Hypothesis Testing, Charts, and Variables

• Alternative hypothesis predicts an effect, indicating experimental manipulation influences variables.

Bar chart

• Graph plotting a summary statistic (usually the mean) on the y-axis.
• Categorical variable is plotted on the x-axis representing groups, times, or conditions.
• The mean for each category is represented by a bar, with different colors indicating levels of a second categorical variable.
• Between-groups design is another term for independent design.
• Between-subjects design is another term for independent design.
• Bimodal describes a distribution with two modes.

Binary Variable

• Categorical variable with only two mutually exclusive categories like dead or alive.

Biserial Correlation

• Measures relationship strength between two variables when one is dichotomous.
• Used when one variable has a continuous dichotomy (underlying continuum in categories).

Bivariate Correlation

• Correlation between two variables.

Bonferroni Correction

• Correction applied to the α-level to control the overall Type I error rate in multiple significance tests.
• Each test uses a significance criterion of α-level (typically 0.05) divided by the number of tests.
• It is a simple but strict correction, especially when performing many tests.

Boredom Effect

• Performance in tasks may be influenced negatively by boredom or lack of concentration.
• It occurs when there are many tasks or the task is lengthy.

Boxplot (Box-Whisker Diagram)

• Graphical representation of key characteristics in a dataset.
• The median is at the center, with a box indicating the interquartile range (middle 50% of observations).
• Whiskers extend to the highest and lowest extreme scores.

Categorical Variable

• Variable made up of categories of objects/entities.
• Example: university attendance, since students are in distinct categories.

Central Limit Theorem

• With large samples (over 30), the sampling distribution becomes a normal distribution.
• This occurs regardless of the population's shape.
• For small samples, the t-distribution better approximates the shape of the sampling distribution.
• The standard deviation of the sampling distribution (standard error of the sample mean) equals the sample standard deviation (s) divided by the square root of the sample size (N).

Central Tendency

• Generic term describing the center of a frequency distribution.
• Measured by mean, mode, or median.
• Chartjunk is superfluous material that distracts on a graph.

Coefficient of Determination

• Proportion of variance in one variable explained by a second variable.
• It is Pearson's correlation coefficient squared.

Concurrent Validity

• Form of criterion validity.
• Scores from an instrument correspond to concurrently recorded external measures conceptually related to the measured construct.

Confidence Interval

• Range of values around a sample statistic likely to contain the true population parameter.
• E.g., a 95% confidence interval means there's a 95% probability of containing the true value, while a 5% probability it won't.

Confounding Variable

• Variable other than the predictor variables that may affect an outcome variable.
• It may or may not have been measured.

Content Validity

• Evidence that a test's content corresponds to the content of the construct it aims to cover.

Continuous Variable

• Variable that can be measured to any level of precision.
• Example: Time

Correlational Research

• Measures the strength of association between two variables.
• Examples include Pearson's, Spearman's, and Kendall's tau correlation coefficients.

Counterbalancing

• Systematically varying the order of experimental conditions to remove bias.
• With two conditions (A and B), half do A then B, and the other half do B then A.
• This removes systematic bias from practice or boredom effects.

Covariance

• Measure of the average relationship between two variables.
• Calculated as the average cross-product deviation (cross-product divided by one less than the number of observations).

Criterion Validity

• Evidence that scores from an instrument correspond with external measures conceptually related to the measured construct
• Can be concurrent or predictive.

Cross-Product Deviations

• Measure of the total relationship between two variables.
• Calculated by multiplying one variable's deviation from its mean by the other variable's deviation from its mean.

Cross-Sectional Research

• Observing variables naturally at a single time point without interference
• In psychology, it involves data from people at different ages, with different individuals at each age.

Degrees of Freedom

• Number of entities free to vary when estimating a statistical parameter.
• Affects significance tests for statistics like F, t, and chi-square, determining the probability distribution's form.

Density Plot

• Similar to a histogram, but it displays each individual score as a dot.
• Shows the shape of a distribution of scores.

Dependent Variable

• Another term for outcome variable, associated with experimental methodology.
• It is not manipulated, and its value depends on manipulated variables.

Deviance

• Difference between the observed variable value and its predicted value from a statistical model.

Discrete Variable

• Variable that can only take on certain values, usually whole numbers.

Ecological Validity

• Results of a study, experiment, or test can be applied and allow inferences to real-world settings.

Error Bar Chart

• Graphical representation of a set of observations mean with the 95% confidence interval.
• The mean is shown as a shape with a line protruding (upwards, downwards or both) from it.
• Error bars can use standard error or standard deviation instead of the 95% confidence interval.
• Experimental hypothesis is a synonym for alternative hypothesis.

Experimental Research

• Manipulates one or more variables to observe effects on an outcome variable.
• Allows cause-and-effect statements, unlike cross-sectional or correlational research.

Experimentwise Error Rate

• Probability of making a Type I error in an experiment with one or more statistical comparisons.
• Assume the null hypothesis is true in each case.

Falsification

• Act of disproving a hypothesis.

Familywise Error Rate

• Probability of making a Type I error in any family of tests when the null hypothesis is true.
• The family of tests is tests conducted on the same data set and addressing the same empirical question.

Fit

• Degree to which a statistical model accurately represents observed data.

Frequency Distribution

• Graph plotting observation values on the horizontal axis and their frequency on the vertical axis (histogram).

Hypothesis

• Proposed explanation for a phenomenon or observation.
• Informed by theory, testable via operationalized predictions.

Independent Design

• Experimental design using different organisms in different treatment conditions.
• Results are independent (between-groups or between-subjects designs).

Independent Variable

• Another term for predictor variable, associated with experimental methodology.
• Manipulated by the experimenter, does not depend on other variables.

Interquartile Range

• Range within which the middle 50% of ordered observations fall.
• It is the difference between the upper and lower quartile values.
• Interval variable has equal intervals along its scale.

Journal

• In academia, journals contain articles reporting new data, theories, or reviews by scientists.

Kendall's Tau

• Non-parametric correlation coefficient similar to Spearman's, best for small datasets with tied ranks.

Kurtosis

• Measures the degree to which scores cluster in the tails of a frequency distribution.
• Positive kurtosis (leptokurtic, kurtosis > 0) means too many scores in the tails and a peaked distribution.
• Negative kurtosis (platykurtic, kurtosis < 0) means too few scores in the tails and a flat distribution.
• Leptokurtic refers to kurtosis.

Level of Measurement

• Relationship between what is measured and the numbers on a scale.

Line Chart

• Graph plotting a summary statistic (usually the mean) on the y-axis with the categorical variable on the x-axis,
• Mean for each category is shown by a symbol, connected with a line.
• Linear model is an equation of the form Y = BX + E.
• Y is the vector of outcome variable scores, B represents the b-values, X the predictor variables, and E the error terms.

Longitudinal Research

• Observing variables naturally over multiple time points without interference.

Lower Quartile

• Value that cuts off the lowest 25% of the data.
• Median of the lower half of ordered scores.

Mean

• Simple statistical model of the center of a distribution.
• A hypothetical estimate of the 'typical' score.

Measurement Error

• Discrepancy between numbers representing what is measured and the actual value.

Median

• The middle score of a set of ordered observations.
• Average of the two scores either side when there is an even number of observations

Method of Least Squares

• Estimating parameters (like mean or regression coefficient) by minimizing the sum of squared errors.

Mode

• Most frequently occurring score in a dataset.
• Multimodal describes a distribution with more than two modes.
• Nominal variable: Numbers represent names only.
• Nonile is a type of quantile dividing data into nine equal parts, used in educational research.

Normal Distribution

• Probability distribution known to have specific properties.
• It is perfectly symmetrical with a skew of 0, and a kurtosis of 0.

Null Hypothesis

• Reverse of the experimental hypothesis, suggesting the prediction is wrong and no effect exists.

One-Tailed Test

• Test of a directional hypothesis.

Ordinal Variable

• Data tells the order and also that things have occurred.
• Ordinary least squares is a regression method estimating model parameters using least squares.

Outcome Variable

• Variable being predicted from one or more predictor variables.

Parameter

• Model component describing relations between variables in the population.
• Constants representing fundamental truths, estimated from sample data.
• Part correlation is another name for semi-partial correlation.

Pearson Correlation Coefficient

• Standardized measure of linear relationship strength between two variables.
• Can range from -1 (perfect negative) to +1 (perfect positive), with 0 indicating no relationship.
• Percentile is a quantile dividing data into 100 equal parts.
• Platykurtic refers to kurtosis.

Point-Biserial Correlation

• Measures relationship strength when one variable is dichotomous being a discrete or true dichotomy.

Population

• Collection of units (people, objects, etc.) to generalize findings.
• Positive skew refers to skew.

Power

• Ability of a test to detect an effect of a particular size.

Practice Effect

• Performance influenced by repeating a task, due to familiarity.
• Predictive validity is a form of criterion validity where scores predict external measures recorded in the future.

Predictor Variable

• Variable to predict an outcome variable from a placed into a statistical model.

Probability Density Function (PDF)

• Function describing the probability of a random variable taking a certain value.

Probability Distribution

• Curve describing the idealized frequency distribution.
• It ascertains the change of the probability with which specific values of a variable will occur.
• Qualitative methods extrapolate evidence for a theory from non-numeric data (e.g., from interviews).

Quantile

• Values that split a dataset into equal portions; quartiles and percentiles are special cases.

Quantitative Methods

• Numeric evidence for a theory through measure of variables that produce numeric outcomes.
• The Quartile is a generic term for values cutting a data set into 4 equal parts.

Randomization

• Doing things unsystematically or randomly, especially assigning participants to treatments.

Range

• Value of the smallest score subtracted from the highest score.
• Ratio variable is an interval variable with meaningful ratios.

Regression Line

• Line on a scatterplot representing regression model.
• Reliability is the consistent results under the same conditions.

Repeated-Measures Design

• Experimental design where the same participants undergo all treatment conditions.
• Resulting data is related.

Sample

• Smaller collection of units to determine truths about a certain population.

Sampling Distribution

• Probability distribution of a statistic.
• If we take lots of samples from the population and calculate the statistic of interest we could create a frequency distribution of the values we get.

Sampling Variation

• Extent to which a statistic varies in samples from the same population.

Scatterplot

• Graph plotting values of one variable against the corresponding values of another.
• Second quartile is another name for the median.

Semi-Partial Correlation

• Relationship between two variables after adjusting for the effects of additional variables on one.

Skew

• Measure of the symmetry of a frequency distribution.
• Symmetrical distributions have a skew of 0.
• If frequent scores cluster at the lower end with the tail points towards the higher or more positive scores, skew will be positive.
• If frequent scores cluster at the higher end with the tail points towards the lower or more negative scores, skew will be negative.

Spearman's Correlation Coefficient

• Standardized correlation measure, does not rely on parametric tests.
• Calculated as Pearson's correlation on ranked data.

Standard Deviation

• Estimate of average variability in same units as original data.
• Square root of the variance.

Standard Error

• Standard deviation of the sampling distribution of a statistic that expresses the mean.
• The standard error indicates statistic variability across samples from the same population.

Standardization

• Converting a variable into standard deviation units (z-scores).
• Allows data comparison across different units.

Systematic Variation

• Variation due to genuine effects, explainable by the fitted model.

Tertium Quid

• An apparent relationship is caused by a third variable affecting both.

Test Statistic

• Test statistic with a known probability distribution (t-distribution).
• Used to test whether a b-value is significantly different from zero (linear model context).
• Test-retest reliability is the consistent results when the same entities are tested at different times.

Theory

• Well-substantiated principle explaining known findings and generating new hypotheses.
• Two-tailed tests test non-directional hypotheses.

Type I error

• Occurs when there is a genuine effect when there isn't.

Type II error

• Occurs when the effect not in the population when it really is.

Unsystematic Variance

• Variation because of differing natural causes.
• Upper quartile refers to a quarter of the values.

Validity

• Study measures what it sets to conceptually.

Variables

• Measured and differing across entities or time.

Variance

• Estimate of average variability (spread) in a dataset.
• Within-subject design is another name for a repeated-measures design.

Z-Scores

• Value of an observation expressed in standard deviation units.
• Z-score is the value of an observation expressed in standard deviation units.
• Alpha level signifies probability of type I error.
• Beta Level signifies type II error.