Tiêu đề 02 PsyAs - Statistics Refresher.pdf ✅

02 – Statistics Refresher PSYAS | 2024 - 2025 | NOT FOR SALE OUTLINE 1. Descriptive Statistics a. Primary Scales of Measurement b. Measures of Central Tendency c. Measures of Variability d. Measures of Location e. Skewness f. Kurtosis g. The Normal Curve and Standard Scores 2. Inferential Statistics a. Hypothesis Testing b. Types of Statistical Tests c. Measures of Bivariate Correlation d. Measures of Prediction e. Chi-Squared Tests f. Comparison of 2 Groups g. Comparison of > 2 Groups DESCRIPTIVE STATISTICS ★ Scale – set of numbers/symbols whose properties model empirical properties of the objects to which the numbers are assigned ○ Continuous Scale – exists when it is theoretically possible to divide any of the values of the scale ○ Discrete Scale – used to measure a discrete variable ★ Measurement – act of assigning numbers or symbols to characteristics of things according to rules ○ Rules – guidelines for representing the magnitude PROPERTIES OF SCALES Magnitude Property of “moreness” Equal Intervals Difference between two points at any place on the scale has the same meaning as the difference between two other points that differ by the same number of scale units Absolute Zero Obtained when nothing of the property being measured exists PRIMARY SCALES OF MEASUREMENT ● Nominal: categorical data set; involve frequency tables (ex. IQ Classifications) ● Ordinal: categorization w/ magnitude; involves ranking (ex. IQ Scores) ● Interval: continuous data set; concept of equal intervals (ex. Statistical Analysis of IQ Scores) ● Ratio: has an absolute 0 (ex. Kelvin) Nominal Ordinal Interval Ratio Category Names ✔ ✔ ✔ ✔ Meaningful Order ✔ ✔ ✔ Equal Distance ✔ ✔ True Zero & Ratios ✔ MEASURES OF CENTRAL TENDENCY Central Tendency – summary measure that attempts to describe a whole set of data with a single value that represents the middle or center of its distribution ● Mean: average score ● Median: midpoint ● Mode: most frequently occuring TYPE OF DATA MEASURE USED Nominal Mode Ordinal Median Interval / Ratio (Skewed) Median Interval / Ratio Mean MEASURES OF VARIABILITY Variability – summary measure that attempts to describe a whole set of data based on how spread out the scores are in a distribution ● Range: the difference between the lowest and highest score in a data set Range = Maximum − Minimum ● Interquartile Range: the difference between the 3rd and 1st quartile IQR = Q3 − Q1 where: Q1 – first quartile (25th percentile) Q3 – third quartile (75th percentile) ● Semi-Interquartile Range: the interquartile range divided by 2 SIQR = Q3 − Q1 2 ● Standard Deviation: distance of the score from the mean 1 | @studywithky
σ = Σ(Xi − x̄) 2 N MEASURES OF LOCATION Location – summary measure that attempts to describe a whole set of data based on its location in the distribution ● Percentile: used to display position or rank Percentile = # of students beaten total # of examinees x 100 ○ Percentage: means of comparing quantities Percentage = # of obtained score total # of items x 100 ● Quartile: the set of values which has three points dividing the data set into four identical parts Quartile = ( p 4 ) x (N + 1) ● Decile: a quantile that groups the data into 10 equal frequencies Decile = ( d 10 ) x (N + 1) SKEWNESS Skewness – the degree of asymmetry observed in a probability distribution; imbalance in the distribution ● Univariate: between -3 to +3 ● Positively-Skewed: its tail is more pronounced on the right side than on the left; represents a difficult test ● Negatively-Skewed: ts tail is more pronounced on the left side than on the right; represents an easy test KURTOSIS Kurtosis – a measure of the tailedness of a distribution; how often outliers occur ● Univariate: between -10 to +10 ● Leptokurtic: high peak ● Mesokurtic: normal peak ● Platykurtic: flat peak THE NORMAL CURVE AND STANDARD SCORES Standard Scores ● Z-Score: Mean = 0 SD = 1 ● t-Score: Mean = 50 SD = 10 ● Stanine: Mean = 5 SD = 2 ● STEN: Mean = 5.5 SD = 2 ● IQ Scores: Mean = 100 SD = 15 Calculating the Z-Score z = x − x̄ SD Calculating Other Standard Scores X = z(SD) + x̄ INFERENTIAL STATISTICS HYPOTHESIS TESTING 2 | @studywithky

Prediction – statistical test that forecast future outcomes; cause and effect Point-Biserial Correlation ● Special type of correlation that can measure causality ● (X): continuous data ● (Y): genuinely / true dichotomous Biserial Correlation ● Special type of correlation that can measure causality ● (X): continuous data ● (Y): artificially dichotomous Logistic Regression ● Classification method that estimates the probability of an event occurring ● (X): continuous data ● (Y): nominal data Multinomial Regression ● Classification method that generalizes logistic regression to multiclass problems ● (X): ≥ 2 continuous data ● (Y): continuous data Simple Linear Regression ● Involves predicting the value of a dependent variable based on an independent variable ● (X): 1 continuous data ● (Y): continuous data Multiple Regression ● Involves predicting the value of a dependent variable based on ≥ 2 independent variables ● (X): ≥ 2 continuous data ● (Y): continuous data Ordinal Regression ● Used to predict behavior of ordinal level dependent variables with a set of independent variables ● (X): ≥ 2 continuous data ● (Y): ordinal data Interpreting Regression Coefficient ★ [R-squared value in percentage] in the total variance of [Y] is significantly accounted for by [X] ★ Example: ○ X = Anxiety Level R-squared = 0.8729 ○ Y = Exam Score p-Value = 0.001 ○ 87.29% in the total variance of the exam score is significantly accounted for by the anxiety level CHI-SQUARED TESTS Chi-Squared Test – primarily used to examine whether two categorical variables are independent in influencing the test statistic; assumption tests; mainly for nominal data sets GOODNESS OF FIT TEST OF INDEPENDENCE What is measures Difference Difference + relationship Type of data Nominal data Nominal data # of variables 1 variable with ≥ 2 levels 2 variables with ≥ 2 categories Example What are the free TV network preferences of college students? What are the free TV network preferences of college students according to sex? COMPARISON OF 2 GROUPS 4 | @studywithky