Introduction to Statistics

What’s it all about?

Why is statistical analysis important? What all do we do with statistics? What are the problems/limitations of

statistical analysis?

The science of psychology

Is psychology scientific? Yes, though some endeavors that fall under the

heading of psychology are not ‘Scientific’ investigation of psychological

phenomena began in the 19th century Although often difficult to come to hard

conclusions, the methods utilized are scientific in nature

What is Science?

Science represents a special kind of epistemology that combines empirical, rational, pragmatic, and aesthetic dimensions.

Science is defined by it’s hypothetico-deductive method.

"...it is not what the man of science believes that distinguishes him, but how and why he believes it. His beliefs are tentative, not dogmatic; they are based on evidence, not on authority." -- Bertrand Russell.

Is Psychology a true science?

For the most part, science is defined by it’s experimental approach

Must be able to see, hear, touch, taste, or smell events to confirm existence

Variables are manipulated and measured This was the approach psychology began in

the 19th century, and has expanded since

What are the Objectives of Science?

Description Prediction Explanation

What are the Techniques of Science?

Observation yields Description. Correlation yields Prediction. Experimentation identifies Cause and

Effect. Explanations (Theories) are statements

about Cause and Effect relationships.

Why do we need to study Psychology?

To further clarify the field – very diverse, thus, very confusing

Attempt to provide answers for questions that have been around for some time

To provide us with a better perspective on who we are and why we do the things we do

Common questions

Are variables related? tv and violent behavior in children

Are groups of people different? Depressed vs Not- realistic view of their environment Is a treatment successful?

Can I predict qualities of one variable based on knowledge of another? Diet and heart disease

Statistics as a tool

Means to an end If we want to speak intelligently regarding

the various realms of psychological investigation (perception, attention, learning, memory, social interaction etc.), we must have a way to do so

Science provides the approach- statistics is thus a tool to reach greater understanding

What are the problems/limitations of statistics?

Statistical analysis will not provide certainty, only probability

Statistics can be easily manipulated using questionable or poor techniques No global warming?

There are various approaches to solving a problem, sometimes it is difficult to discern what might be the best

Some Distinctions

Descriptive vs. Inferential stats

Population vs. Sample

Control vs. Experimental group

Types of data

Descriptive Statistics

Used to describe the data collected.

Examples: graphing, calculating, averages, looking for extreme scores.

When we speak of descriptive or summary statistics we are talking about statistics that describe only the data on hand and do not refer to anything beyond

Inferential statistics

Allow you to infer something about the parameters of the population based on the statistics of the sample.

The goal of research rarely stops at simply describing the data on hand.

We want to generalize beyond the data to make global statements about the topic of study

Population

The entire collection of events that you are interested in. For example, our population could be the students in this class, UNT students, all students in U.S., people in general.

Although we wish to make claims about the entire population, it is often too large to deal with, and so we will take a portion of it to study.

There are two ways to do this appropriately: random sampling and random assignment.

Random Sampling

Choose a subset of the population ensuring that each member of the population has an equivalent chance of being sampled.

Examine that sample and use your observations to draw inferences about the population.

Example : Voting polls, television ratings, rolling a die.

Random Sampling (cont.)

Note, however, that the inferences drawn are only as good as the randomness of the sample.

If the sample is not random, it may not be representative of the population. When a sample is not representative of its parent population, the external validity of any inference is called into question. Example : Most psychology experiments involve

freshman psych students.

Random Assignment

When studying the effects of some treatment variable, it is also important to randomly assign subjects to treatments.

Random assignment reduces the likelihood that groups differ in some critical way other than the treatment since everyone has an equal chance to be put in one of the treatment groups.

Random Assignment (cont.)

If random assignment is not used then the internal validity of the experimental results may be compromised.

Example: don’t randomly assign male/females to receive treatment effects seen due to gender rather than treatment

Control vs. Experimental group

Oftentimes we want to look at the effects of some treatment e.g. a drug, teaching strategy, memory technique etc.

To study the effects of the treatment we’ll often give one or more groups the treatment and one group no treatment and then compare the groups

Some methods of investigation

Naturalistic observation Observation of events in natural environment

Archival data Studies involving data previously collected,

often for other purposes

Some methods of investigation

Survey research Notoriously fraught with difficulty and poor

implementation When done appropriately can be very revealing

Experiment Provides greatest control

Variables

Assume we have a random sample of subjects that we have randomly assigned to treatment groups.

Example: Stop-smoking study.

Variables (cont.)

Now we must select the variables we wish to study, with the term variable referring to a property of an object or event that can take on different values.

Example: # of cigs smoked, abstinence after one week.

Variables (cont.)

Another distinction related to variables concerns variables we measure (dependent variables) versus variables we manipulate experimentally and/or are assumed to predict the dependent variable (independent variables). Example: Whether or not we give a subject the stop-

smoking treatment would be the independent variable, and the # of cigarettes smoked would be a dependent variable.

Other examples: age to income, shoe size to intelligence

Types of data

Measurement (quantitative, magnitude) Data Continuous vs. Discrete

Example: GPA during college vs. GPA for class Example: 9 point “Likert” scale- continuous or discrete? 20 point?

Categorical (nominal, qualitative) Data Named data e.g. different brands, political party, race, gender

Can use continuous data to create categorical Example: use depression scores to classify as clinically depressed or

not

Measurement Scales

Nominal- category labels assigned in some meaningful way (e.g. gender, political party)

Ordinal- orders or ranks objects on some continuum (e.g. military ranks)

Measurement scales (cont.)

Interval Can speak of differences between scale points, arbitrary

zero point (Fahrenheit scale- 30°-20°=20°-10°, but 20°/10° is not twice as hot!)

Can think of as ordinal except where differences are the same between like measurements

Probably most common in psych Ratio

Same as interval but with true zero point (distance, weight, Kelvin- physical measurements). Ratios are interval scales too but not the other way around.

Measurement scales (cont.)

There is much debate with regard to scale distinction and how to deal with different data types. Even some types of data seem to qualify as more than one type. Although some analyses will result in the same outcome whatever you want to call your data, which analysis you perform may be affected by what you see the underlying construct to be, and so it is important that you give it some thought.