EDU 533 P3 PDF - Graphs and Data Presentation

Sas #19 Organization of Data Using Graphs: Presenting Graphical Data; Variations in shapes in frequency distribution Once you have collected data from observation sessions, it is important to organize the information in such a way that it is easy to interpret. It can be difficult to see patt...

Sas #19 Organization of Data Using Graphs: Presenting Graphical Data; Variations in shapes in frequency distribution Once you have collected data from observation sessions, it is important to organize the information in such a way that it is easy to interpret. It can be difficult to see patterns by simply looking at long lists of numbers or reading data collection sheets across different days. GRAPHS - can provide quick and easy visual summaries that allow teachers to determine patterns of behavior, evaluate the results of new teaching strategies, and establish whether or not interventions are having the desired effects. This information can then be used to provide students with feedback on their performance. DIFFERENT TYPES OF GRAPHS 1. LINE GRAPH - The most common type of graph used to evaluate behavioral data. - A line graph shows individual data points connected by line, creating a path. Over time, this path can show a visual pattern that helps you evaluate the overall directions of a behavior. 2. BAR GRAPH - Another common graph often used when portions of a whole are being represented or when reporting a percentage. - The bar graph focuses on the height of the data rather than the trend in the data, and is most often used when non-consecutive data points are being evaluated. - This is a particularly useful method when comparing information across individuals, settings, or situations. 3. HISTOGRAM - is a type of graph appropriate for quantitative data such as test scores. This graph consists of a column-each has a base that represents one class interval, and its height represents the number of observations or simply the frequency in the class interval. 4. FREQUENCY POLYGON - is also used for quantitative data, and it is one of the most commonly used methods in presenting test scores. It is the line graph of a frequency polygon. - Very similar to histogram but instead of bars it uses lines to compare sets of test data in the same axes. - You can manually construct a frequency polygon manually using the histogram using these steps: 1. Locate the midpoint on the top of each bar, Bear in mind that the height of each bar represents the frequency in each class interval. As such, that point in the middle of each bar is actually the midpoint of that class interval. 2. Draw a line to connect all the midpoints in consecutive order. 3. The line graph is an estimate of the frequency polygon of the test scores. - Frequency polygons can also be drawn independently without drawing histograms. In your algebra, you need an ordered pair (x,y) to graph a point in the coordinate system. For this the midpoints of the class intervals are used to plot points. The midpoints will be the x values and y will be the respective frequencies in each class interval. 5. CUMULATIVE FREQUENCY - Cumulative frequency polygon is quite different from a frequency polygon because cumulative frequencies are plotted. In addition, you plot a point above the exact limits of the interval. As such, a cumulative polygon gives a picture of the number of observations that fall below a certain score instead of the frequency within a class interval. 6. BOX AND WHISKERS - Box-and-whiskers plots are very useful graph depicting the distribution of test scores through their quartiles. - For many computations in statistics, it is assumed that your data points (that, is, the numbers in your list, are clustered around some central value; in other words, it is assumed that there is an "average" of some sort. The - "box" in the box-and-whisker plot contains, and thereby highlights, the middle portion of these data points. - To create a box-and-whisker plot, we start by ordering our data (that is, putting the values) in numerical order, if they aren't ordered already. Then we find the median of our data. The median divides the data into two halves. To divide the data into quarters, we then find the medians of these two halves.  - Note: If we have an even number of values, so the first median was the average of the two middle values, then we include the middle values in our sub-median computations. If we have an odd number of values, so the first median was an actual data point, then we do not include that value in our sub-median computations. That is, to find the sub-medians, we're only looking at the values that have not yet been used. - So we have three points: the first middle point (the median), and the middle points of the two halves (what I've been calling the "sub-medians"). These three points divide the entire data set into quarters, called "quartiles". - The top point of each quartile has a name, being a "Q" followed by the number of the quarter. So the top point of the first quarter of the data points is "Q1", and so forth. Note that Q1 is also the middle number for the first half of the list, Q2 is also the middle number for the whole list, Q3 is the middle number for the second half of the list, and Q4 is the largest value in the list. Once we have found these three points, Q1, Q2, and Q3, we have all we need in order to draw a simple box-and-whisker plot. 7. PIE GRAPH - may be useful when representing portions of a whole. For instance, it might be helpful to create a pie chart indicating the amount of time a student spends actively engaged in activities. SKEWNESS - is the degree of asymmetry of a graph. - Basic principle of a coordinate system tells you that as you move toward the right of the x-axis, the numerical value increases. Likewise, as you move up the y-axis, the scale value becomes higher. - Thus, in a negatively skewed distribution, there are more who get higher scores and the tail, indicating lower frequencies of distribution points to the left or to the lower scores, - On the other hand, in positively skewed distribution, lower scores are clustered on the left side. This means that there are more who get lower scores and the tail indicates the lower frequencies are on the right or the higher scores. Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graph form, normal distribution will appear as a bell curve as shown above. A normal distribution is the proper term for a probability bell curve. In a normal distribution the mean is zero and the standard deviation is 1. It has zero skew and a kurtosis of 3. Normal distributions are symmetrical, but not all symmetrical distributions are normal. The MODALITY of a distribution is determined by the number of peaks it contains. Most distributions have only one peak but it is possible that you encounter distributions with two or more peaks. KURTOSIS is a statistical measure used to describe the degree to which scores cluster in the tails or the peak of a frequency distribution. The peak is the tallest part of the distribution, and the tails are the ends of the distribution. There are three types of kurtosis: 1. Leptokurtic: More values in the distribution tails and more values close to the mean (i.e. sharply peaked with heavy tails). Positive values of kurtosis indicate that a distribution is peaked and possesses thick tails. Leptokurtic distributions have positive kurtosis values. A leptokurtic distribution has a higher peak and taller (i.e. fatter and heavy) tails than a normal distribution. 2. Mesokurtic: Distributions that are moderate in breadth and curves with a medium peaked height. When kurtosis is equal to 0, the distribution is mesokurtic. This means the kurtosis is the same as the normal distribution, it is mesokurtic (medium peak). The kurtosis of a mesokurtic distribution is neither high nor low, rather it is considered to be a baseline for the two other classifications. 3. Platykurtic: Fewer values in the tails and fewer values close to the mean (i.e. the curve has a flat peak and has more dispersed scores with lighter tails).Negative values of kurtosis indicate that a distribution is flat and has thin tails. Platykurtic distributions have negative kurtosis values. A platykurtic distribution is flatter (less peaked) when compared with the normal distribution, with fewer values in its shorter (i.e. lighter and thinner) tails. Sas #22 Grading and Reporting of Test Results Purpose of Grading and Reporting. Methods in Scoring Performance Tasks GRADES - are alphabetical or numerical symbols/ marks that indicate the degree to which learners are able to achieve their learning objectives. - They are part of the instructional process and serve as feedback on What specific topic/s learners have mastered and what they need to focus more when they need to prepare for summative assessments. - Sometimes, grades may serve as motivators to some learners to maintain or improve their performance. - They give parents information about their children's achievements. - They are also useful for administrators who want to evaluate the effectiveness of the instructional programs in developing the needed skills and competencies of the learners Traditional Methods in scoring performance tasks and for written works 1. NUMBER RIGHT SCORING (NR) - entails assigning positive values only to correct answers while giving a score of zero to incorrect answers. - The test score is the sum of the scores for correct responses. - One major concern with this scoring method is that learners may get the correct answer by guessing; affecting the test reliability and validity. 2. NEGATIVE MARKING (NM) - entails assigning positive values to correct answers while punishing the learners for incorrect responses (right minus wrong method) - In this model, a fraction of the number of wrong answers is subtracted from the number of correct answers. - Other models for this type of scoring includes: a. giving positive score to correct answer while assigning no mark for omitted items b. rewarding learners for not guessing by awarding point rather than penalizing for incorrect Non Conventional Methods in scoring performances 1. PARTIAL CREDIT SCORING METHODS - attempt to determine a learner's degree of level of knowledge with respect to each response option given. This method of scoring takes into account partial knowledge mastery of learners. It acknowledges that, while others cannot always recognize the correct answer, they can discern that some response options are clearly incorrect. a. Liberal Choice test- allows learners to select more than one answer to a question if they feel uncertain which option or alternative is correct  b. Elimination testing (ET) - instructs learners to cross out all alternatives they consider to be incorrect c. Confidence Weighing (CW)- asks learners to indicate what they believe is the correct answer and how confident they are about their choice. 2. RETROSPECTIVE CORRECTING FOR GUESSING - considers omitted or no-answer items as incorrect, forcing & learners to give an answer for every item even if they do not know the answer. The correction for guessing is implemented later or retroactively. This can be done through comparing leamer's answers in multiple-choice items with their answer on the other test formats such as short answer 3. ANALYTIC SCORING - Involves assessing each aspect of a performance task and assigning a score for each criterion, Sometimes, an overall score is given by averaging the scores One advantage of analytic scoring is its reliability. - It also provides information that can be used as diagnostic as it presents learners strengths and weaknesses and in what area/s and eventually as a basis for remedial instructions. However, it is more time consuming and therefore expensive. - It is also prone to halo effect, wherein scores in one scale may influence the ratings of the others. It is also difficult to create. 4. STANDARD- SETTING - entails using standards when scoring multiple- choice items particularly standards set through norm-referenced or criterion- referenced assessments. - Standards based on norm-referenced assessments are derived from the test performance of a certain group of learners, while standards from criterion-referenced assessment are based on preset standards specified from the very start by the teacher or school in general. 5. HOLISTIC SCORING - involves giving a single, overall assessment score for an essay, writing composition, or other performance-type assessment as a whole. - Although the scoring rubric for holistic scoring lays out specific criteria for evaluating a task, raters do not assign a score for each criterion. Instead, they read a writing task or observe a performance task, they balance strengths and weaknesses among the various criteria to arrive at an overall assessment. - Holistic scoring is considered efficient in terms of time and cost. It also does not penalize poor performance based on only one aspect (eg. content, delivery, organization) However, it is said that holistic scoring does not provide sufficient diagnostic information about the students' ability as it does not identify the areas for improvement and is difficult to interpret as it does not detail the basis for evaluation. 6. PRIMARY TRAIT SCORING - focuses on only one aspect or criterion of a task, and a learner's performance is evaluated based on a trait. - This scoring system defines a primary trait in the task that will then be scored. For example if a teacher in a political science class asks his students to write an essay on the advantages and disadvantages of Martial Law, the basic question addressed in scoring is, "Did the writer successfully accomplish the purpose of this task?" With this focis, the teacher would ignore errors in conventions of written language but instead focus on the overall rhetorical effectiveness. One disadvantage on this scoring scheme is that it is often difficult to focus exclusively on one trait, such  that other traits may be included when scoring. Thus, it is important that a very detailed scoring guide is used for each specific task. 7. MULTI-TRAIT SCORING - requires that an essay test or performance task is scored on more than one aspect, with scoring criteria in place so that they are consistent with the prompt. Multiple trai scoring is task specific, and the features to be scored vary from task to task, thus requiring separate scores for different criteria. - Multiple-trait scoring is similar to analytic scoring because of its focus on several categories of criteria. However, while analytical scoring evaluates more traditional and generic dimensions of language production, multiple-trait scoring focuses on specific features of performance required to fulfill the given task or tasks. For example, in a PE class, basketball, one may be scored based on different skills such as dribbling, passing, rebound, blocking, stealing etc. Sas #23 Grading and Reporting Test Result: Types of Test Scores and Guidelines in Test Grading or Performance Tasks TYPES OF TEST SCORES 1. RAW SCORE - is simply the number of items answered correctly in a test. A raw score provides an indication of the variability in the performance of students in the class. - However, a raw score has no meaning unless you know what the test is measuring and how many items it contains. - A raw score also does not mean much because it cannot be compared with a standard or with the performance of another learner or of the class as a whole. 2. PERCENTAGE SCORE - refers to the percent of items answered correctly in a test. The number of items answered correctly is typically converted to percent based on the total possible score. - The percentage score is interpreted as the percent content, skills or knowledge that the learner has a solid grasp of. - Just like raw score, percentage score has limitations because there is no way of comparing the percentage correct obtained in a test with the percentage correct in another test with a different difficulty level. - Percentage score is most appropriate to use in a teacher-made test or criterion-referenced test. - Percentage score is appropriate to use in a teacher-made test that is administered commonly to a class or to students taking the same course with the same course syllabus. In this way, the students' test performances can be compared among each other in the class or with their peers in another section. In the same manner, percentage score is suitable to use in subjects where a standard score has been set. 3. CRITERION-REFERENCED GRADING SYSTEM - is a grading system wherein learners test scores or achievement levels are based on their performance in specific learning goals and outcomes for standards. a. Pass or fail grade is most appropriate if the test or assessment is primarily or entirely to make a pass or fail decision. In this type of scoring, a standard or cutoff score is preset, and a learner is given a score of pass if he or she surpassed the expected level of performance or cutoff score. This is most appropriate for comprehensive or licensure exams because there is no limit to the number of examinees who can pass or fail. Each individual examine's performance is compared to an absolute standard and not to the performance of others. Advantages: i. takes pressure off the learners in getting a high numerical score ii. gives learners a clear cut idea of their strengths and weaknesses  iii. allows learners to focus on true understanding or learning of the course content rather than on specific details that will help them receive a high leter or numerical score b. Letter grade is one of the most commonly used grading systems. Letter grades are usually composed of a five-level grading scale labeled from A to E or F with A representing the highest level of performance. Letters A B C D E Interpretation Excellence Good Satisfactory Poor Unacceptable c. plus (+) and minus (-) letter grades provide a more detailed descriptions of the level of learners' achievement or task performance by dividing each grade category into three levels such that a grade of A can be assigned as At or A- and so on. d. Categorical Grades is generally more descriptive than letter grades, especially if couples with verbal labels, Verbal labels eliminate the need for a key or legend to explain what each grade category means 4. NORM-REFERENCED GRADING SYSTEM - compared learners' test scores with their peers' test scores. - This involves ranking to express the learner's score in relation to the achievement of the group. This allows teachers to: a. compare learners' test performance with that of other students b. compare learners performance in one test with another test (subtest); c. compare learners, performance in one form of the test with another form of the test submitted at an earlier dates - Types: a. Developmental Score are scores transformed from raw scores and reflect the average performance at age and grade levels i. grade-equivalent score is described as both a growth score and status score. The grade equivalent score of a given raw score in any test indicates the grade level at which the typical learner earns his raw score. A decimal point is used between a  grade and month in grade equivalence. Ex. a score of 6.5 means that the learner did as well as a grade 6 taking the test at the end of the fifth month of the school year ii. age-equivalent score indicated the age level that is typical to a learner to obtain such raw score, it reflects a learners performance in terms of the chronological age as compared to those in the norm group. These scores are written with a hyphen between the years and months. If a learners score is 12-3, his age equivalence is 12 years and 3 months old, indicating a test performance that is similar to that of a 12.3 year-olds in a group. b. Percentile rank indicates the percentage of scores that fall at or below a given score, Percentile ranks range from 1-99. For example, if a student obtained a score of 85th percentile rank in a standardized achievement test, it means that the learner was able to get a higher score than 85% of the learners in the norm group. c. Stanine Score expresses test results in nine equal steps which range from one (lowest) to nine (highest) A stanine score of 5 is interpreted as average stanine. Percentile ranks are grouped into stanines with the following interpretations": d. Standard Scores discussed in the previous modules 1. Z-score 2. T-score GUIDELINES IN GRADING TEST/PERFORMANCE TASKS 1. Stick to the purpose of the assessment. 2. Be guided by the desired learning outcomes 3. Develop grating criteria 4. Inform learners what scoring methods are to be used 5. Decide on what type of test scores to use GUIDELINES IN GRADING ESSAY TEST 1. Identify the criteria for writing essay 2. Determine the type of rubric to be used 3. Prepare the rubric 4. Evaluate the essay anonymously 5. Score one essay at a time 6. Be conscious of your own biases when evaluating paper 7. Review initial scores and comments before giving the final rating 8. Get two or more raters 9. Write comments (feedback) SAS #24 Grading System of the K-12 Program - The K to 12 Basic Education Program uses a standards- and competency-based grading system. These are found in the curriculum guides. - All grades will be based on the weighted raw score of the lemurs' summative assessments. The minimum grade needed to pass a specific leaming area is 60, which is transmuted to 75 in the report card. - The lowest mark that can appear on the report card is 60 for Quarterly Grades and Final Grades. - For these guidelines, the Department will use a floor grade considered as the lowest possible grade that will appear in a leamer's report card. - Learners from Grades 1 to 12 are graded on Written Work, Performance Tasks, and Quarterly Assessment every quarter. These three are given specific percentage weights that vary according to the nature of the leaming area.  - Guidelines specific to the assessment of Kindergarten learners will be issued in a different memorandum or order. - However, for Kindergarten, checklists and anecdotal records are used instead of numerical grades. These are based on learning standards found in the Kindergarten curriculum guide. - It is important for teachers to keep a portfolio, which is a record or compilation of the learner's output, such as writing samples, accomplished activity sheets, and artwork. - The portfolio can provide concrete evidence of how much or how well the learner is able to accomplish the skills and competencies. - Through checklists, the teacher will be able to indicate whether or not the child is able to demonstrate knowledge and/or perform the tasks expected of Kindergarten learners. - Through anecdotal records or narrative reports, teachers will be able to describe learners' behavior, attitude, and effort in school work. For grades 1-12, in a grading period, there is one Quarterly Assessment but there should be instances for students to produce Written Work and to demonstrate what they know and can do through Performance Tasks There is no required number of Written Work and Performance Tasks, but these must be spread out over the quarter and used to assess learners' skills after each unit has been taught.