Cohen_10e_chapter_3

Focus on the essential components of statistics relevant for learning and application.
Understanding the legal restrictions regarding the usage of educational material provided by McGraw Hill.

Continuous Scales: Values can take any real number within a specified range.
Discrete Scales: Designed for measuring discrete variables.
Error: The impact of unmeasured factors influencing test scores.

Nominal Scales: Categorize data without any order; subjects must fit exclusive categories.
Ordinal Scales: Similar to nominal scales but allow for ranking.
Interval Scales: Have equal intervals between values, without a true zero point.
Ratio Scales: Similar to interval scales but have an absolute zero, allowing for meaningful ratios.
Psychological measurement relies on ordinal and interval measures but needs caution due to potential inequality in intervals (Kerlinger).

Example: Frequency distribution table illustrates scores alongside their frequency.

Class intervals provide a summarized view rather than exact scores, aiding in understanding distributions.
Example: Groupings and their frequencies are showcased.

Histogram: Displays frequency using contiguous rectangles representing class intervals.
Bar Graph: Shows frequency indicators using bars for categorical data.
Frequency Polygon: Connects frequency points across test scores to visualize distribution.

Mean: Average of all scores.
Median: Middle value when scores are ordered.
Mode: Most frequent score, which can lead to bimodal distributions when two modes exist.

Assess how scores spread within a distribution.
Range: Difference between highest and lowest scores.
Interquartile Range: Difference between first and third quartiles.
Standard Deviation: Indicates dispersion of scores around the mean; calculated as the square root of variance.
Kurtosis: Measures the peakness of a distribution.

Symmetrical, bell-shaped curve representing normal distributions.
Standard deviations define the areas under the curve, enabling comparisons of distributions.

Z Score: Represents how many standard deviations a score is from the mean.
T Scores: Standard score with a mean of 50 and standard deviation of 10.
Stanine: Scale (mean of 5, SD of 2) divided into nine units: useful for educational assessments.
Normalization: Adjusting skewed distributions to approximate a normal distribution.

Correlation Coefficient: Indicates strength and direction of relationships between variables.
Positive Correlation: Both variables move in the same direction.
Negative Correlation: One variable increases while the other decreases.
Correlations do not imply causation.

Scatterplot: Visual representation of relation between two variables.
Identifies both positive and negative relationships and their strengths via clustering.

Unusual data points that are significantly different from others can skew correlation analysis.
Restriction of Range: Limits on data input can weaken correlation coefficients.

Combines data from multiple studies to provide a comprehensive estimate of effect sizes, often represented by correlation coefficients.