Statistics and Scientific Methods Quiz

Statistics and Scientific Methods

• Statistics is the process of identifying patterns in data, finding out about patterns in the world using real data.
• Deterministic models assume no randomness; outcomes are always the same with identical conditions.
• Probabilistic models incorporate randomness, resulting in varied outcomes even with consistent starting points.
• Unsystematic variation arises from unknown, uncontrolled factors (e.g., participant mood, intelligence, education). Random assignment of participants can limit this variation.
• Systematic variation results from manipulations of the independent variable.
• Descriptive statistics summarize data characteristics (central tendency, variability, frequency).
• Inferential statistics uses sample data to estimate larger population characteristics.

Scientific Methods

• Experiments investigate cause-and-effect relationships by manipulating an independent variable (IV) and measuring the dependent variable (DV), controlling extraneous variables. This requires control and treatment groups to avoid confounding variables.
• Quasi-experiments explore cause-and-effect but lack random assignment of participants to groups. Researchers have less control over conditions.
• Correlational methods examine the association between variables without manipulation or intervention; variables are only observed.

Variables

• Categorical variables classify data into distinct groups.
  • Nominal variables have no inherent order (e.g., hair color).
  • Ordinal variables have a meaningful order (e.g., educational level; discrete variables).
• Continuous variables can take on any value along a scale.
  • Interval scales indicate equal differences but lack a meaningful zero point (e.g., temperature).
  • Ratio scales have equal intervals and a meaningful zero point (e.g., height).
• Independent variable (IV) is the manipulated factor in an experiment, expected to affect the dependent variable (DV).
• Dependent variable (DV) is the measured outcome.

Experimental Designs

• Between-subjects design: different groups experience different conditions.
  • Weaknesses: participant variability, time-consuming.
  • Strengths: avoids practice effects, demand characteristics, and only has one condition.
• Within-subjects design: one group experiences all conditions.
  • Weaknesses: order effects, carryover effects.
  • Strengths: fewer participants, less participant variability.
• Matched-pairs design: participants matched based on a characteristic, each experiences different conditions.
  • Strengths: reduces individual differences.
  • Weaknesses: time-consuming, smaller sample size.
• Extraneous variables are uncontrolled variables potentially affecting results.
• Confounding variables systematically influence both the IV and DV.

Hypothesis Testing

• Hypothesis: a testable prediction.
• Alternative hypothesis: predicts a difference between groups.
• Null hypothesis: predicts no difference between groups.
• P-value: probability of observing results by chance.
  • A low p-value (<0.05) suggests the null hypothesis is likely false.
• Type I error: incorrectly rejecting the null hypothesis (false positive).
• Type II error: incorrectly accepting the null hypothesis (false negative).
• Validity: accuracy of a test in measuring what it intends to measure.
  • Internal validity: related to order, practice, boredom effects within an experiment.
  • Ecological validity: generalizability to real-world situations.
  • Demand characteristics: influence from participants' expectations.
  • Reliability: consistency of a measure, including inter-rater reliability and test-retest.

Descriptive Statistics

• Central tendency: average value; measures central position.
  • Mode: most frequent observation; can be used with categorical data.
  • Median: middle observation; unaffected by extreme values; suitable for ordinal, interval, and ratio data.
  • Mean: average of all values; uses all data; sensitive to extreme values.
• Measures of spread: variability around a central tendency.
  • Range: difference between highest and lowest values; sensitive to outliers.
  • Interquartile range (IQR): spread of the middle 50% of data; robust to outliers.
  • Variance: average squared deviation from the mean; useful with normal distributions; sensitive to outliers; dimensionless.
  • Standard deviation: square root of variance; same units as the original data; higher deviation indicates greater variability.
• Standard Error of the Mean (SEM): measure of how precisely a sample mean estimates the population mean.
• Z-scores: measure of how many standard deviations a data point falls from the mean.
• Normal distribution: symmetrical bell-shaped curve; mean=median=mode; common in many natural phenomena.
• Skewed distribution: majority of scores on one side

Statistical Tests

• Kolmogorov-Smirnov test: tests if data is normally distributed.
• Levene's test: tests for equality of variances between groups.

Correlation

• Correlation: measures the association between two variables.
• Covariance: measures the relationship between two random variables, influenced by measurement units.
• Correlation coefficient: indicates magnitude (-1 to +1) and direction of relationship.
  • Pearson's correlation: uses continuous variables; assumes a linear relationship.
  • Spearman's rank correlation: uses ranked data; good for ordinal data.
• Variance explained: squared correlation coefficient; percentage of variation in one variable explained by the other.
• Partial correlation: examines association controlling for other variables.
• Zero-order correlation: simple bivariate correlation.
• First-order/second-order partial correlation: examines relationships with one or more variables held constant.

Regression

• Regression analysis: predicts a variable (dependent variable) from other variables (independent variables).
  • Linear regression: predicts a dependent variable from one independent variable using a straight line.
  • Multiple regression: predicts a dependent variable from multiple independent variables.
• Reporting regression in APA: includes R-squared, F-statistic, p-value, t-tests for each predictor, unstandardized estimates (coefficients), and explanations of coefficients; describes how changes in IVs affect the DV. Explains significant relationships.