Group Presentation Chapter 4_ Statistics PDF

CHAPTER 4: Statistics What Test Scores Mean Jessica James & Briana Ross  We will learn: Basic concepts needed to understand statistics Scales of measurements, distributions, measures of central tendency, measures of dispersions, and measure of relation...

CHAPTER 4: Statistics What Test Scores Mean Jessica James & Briana Ross  We will learn: Basic concepts needed to understand statistics Scales of measurements, distributions, measures of central tendency, measures of dispersions, and measure of relationship.  4-1: Descriptive Statistics Used to describe or summarize data. Scores on: several on one individual one score on several individuals several scores on several individuals Basic Statistical Notation Common symbols seen in statistics: Page 36 Scales of Measurement Data can be summarized in different ways depending on the scale the scores are expressed Nominal Ordinal Ratio Equal- Orders values Has an absolute Interval Classifies data Differences into distinct from worse to zero which better allows for between values categories Values show an meaningful are consistent without any order. order but not comparisons and meaningful Ex. Types of fruit, no clearly measured No absolute zero specific order Ex. Ex. Height: You can Ex. Temp in degrees C say that 100 lbs is Difference between each Movie ratings, good 2x heavier than 50 value = same movie to bad movie Zero does not mean no lbs, zero meaning temp no weight at all  Characteristics of Distributions Distribution's Shape: Two-dimensional plot of scores by the # of people earning each score Four Characteristics: Symmetrical Negatively Skewed: Mean: Average of scores Distribution When distribution is “easy” These data points from left Variance: Average distance Many students earn high and right ”mirror each between ach score other” scores, few earn low scores Example: Normal Skew: The asymmetry of a Positively Skewed: Distribution distribution Important for interpreting student assessment data When distribution is difficult Kurotosis: The peak of a as it shows performance Many students earn low curve, where is rises and falls levels. scores while few earn high Page 40 Average Scores How a group as a whole performed. Mode: Median: Mean: Score most Point above which Average of scores frequently obtained are 50% of test *Most important Distributions can takers, & below for use in have 2 modes or which are 50% of assessment* more than 2 test takers. Sum of scores (∑X) divided by the # of score (N); it’s symbol is X. Mean = X = ∑X/N Measures of Dispersion Tells us how scores are spread above and below the average score. Based off of three measures: Range: Distance between the extremes of distributions Usually the highest score minus the lowest score *Variance: Describes dispersion of a set of scores around the mean using the equation: *Standard Deviation: Describes the dispersion of a set of scores around the mean Calculated as the positive square root of the variance Used as a unit of measurement  Correlation Quantifies relationships between variables. Correlation Coefficients: Numerical indexes of the relationship between two variables (Multiple correlations = three or more variables) Crucial to assessment Tells us which variables go together, what chances in a variable are reflected by changes in the other variable Expressed as a decimal value with a + or - sign + indicates the relationship (low/high values) Used to estimate the amount of error associated w/ measurement Value range:.00 to +1.00 or =1.00 (Indicates magnitude of relationship)  4-2: Scoring Student Performance Types of scoring, scoring systems, and implications of instruction. Covered in this section will be: Subjective and objective scoring,summarization of student performance and how to intercept test scores. Subjective vs. Objective Scoring Subjective: Objective: Based on personal judgement. Based on solid clear, standardized Influenced by biases, criteria. experiences, and perspectives. Rather than subjective, no matter This type of scoring can be who proctors these tests scoring is used in essays, presentations, based on the criteria represented. portfolios and performances. VS Examples include:multiple choice, If using subjective scoring and fill in the blank. It's either the because of inconsistencies, answer is right or wrong. the use of rubrics that is Although it gets rid of biases, detailed, clear and concise others may argue that this limits can help support expectation critical thinking skills and deeper and scoring. thinking as a whole. Summarizing Student Performance Accuracy: Criterion-referenced & formative assessments can be used to measure accuracy. Setting a baseline for accuracy allows educators to track improvement. Fluency: We often see fluency assessed through timed tests and repeated practice. Incorporating fluency practice in your everyday instruction can help a students ability to engage in complex tasks. Applications in real life classroom for this example: Running records Retention: Assessed through follow up tests and assessments without practice. Sees if student have retained a skill previously learned. To gauge long term retention, educators should enforce cummalive assessments to help created targeted instructional plans and intervention. Interpreting Test Performance Criterion-Referenced Standards-Referenced Norm-Referenced Interpretations: Interpretations: Interpretations: Assesses if a student is Assess student performance Compares a students meeting specific against academic standards. performance to a performance criteria or Can be useful for normative group. learning objectives. accountability purposes Helps educators Helps educators determine if when helping students understand general students have met the determine if they are meeting performance trends. learning objective. state standards Can help identify strengths Helps know if the students and weaknesses. are meeting expected learning outcomes. Interpreting Test Performance Developmental Scores: These scores help provide an estimate of a students skill level. This helps track progress over time. With this, educators can identify delays and plan appropriate intervention. Scores of Relative Standing: This indicates how well a student performed in comparison to their peers. Although this can provide abilities of students, it doesn't necessarily reflect that students can master these skills. 4-3: Normative Sample Group of persons used as a standard to compare and evaluate performance of others on a specific assessment. Provides understanding on an individuals performance and then compares to others in the same age , grader ability group. Important Characteristics Gender: Differences in gender can effect a student’s test score Age: This score is used to compare the performance of children who are the same age with one another. Grade in School: This score is used to compare the performance of children who are the same grade with one another. Acculturation of Parents: Understanding of language, history, values, & social conventions of society, can be hard to define or measure precisely Racial Identity: Understanding that these differences must be considered in developing norm groups Geography: Differences in individuals living in different regions Intelligence: Related to # of variables that are considered in psychoeducational assessment Other Characteristics Norms are plural: Tests use multiple normative samples (Norm Sample) Each norm group should be large enough to ensure stability and represent diverse characteristics Min of 100 participants = accurate representation of population Age of Norms: Norm sample must reflect current population abilities, which change over time Norm-referenced achievement tests can become outdated (5-7 years) where students may score above average, the norms are no longer accurately representing population Norm samples should be updated every 7-15 years Specialized Norms: National norms assess students overall intellectual, perceptual, linguistic, or physical development Local norms help evaluate how a student is benefiting from their education  Chapter Comprehension Questions 1.Compare and contrast the two scales of measurement most commonly used in educational and psychological measurement. In the book the authors focus on the nominal scale and the ordinal scale. A nominal scale categorizes data without quantitative value. This is generally used in demographic data collection. An ordinal scale also categorizes data but provides a rank order. This can be used in assessing students satisfaction, levels of achievement etc, where ranking is important. Nominal is best suited for classification without a specific order and ordinal is best suited for classification with a specific order (ranking). 2.Explain the following terms: mean, median, mode, variance, skew, and correlation coefficient. The terms mean, median, mode, variance, skew, and correlation coefficient are important for understanding data. The mean is the average of a group of numbers. The median is the middle number when the numbers are arranged in order; if there’s an even amount, it’s the average of the two middle numbers. The mode is the number that appears most often in a set. Variance tells us how spread out the numbers are from the average; it shows how much the numbers differ from one another. Skew describes the shape of the data distribution: if the data is negatively skewed, it has a long tail on the left side, and if positively skewed, it has a long tail on the right side. The correlation coefficient measures how strongly two things are related to each other, ranging from -1 to 1. A score close to 1 means they move in the same direction, while a score near -1 means they move in opposite directions. A score around 0 suggests there’s no real relationship. These are important because it helps analyze and understand patterns in data.  Chapter Comprehension Questions 3.Explain the statistical meaning of the following scores: percentile, z score, IQ, NCE, age equivalent, and grade equivalent. Percentile: Indicates the percentage of scores below a specific score (e.g., 80th percentile means better than 80% of the group). Z Score: Measures how many standard deviations a score is from the mean (e.g., a z score of 0 is at the mean). IQ (Intelligence Quotient): Standardized score reflecting cognitive ability, with a mean of 100 and a standard deviation of 15. NCE (Normal Curve Equivalent): Ranges from 1 to 99, with 50 as the median, allowing for comparisons in a normal distribution. Age Equivalent: Indicates the age at which a typical student would achieve a certain score (e.g., a 7-year-old scoring at a 9-year-old level). Grade Equivalent: Reflects the grade level at which a student’s performance matches that of typical students (e.g., 5.2 means performing like a fifth grader in the second month). 4.Why is the acculturation of the parents of students in normative samples i mportant? The acculturation of parents in normative samples is crucial because it influences their values, educational expectations, language proficiency, and social support networks, all of which impact their children's development and academic performance. Understanding parents' acculturation helps ensure that assessments are interpreted within the right cultural context, making benchmarks more valid and relevant. Additionally, parental acculturation can affect psychosocial factors that influence children's well-being, highlighting the need for a holistic approach in educational assessments  Exit Ticket What did we learn today? Let’s play a kahoot!  References: Salvia, John, et al. Assessment in Special and Inclusive Education. Cengage Learning, 2017.