Chapter 1- Introduction to Statistics

• Why do we need Statistics?

  • Psychology is an empirical science. 

  • Researchers gather information

  • Statistics help researchers make sense of the information and data that they gather

    • Organize & summarize 

    • Communicate to others

    • Decide whether conclusions are justified based on results obtained

•  Psychological Research

Two elements:

1.) Research Methods: make observations & formulate questions. The architect of the study.

  2.) Statistics: the tools that you use to answer those questions. The contractor of the study.

• Definition of Statistics

  • A set of methods and rules for organizing, summarizing, and interpreting information.-----data

    • “ . . . order out of chaos”

    • “a set of standardized techniques that are recognized and understood throughout the scientific community”

• Descriptive statistics:

Summarize, organize, simplify data (focus for chapters 1-5) ex. Average of something

• Inferential statistics:

Methods that use sample data to make general statements about a population

Used to draw conclusions about a population

• Populations vs. Samples

  • Population: set of all individuals of interest in a particular study

  • Sample: set of individuals selected from the population of interest, which are intended to represent the population

• Variables = characteristic or condition that changes or has different values for different individuals; also environmental variables

  • Data (plural) = measurements or observations

  • Datum (aka raw score)

  • Data set

Scales of Measurement

Nominal Scale:

(A set of categories)

Ex: Academic majors, gender, name of cookies

Ordinal Scale:

(Categorized ranked observations)

Ex: freshman, sophomore, junior, senior, birth order, book edition ranking of favorite cookies

Interval Scale:

• Ordered categories are intervals of exactly the same size

• Arbitrary zero point, therefore can’t determine exact differences between scores

  • Ex: shoe size, temperature of cookies (no such thing as no temp.)

• With interval data, we can add and subtract, but cannot multiply or divide.  Confused?  Ok, consider this: 10 degrees + 10 degrees = 20 degrees.  No problem there.  20 degrees is not twice as hot as 10 degrees, however, because there is no such thing as “no temperature” when it comes to the Celsius scale.

Ratio Scale:

• Interval scale with an absolute zero point

• Ratio scales allow you to compute the actual difference between two scores

Ex: height, weight, exam score, How many cookies are left?

Sampling Error: 

• Estimated error between the data obtained from a sample and the population intended to study

  • Example: GPA of this class will not be exactly the same as GPA of all college students in US…

Variables in Research

• Independent

That you manipulate or categorize

• Dependent

That you measure; it depends on the independent variable

• Confounding

Systematically varies with the independent variable and so you try to control or randomize away

Constructs

• Definition: hypothetical concepts that are used to help define behavior

• Have to define a construct to be measured

• Operational definition: 

• defines a construct in terms of an observable and measurable response

Examples: Anxiety, depression, IQ, self-esteem

Selecting and Assessing Variables

• Operational definition

Exactly what you are studying

• Reliability

Consistency of the measure

• Validity 

Extent the test measures what it is supposed to measure

Hypothesis Testing

• The process of drawing conclusions about whether a relation between variables are supported or not supported by the evidence

One Goal, Two Strategies

Between-groups designs

Different people complete the tasks, and comparisons are made between groups

Within-groups designs

The same participants do things more than once, and comparisons are made over time

An example of the experimental method

Quasi-Experimental Method

• Comparing groups which were NOT created by manipulating an independent variable

• Groups are determined by a participant variable

Real limits

• Definition:

  • Boundaries of intervals for scores represented on a continuous number line

  • Limit separating 2 scores is located exactly halfway between them

  • Each scores has 2 real limits

    • Upper real limit

    • Lower real limit

Scores:

X = scores for a variable

N = no. of scores in the population

n = no. of scores in the sample

Sigma:

Σ = summation X = 20   13   7   9   8

ΣX = 57, n = 5