graph. So it is possible to see the entire set of
scores.
- Also uses computation of the average.
Inferential Stats: consists of techniques that allow us to study samples and then make
generalizations about the populations from which they were selected.
1
,Psychology 253 Chapter 1
Sampling Error: the naturally occurring discrepancy, or error, that exists between a sample
statistic and the corresponding population parameter.
- One issue with samples is that they provide limited information about the population
= a discrepancy between a sample statistic and the corresponding population
parameter.
- “margin of error”
VARIABLES AND MEASUREMENTS
Constructs and Operational Definitions:
Variables like intelligence, anxiety, and hunger are called constructs, and because they are
intangible and cannot be directly observed, they are called hypothetical constructs.
Operational Definition: defines a construct in terms of external behaviors that can be
observed and measured.
- Intelligence can be measured through performance on an IQ test.
- Identifies a measurement procedure (a set of operations) for measuring an external
behavior and uses the resulting measurements as a definition and a measurement of
a hypothetical construct.
- An operational definition has two components:
o First, it describes a set of operations for measuring a construct.
o Second, it defines the contrast in terms of the resulting measurements.
Constructs: internal attributes or characteristics that cannot be directly observed but are
useful for describing and explaining behavior.
Discrete and Continuous Variables:
Discrete Variable: consists of separate, indivisible categories.
- No values can exist between two neighboring categories.
- Commonly restricted to whole, countable numbers.
- Can also consist of qualitative observations (occupation; academic major etc.).
Continuous Variable: an infinite number of possible values that fall between any two observed
values.
- Is divisible into an infinite number of fractional parts.
- Time; height; weight etc.
- Two Other Factors Apply to Continuous Variables:
o When measuring a continuous variable, it should be very rare to obtain
identical measurements for two different individuals.
o Researchers must first identify a series of measurement categories on the scale
of measurement.
2
,Psychology 253 Chapter 1
1) Each measurement category is actually an interval that must be defined
by boundaries.
- Real Limits: are the boundaries of intervals for scores that are represented on a
continuous number line.
o The real limit separating two adjacent scores is located exactly halfway
between the scores.
o Each score has two real limits.
1) The upper real limit is at the top of the interval and the lower real limit
is at the bottom.
Scales of Measurement:
Measurement involves assigning individuals or events into categories.
Scale of Measurement: the categories used to measure a variable and the relationships
between the categories determine different types of scales.
- Distinctions among the scales are important because they identify the limitations of
certain types of measurements.
The Nominal Scale: consists of a set of categories that have different names. Measurements
on a nominal scale label and categorize observations, but do not make any quantitative
distinctions between observations.
- “Nominal” means ‘having to do with names’.
- Involves classifying individuals into categories that have different names but are not
related to each other in any systematic way.
o Academic majors: art, bio, business etc.
o Race, gender, occupation etc.
- The measurements from a nominal scale allow us to determine whether two
individuals are different, but they do not identify either the direction or the size of the
differences.
The Ordinal Scale: consists of a set of categories that are organized in an ordered sequence.
- Rank observations in terms of size or magnitude.
- Organized in a fixed order corresponding to differences of magnitude.
- Consists of a series of rank (1st, 2nd, 3rd etc.).
- S, M, L.
o The categories form an ordered sequence = there is a directional relationship.
- Determine whether two individuals are difference and you can determine the
direction of difference.
- Ordinal measurements do not allow you to determine the size of the difference
between two individuals.
3
, Psychology 253 Chapter 1
The Interval and Ratio Scales:
- Both consist of a series of ordered categories (like an ordinal scale) BUT with the
additional requirement that the categories form a series of intervals that are all exactly
the same size.
o This allows one to determine both the direction and the size of the difference
between the two measurements.
- What differentiates the two is the nature of the zero point.
o An interval scale has an arbitrary zero point – the value of 0 is assigned to a
particular location on the scale as a matter of convenience/reference.
o A ratio scale is anchored by a zero point that is not arbitrary but rather a
meaningful value representing none (a complete absence) of the variable being
measured.
- Interval Scale: consists of ordered categories that are all intervals of exactly the same
size.
o Equal differences between numbers on scale reflect equal differences in
magnitude.
o However, the zero point on an interval scale is arbitrary and does not indicate
a zero amount of the variable being measured.
- Ratio Scale: an interval with the additional feature that a score of zero indicates none
of the variable being measured.
o Ratios of numbers do reflect ratios of magnitude.
Data Structure 1: One Group with One or More Separate Variables Measured for Each
Individual – DESCRIPTIVE Research
- Some research studies are conducted simply to describe individual variables as they
exist naturally.
o Although the research might measure several different variables, the goal of
the study is to describe each variable separately.
o Not concerned with relationships between variables.
- Descriptive Research/ Descriptive Research Strategy: involves measuring one or more
separate variables for each individual with the intent of simply describing the
individual variables.
Data Structure 2: One Group with Two Variables Measured for Each Individual – The
CORRELATIONAL Method
- Examining the relationship between variables – observe the two variables as they exist
naturally for a set of individuals.
- Scatter plots.
- Correlational Method: two different variables are observed to determine whether
there is a relationship between them.
o A research study that measures x2 different variables for each individual.
o Chi-square test – non-numerical data.
4
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Selene101. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R105,00. You're not tied to anything after your purchase.
