Stats Ch 1 & 2
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A set of mathematical procedures for organizing , summarizing, and interpreting information
A group of two or more individuals or things that share one or more common characteristics
A subgroup of two or more individuals or things from a population
A subgroup of two or more individuals or things randomly and independently selected * from a population
· Randomly and independently selected means each member of the population has an equal opportunity of being included in the sample Parameter
Usually a numerical value, that describes a population.
Relationship between a population and sample (graph: slide 4)
A value, usually a numerical value that describes a sample.
- measurements or observations
- Descriptive Statistics
- Statistical procedures used to summarize, organize and simplify data.
- Inferential Statistics
- Techniques that allow us to study samples and then make generalization about the population from which they were selected.
The discrepancy, or amount of error, that exists between a sample statistic and the corresponding population parameter
Variable and Constant
Variable: A characteristic or condition that changes or has different values for different individuals
Constant: A characteristic or condition that does not vary but is the same for every individual.
- Observing naturally occurring phenomena
- · Naturalistic observation
- · Archival research
- · Case histories
- · Surveys
- --> does not equal causality
Is variable X associated with variable Y?
- ex: Is watching WWE related to aggressive behavior in children?
- –How can we describe this relationship?
Correlational Research: Advantages
- – A good place to start & explore (especially if relevant theory is lacking)
- – Often cheapest & easiest option
- – Can look at more variables simultaneously / greater realism
Fewer ethical issues…
Experimental Research: Manipulation & Measurement
- - Independent (manipulated) variables
- – Dependent (measured) variables
- – Does manipulating IV “X” cause changes in DV “Y?”
- – Example: Does assigning some children to watch WWE cause them to behave more aggressively than other children?
- Experimenter bias, for example
- • Affects treatments
- • Affects measurements
Experimental Research: Limitations
- - Often harder, more time consuming, &/or expensive
- – Some variables can’t be manipulated
- – Difficult to control for all extraneous variables (hold them all constant)
- – Difficult to make the experimental situation realistic
- – Procedural mistakes or flawed sampling can make findings useless
Greater ethical obligations
- – Some variables shouldn’t be manipulated, or only with great caution
- Repeat as necessary to build, refine, or discard theory
- – Theories allow us to generate testable hypotheses
- – When hypotheses are supported by evidence, the theory is considered the best explanation so far
- -When hypotheses are not supported, the theory is refined or discarded
Role of statistics in experimental research (table: slide 14)
Criteria for evaluating evidence:
- Observations must be
- – Public
- – Replicable
- • Can be repeated by others using same procedures; Reliable
- • Consistent across measurements &/or observers
Hypothetical results from a correlational study (table: slide 16)
– Defining a construct in terms of the operation(s) used to measure it Ways to measure fear? attraction?
- Poor operational definitions-->bad research / misleading results
- – Problems with reliability of observations
- – Problems with interpretation of results
Independent and Dependent Variables
Independent variable: The variable that is manipulated by the researcher. Independent variable consists of the antecedent condition that were manipulated prior to observing the dependent variable.
Dependent variable: The variable that is observed in order to assess the effect of the treatment.
Control condition: Individuals do not receive experimental treatment.
Experimental condition: individuals receive experimental treatment.
Confounding variable: An uncontrolled variable that is unintentionally allowed to vary systematically with the independent variable.
An example of a confounding variable (Instructor: slide 21)
Discrete vs. Continuous Variables (table 23)
- Discrete: each item corresponds to a separate value of the variable
- Values/categories do NOT overlap or “touch” on the scale.There are no values “in between”
- Continuous: each item corresponds to an interval on the scale of measurement. Intervals defined by upper & lower real limits
- Real limits are continuous (“they touch”)
Properties of scales of measurement:
4 Types of scales:
- Each scale has all the properties of the ones below it plus an additional property.T
- he higher-level measurements contain more detailed information about observations & allow more complex analyses.
Types of scales: Nominal, Ordinal, Interval, Ratio
- -Identification (Name): allows you to label observations.
- -Applies to category labels & numbers used as labels.
- -Examples: college major, any “yes/no,” participant number, etc…
-Magnitude (Order): allows you to make statements about relative size or ordering/ranking of observations.
-Applies to ordered category labels & numbers used as ranks.
-Examples: any “high/medium/low,” class rank, etc…
-Equal Intervals: allows you to assume that the distances between numbers on the measurement scale are equal & correspond to equal differences in the variable being measured.
-Applies to numbers, often scores or ratings.
-Examples: attitude as preference ratings, etc...
-Absolute Zero: allows you to assume that a score of “0” on a variable really means the absence of that property, & that you can make meaningful ratio statements.
-Applies to numbers, often tallies or physical measurements.
-Examples: stress as change in BP, memory performance as # of words recalled, etc...
Frequency distribution table:
shows a range of possible values for a single variable (X) & the number of observations of each value (f).
Displaying our observations: Frequency distribution tables & graphs of frequency distributions
Example: X =gender of class members (1 = male; 2 = female)
Rank or percentile rank
A particular score is defined as the percentage of individuals in the distribution with scores at or below the particular value.Calculating cumulative frequencies (cf) & cumulative percentages (cum%)
cf = # of observations at or below a given value of X add up frequencies from bottom of table upwards
cum(cumulative)% = percentage of observations at or below a given value of X divide cf/N for each row (better—less rounding error)OR add up percentages from bottom of table upwards
Characteristics of distributions
Symmetry vs. skewness, number of modes or “pileups”
The Normal Distribution
- mean = median = mode
- Many complexly-determined traits are normally distributed
- e.g. IQ & SAT scores.
A symmetrical bimodal distribution
mean = median, with 2 modes
Bimodal distributions may also be asymmetrical (mean, median), & multimodal distributions are possible.
A positively skewed distribution
(tail --> positive end of scale)Mode<median<mean
A negatively skewed distribution
- (tail -->negative end of scale)
Skewed Distributions Image
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