PSYCH STATS REVIEWER

Branches of Statistics

• Statistics is a branch of mathematics that involves data collection, analysis, and presentation.
• It has two main branches: Descriptive Statistics and Inferential Statistics.

Key Concepts

• Population: the entire group of individuals that a researcher wants to study.
• Sample: a small group of individuals selected from a population, usually to describe the population.
• Variable: a characteristic or condition that is not constant and can change or have different values for different individuals.

Types of Variables

• Quantitative Variable: a variable where the data represent amounts.
• Discrete Variable: a type of quantitative variable that can be counted in a finite amount of time.
• Continuous Variable: a type of quantitative variable that can take an uncountable set of values.

Levels of Measurement

• Nominal Level: a level of measurement with no order or numeric value (e.g., gender, race, eye color).
• Ordinal Level: a level of measurement with order, but no numeric value (e.g., ranking).
• Interval Level: a level of measurement with ordered numbers that have meaningful divisions, but no absolute zero.
• Ratio Level: a level of measurement with an absolute zero and all characteristics of an interval scale.

Descriptive Statistics

• Frequency Distributions: a way of presenting data to make patterns easier to see.
• Class Interval, Class Limit, Class Frequency, Class Size, and Class Mark: components of a frequency distribution.

Measures of Central Tendency

• Mean: the most commonly used measure of central tendency.
• Median: used when the mean might not be representative of a distribution.
• Mode: the score in a distribution that occurs with the greatest frequency.

Measures of Variability

• Range: the distance covered by the scores in a distribution.
• Standard Deviation: a measure of the standard, or average, distance from the mean.
• Variance: the average distance from the mean.

Hypothesis Testing

• Null Hypothesis (Ho): there is no change, no difference, or no relationship.
• Alternative Hypothesis (Ha): there is a change, a difference, or a relationship.
• Alpha Level (level of significance): a probability value used to define the concept of "very unlikely" in a hypothesis test.
• Critical Region: composed of extreme sample values that are very unlikely to be obtained if the null hypothesis is true.
• Directional Hypothesis Test (one-tailed): a test that makes a specific prediction about the direction of the treatment.
• Non-Directional Hypothesis Test (two-tailed): a standard hypothesis testing procedure.

T-Statistics

• T-Test: used to test hypotheses about an unknown population.
• Assumptions: population mean is known, but the population standard deviation(s) is not known; sample size is less than 30.
• Types of T-Tests:
  • Independent Samples T-Test (two-sample): two distinct groups are being measured.
  • One-Sample T-Test: compares a sample mean to a population mean.
  • Paired T-Test (dependent means): same group measured twice.

Analysis of Variance (ANOVA)

• One-Way ANOVA: compares the differences in the means of two or more groups.
• Factor: the variable that distinguishes the groups.
• Levels of Factor: individual conditions or values that define the factor.
• Levene's Statistic: assumes equal variances or not.
• Post-hoc test: identifies exactly the comparisons that have significant differences.

Correlation

• Correlation Coefficient: measures the degree of relationship between two variables.
• Magnitude: strength of the relationship, determined by the correlation coefficient.
• Scatter Plot (Scattergram): graphically represents a correlation coefficient.
• Positive Relationship: an increase in one variable is related to an increase in the other.
• Negative Relationship: an increase in one variable is related to a decrease in the other.