PSYC 2002: Introduction to Statistics in Psychology

Contents

1. 1. Statistical Terminology
2. 2. Scientific Research Methods
3. 3. Scales of Measurement
4. 4. Experimental Designs
   1. 4.1. Experimental Design (True Experiments)
   2. 4.2. Quasi-Experimental Research

1. Statistical Terminology

Statistics: the process of collecting data in a systematic way and making decisions based on probability. They allow us to make educated, mathematical decisions based on probabilities. There are two ways statistics are used:

• Descriptive Statistics: used to describe a group or particular data sample.
• Inferential Statistics: used to make inferences about population parameters based on sample statistics (i.e., where we generalize from a sample to a population)

Let's review some important definitions:

• Population: the entire group of individuals you could possibly measure on a variable.
  • A parameter is a summary value that describes a population (e.g., the average score for a population).
  • Population number ($N$).
  • Standard deviation ($\sigma$) (sigma).
  • Mean ($\mu$) (mu).
  Population uses uppercase alphabet and greek letters.
• Sample: the group of individuals or scores that you select from a population and measure in your experiment. They have the same characteristics as the population you're interested in studying.
  • A statistic is a summary value that describes a sample (e.g., the average score for a sample). These are used to estimate population parameters but they're not perfect because of sampling errors.
  • Sample number ($n$).
  • Standard deviation ($s$).
  • Mean ($\bar{x}$) (x-bar)
  Samples use lowercase alphabet and greek letters.
• Random Sample: a sample where each individual in the population has an equal chance of being selected.
• Random Assignment: where each individual has an equal chance to be placed in each treatment condition.
• Sampling Error: a naturally occurring difference between a sample statistic and its corresponding population parameter.

2. Scientific Research Methods

Research Design: the systematic process of collecting data in order to answer specific questions. There are two major classifications:

1. Experimental: tests your hypotheses on the causal effects of the Independent Variable (IV) on the Dependent Variable (DV). The IV is actively manipulated and there are two levels. Your participants must be randomly assigned to conditions and you need to specific your procedures for testing your hypothesis. Also, you have to control for major threats to internal validity.
2. Non-Experimental:
   1. Descriptive Research: describes a group using numerical scores on variables.
      1. Use: often a starting point in research.
      2. Statistics: mean, median, and standard deviation.
   2. Correlation Research: where we look for relationships between two or more vairables. We measure each participant on each variable but there is no causal inferences.
      1. Use: for testing theories and help form predictions; often as a secondary analysis.
      2. Statistics: often requires a linear relationship which is evaluated on strength and direction.
   3. Quasi-Experimental Research: where we test our hypotheses about relationships between the IV and DV but we have limited ability to actively manipulate the IV or randomly assign participants to conditions. We must still include specific procedures for testing the hypotheses and still control for the major threats to internal validity. We cannot make true causal inferences.

Variables: a characteristic or condition that changes or has different values for different individuals; any measure or characteristic that we use in research.

There are three types of experimental variables:

1. Independent Variables (IV): what we manipulate.
   1. Experimental: where the experiment manipulates the variable.
   2. Subject: where the variable is predefined (e.g., gender, smoker versus non-smoker).
2. Dependent Variables (DV): what we analyze or measure.
3. Extraneous Variables (EV): any other variable (confound or not) that is not an IV or a DV.

There are two ways to describe variables:

1. Qualitative (categorical): descriptive qualities that describe something (e.g., male/female, University attended).
   • Discontinuous (discrete): values that can only be whole numbers (no number in between). Measurements are exact (e.g., you have a whole person, not half of a person).
2. Quantitative (numerical): quantifiable qualities that describe something (e.g., age, height)
   • Continuous (infinite): where they can be any number of values between two numbers.
   • Discontinuous (discrete).

In other words, qualitative variables are always discontinuous whereas quantitative variables can be either continuous or discontinuous.

3. Scales of Measurement

The level of measurement determines the types of questions we can ask, the types of analyses we can perform, and the conclusions we can draw. There are four ways to measure variables (NOIR):

1. Nominal: categorizing variables in no particular order.
   • E.g., by gender (male/female/other), or religion (Jewish, Muslim, Hindu)
   • Statistics: chi-square; proportions, percentages, and mode.
2. Ordinal: categorizing variables unequally along a continuum. (We can talk about magnitude.)
   • E.g., by satisfaction (1 through 7).
   • Statistics: Mann-Witney U; proportions, percentages, mode, and median.
3. Interval: categorizing variables equally along a continuum. There is no true zero.
   • E.g., (temperature) it can be 10°C today and 20°C tomorrow but that doesn’t mean that tomorrow will be twice as hot as today.
   • E.g., (IQ) if you have an IQ of zero, you don’t have an absence of intelligence.
   • Statistics: t-test or ANOVA; median, mean and standard deviation.
4. Ratio: categorizing variables equally along a continuum with a true zero.
   • E.g., length, height, and reaction times can all have zero values. A 10 second reaction time is twice as fast as a 5 second reaction time.
   • Statistics: t-test or ANOVA; median, mean and standard deviation.

In Psychology, we normally use interval scales in tests and measurements.

4. Experimental Designs

4.1. Experimental Design (True Experiments)

As summarized above, you are testing your hypothesis on the causal effects of the IV on the DV. Your goal is to determine if there exists a cause-and-effect relationship.

The general process is to randomly select individuals from the population; randomly assign them to different treatment conditions; expose subjects to different levels of the IV; and compare DV differences between conditions.

We must control our confounding variables only when:

• A variable changes systematically with the IV; or
• A variable influences the DV.

4.2. Quasi-Experimental Research

4.2.1. Descriptive Research

You are trying to obtain an accurate description of a population with numerical values. You cannot draw a conclusion - only describe!

The general process is to collect data on variables of interest and use descriptive statistics to summarize the data that you collect.

4.2.2. Correlational Research

As summarized above, you are trying to determine if there exists a relationship between two or more variables. You cannot determine causality or directionality.

The general process is to randomly select individuals from the population (using something like simple random sampling); collect information on the variables of interest; and calculate a correlation coefficient ($r$).

4.2.3. Comparing Intact Groups

This is where we are trying to determine if there exists a relationship between a grouping variable and some other variable. You can find significant differences between groups but you still cannot determine causality and direction.

The general process is to randomly select individuals from the population; place individuals into a group based on a person-variable (e.g., smoker versus non-smoker); and compare the group differences. (Think: non-equivalent group, pre-post group, and developmental designs.)