The document discusses analyzing test item data through item analysis. Item analysis examines student responses to test items and is used to select the best items, identify flaws, detect learning difficulties, and identify student weaknesses. An item's characteristics, difficulty level, discrimination power, and effectiveness of distractors are evaluated. Data is organized and measures like difficulty index, discrimination index, and attractiveness of distractors are calculated to evaluate items. The summary provides an overview of the key aspects and purposes of item analysis.
The document discusses various methods for organizing and analyzing test score data, including:
1) Organizing scores in ascending or descending order. Ranking scores from highest to lowest.
2) Creating a stem-and-leaf plot to separate scores into "stems" and "leaves".
3) Calculating measures of central tendency (mean, median, mode) and using frequency distributions to analyze grouped score data.
1. The document discusses organizing test scores into a single value frequency distribution by arranging scores in descending order, tallying each score, adding tally marks, and summing the totals.
2. It also discusses setting class boundaries for a grouped frequency distribution, which involves determining class limits, both apparent and real. Real limits extend from half a unit below and above the class values.
3. The document also defines class marks as the midpoint of a class, which is calculated by taking the average of the lower and upper class limits.
The document discusses two common measures of the relationship between two sets of scores: Pearson's Product-Moment Correlation and Spearman's Rho. Pearson's correlation measures the linear relationship between metric variables and involves calculating the covariance between the variables and dividing by the product of their standard deviations. Spearman's Rho measures the monotonic relationship between ordinal or ranked variables and involves calculating the difference between the ranks of each variable and finding the average squared difference. Both measures result in a correlation coefficient between -1 and 1, where values closer to 1 or -1 indicate a strong relationship and values near 0 indicate no relationship.
Here are the steps to solve this problem:
1. Prepare the frequency distribution table with the class intervals, frequencies, and calculate fX.
2. Find the mean (x) using the formula x = fX/f.
3. Calculate the deviations (X - x).
4. Square the deviations to get (X - x)2.
5. Multiply the frequencies and squared deviations to get f(X - x)2.
6. Calculate the variance using the formula σ2 = f(X - x)2 / (f - 1).
7. Take the square root of the variance to get the standard deviation.
8. The range is the difference between the upper
This module discusses computing measures of central tendency (mean, median, mode) for grouped data using two methods: 1) class marks and 2) coded deviations. It provides examples and practice problems for finding the mean of grouped data using both formulas. Students are expected to learn how to calculate and interpret the mean, median, and mode of grouped data.
The document discusses various measures of variability and statistical analysis that can be used to analyze data, including range, standard deviation, z-scores, quartile deviation, and correlation. It also provides examples of how to calculate these measures, such as calculating the range by subtracting the lowest score from the highest, and how to interpret the results, like higher standard deviation indicating more variation in the data. The document also covers topics like grades, grading systems, and guidelines for effective grading.
1) Derived scores help interpret raw scores and make them comparable by expressing them in terms of standard deviations from the mean.
2) There are two main types of derived scores - standard scores (z-scores) which indicate how many standard deviations a score is from the mean, and percentile ranks which show the percentage of scores in the group that are the same or lower.
3) Z-scores are calculated using the formula z = (x - M) / SD, where x is the raw score, M is the mean, and SD is the standard deviation. This expresses how many standard deviations a score is from the mean.
The document discusses various methods for organizing and analyzing test score data, including:
1) Organizing scores in ascending or descending order. Ranking scores from highest to lowest.
2) Creating a stem-and-leaf plot to separate scores into "stems" and "leaves".
3) Calculating measures of central tendency (mean, median, mode) and using frequency distributions to analyze grouped score data.
1. The document discusses organizing test scores into a single value frequency distribution by arranging scores in descending order, tallying each score, adding tally marks, and summing the totals.
2. It also discusses setting class boundaries for a grouped frequency distribution, which involves determining class limits, both apparent and real. Real limits extend from half a unit below and above the class values.
3. The document also defines class marks as the midpoint of a class, which is calculated by taking the average of the lower and upper class limits.
The document discusses two common measures of the relationship between two sets of scores: Pearson's Product-Moment Correlation and Spearman's Rho. Pearson's correlation measures the linear relationship between metric variables and involves calculating the covariance between the variables and dividing by the product of their standard deviations. Spearman's Rho measures the monotonic relationship between ordinal or ranked variables and involves calculating the difference between the ranks of each variable and finding the average squared difference. Both measures result in a correlation coefficient between -1 and 1, where values closer to 1 or -1 indicate a strong relationship and values near 0 indicate no relationship.
Here are the steps to solve this problem:
1. Prepare the frequency distribution table with the class intervals, frequencies, and calculate fX.
2. Find the mean (x) using the formula x = fX/f.
3. Calculate the deviations (X - x).
4. Square the deviations to get (X - x)2.
5. Multiply the frequencies and squared deviations to get f(X - x)2.
6. Calculate the variance using the formula σ2 = f(X - x)2 / (f - 1).
7. Take the square root of the variance to get the standard deviation.
8. The range is the difference between the upper
This module discusses computing measures of central tendency (mean, median, mode) for grouped data using two methods: 1) class marks and 2) coded deviations. It provides examples and practice problems for finding the mean of grouped data using both formulas. Students are expected to learn how to calculate and interpret the mean, median, and mode of grouped data.
The document discusses various measures of variability and statistical analysis that can be used to analyze data, including range, standard deviation, z-scores, quartile deviation, and correlation. It also provides examples of how to calculate these measures, such as calculating the range by subtracting the lowest score from the highest, and how to interpret the results, like higher standard deviation indicating more variation in the data. The document also covers topics like grades, grading systems, and guidelines for effective grading.
1) Derived scores help interpret raw scores and make them comparable by expressing them in terms of standard deviations from the mean.
2) There are two main types of derived scores - standard scores (z-scores) which indicate how many standard deviations a score is from the mean, and percentile ranks which show the percentage of scores in the group that are the same or lower.
3) Z-scores are calculated using the formula z = (x - M) / SD, where x is the raw score, M is the mean, and SD is the standard deviation. This expresses how many standard deviations a score is from the mean.
This presentation includes the following subtopics
• Norm- Referenced and Criterion Referenced Assessment
• Measures of Central Tendency
• Measures of Location/Point Measures
• Measures of Variability
• Standard Scores
• Skewness and Kurtosis
• Correlation
This module discusses measures of central tendency for grouped data. It introduces computing the mean, median, and mode for grouped data using class marks and frequencies. It provides formulas and examples for finding the mean using class marks and the coded deviation method. Students are given practice problems to calculate the mean of various grouped data sets involving test scores, heights, ages, incomes, and more using both methods.
1) The document discusses various measures of central tendency including mean, median, and mode for grouped and ungrouped data. It provides formulas to calculate mean, median, and mode for different data sets.
2) Formulas are given to find the mean, median, and mode of grouped data using class boundaries and frequencies. The direct method and assumed mean method for calculating the mean of grouped data are described.
3) Relationships between mean, median and mode are discussed. The document also covers topics like cumulative frequency, modal class, and finding measures of central tendency for discrete data series.
This document discusses frequency distributions, which organize and simplify data by tabulating how often values occur within categories. Frequency distributions can be regular, listing all categories, or grouped, combining categories into intervals. They are presented in tables showing categories/intervals and frequencies. Graphs like histograms and polygons also display distributions. Distributions describe data through measures of central tendency, variability, and shape. Percentiles indicate the percentage of values at or below a given score.
There are three common measures of central tendency: mean, median, and mode. The mean is the average value found by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently. Each measure provides a single number to represent the central or typical value in a data set.
This document discusses measures of central tendency (mean, median, mode) and measures of spread (range, variance, standard deviation). It provides formulas and examples to calculate each measure. It also presents two problems, asking to calculate and compare various descriptive statistics for different data sets, such as milk yields from two cow herds and weaning weights of lambs from two breeds. A third problem asks to analyze and compare price data for rice from two markets.
Group 3 measures of central tendency and variation - (mean, median, mode, ra...reymartyvette_0611
This document discusses various measures of central tendency and variation. It defines central tendency as indicating where the center of a distribution tends to be, and mentions that measures of central tendency answer whether scores are generally high or low. It then discusses specific measures of central tendency - the mean, median, and mode - and how to calculate each one for both ungrouped and grouped data. It also discusses other measures of variation like range and standard deviation, and how to compute standard deviation for ungrouped and grouped data.
Organizing test scores for statistical analysisneliababy
This chapter discusses organizing test scores for statistical analysis through ordering, ranking, and frequency distribution. Ordering refers to arranging scores numerically in ascending or descending order. Ranking determines the relative position of scores by assigning serial numbers from highest to lowest, with the highest score ranked 1. Tied scores are given the average of their serial numbers. Frequency distribution and stem-and-leaf plots are also examined as ways to organize test scores.
Mean, Median, Mode: Measures of Central Tendency Jan Nah
There are three common measures of central tendency: mean, median, and mode. The mean is the average value found by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently. Each measure provides a single number to represent the central or typical value in a data set.
This document discusses different measures of central tendency including the mode, median, and mean. It provides examples of how to calculate each measure using both raw and grouped data. The mode is the most common value, and is appropriate for qualitative or nominal level data. The median is the middle value when data is ordered from lowest to highest, and is used for ordinal or interval level data. The mean is the average and is calculated by summing the product of each value and its frequency, divided by the total number of values. It requires interval level data. The appropriate measure depends on the level of measurement and research objective.
This document provides information about frequency distributions and constructing frequency distribution tables. It defines a frequency distribution as a representation of data in a tabular format showing the number of observations within intervals. It then outlines the general process for constructing a frequency table which includes determining the range, number of classes, class width, and recording the frequencies in a table. An example is provided of constructing a frequency table from data on the ages of 50 men who died from gunfire using 7 classes. Guidelines for constructing frequency tables are also listed.
This document discusses measures of central tendency, variation, and dispersion in statistical data. It explains that measures of central tendency alone are not enough to understand differences between data sets. Measures of variation such as range, variance, and standard deviation provide additional important information. The document uses an example of returns on stocks to illustrate this point, defining key terms like rate of return. It states that the variation or dispersion in historical returns can help predict future performance beyond just average returns.
Mode of Grouped Data - Math 7 (4th Quarter)Carlo Luna
This document discusses the concept of mode in grouped data. It provides examples of calculating the mode of different data sets. The mode is the value that occurs most frequently in a data set. For grouped data, the mode is calculated using a formula that considers the lower boundary of the modal class, the frequency of the modal class, and the frequencies of neighboring classes. Worked examples demonstrate applying this formula to frequency distributions to determine the modal value.
This document discusses various measures of central tendency including arithmetic mean, median, and mode. It provides definitions and formulas for calculating each measure along with examples using raw data and grouped data. The three main points covered are:
1. Measures of central tendency (mean, median, mode) calculate the central or typical value in a data set and are used to describe data distributions.
2. The arithmetic mean is the sum of all values divided by the number of values, the median is the middle number when values are arranged in order, and the mode is the most frequent value.
3. Formulas and methods are provided for calculating each measure using both raw ungrouped data as well as grouped frequency distribution data
Measures of Variability of Grouped and Ungrouped DataJunila Tejada
Here are the scores of the three students in their Mathematics quizzes:
Student A: 75, 80, 85, 90
Student B: 70, 72, 78, 82
Student C: 65, 68, 73, 77
Range of Student A: 90 - 75 = 15
Range of Student B: 82 - 70 = 12
Range of Student C: 77 - 65 = 12
Mean Deviation of Student A: |75 - 82.5| + |80 - 82.5| + |85 - 82.5| + |90 - 82.5| = 17.5
Mean Deviation of Student B: |70 - 76| + |72 - 76| + |
This document discusses different measures of variability in data, including range, interquartile range, standard deviation, and variance. It provides examples calculating each measure using students' quiz scores. Range is the distance between the highest and lowest values, while interquartile range describes the middle 50% of scores. Standard deviation and variance measure how dispersed all values are from the mean by taking the average of squared deviations from the mean. Standard deviation is the square root of variance and is commonly used in inferential statistics.
This document discusses descriptive statistics concepts including measures of center (mean, median, mode), measures of variation (range, standard deviation, variance), and properties of distributions (symmetric, skewed). Frequency tables are presented as a method to summarize data, including guidelines for construction and different types (relative frequency and cumulative frequency). Common notation and formulas are provided.
Central tendency refers to measures that characterize the middle or center of a data set. The three most common measures of central tendency are the mean, median, and mode. The mean is the average value found by dividing the sum of all values by the number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently in the data set. These measures help analyze and understand data in a statistical analysis.
This document provides information about various statistical measures of central tendency including the median, mode, and quartiles. It defines each measure and provides examples of how to calculate them from both grouped and ungrouped data sets. Formulas are given for calculating the median, quartiles, deciles, and percentiles for grouped data. The mode is defined as the value that occurs most frequently in a data set, and a formula is provided for calculating it from grouped frequency distributions.
Presentation on methods to analyse student's performance. The presentation includes - Measures of central tendencies (Mean, Median, Mode), Percentile and Percentile rank, Standard scores - Z and T scores
This presentation includes the following subtopics
• Norm- Referenced and Criterion Referenced Assessment
• Measures of Central Tendency
• Measures of Location/Point Measures
• Measures of Variability
• Standard Scores
• Skewness and Kurtosis
• Correlation
This module discusses measures of central tendency for grouped data. It introduces computing the mean, median, and mode for grouped data using class marks and frequencies. It provides formulas and examples for finding the mean using class marks and the coded deviation method. Students are given practice problems to calculate the mean of various grouped data sets involving test scores, heights, ages, incomes, and more using both methods.
1) The document discusses various measures of central tendency including mean, median, and mode for grouped and ungrouped data. It provides formulas to calculate mean, median, and mode for different data sets.
2) Formulas are given to find the mean, median, and mode of grouped data using class boundaries and frequencies. The direct method and assumed mean method for calculating the mean of grouped data are described.
3) Relationships between mean, median and mode are discussed. The document also covers topics like cumulative frequency, modal class, and finding measures of central tendency for discrete data series.
This document discusses frequency distributions, which organize and simplify data by tabulating how often values occur within categories. Frequency distributions can be regular, listing all categories, or grouped, combining categories into intervals. They are presented in tables showing categories/intervals and frequencies. Graphs like histograms and polygons also display distributions. Distributions describe data through measures of central tendency, variability, and shape. Percentiles indicate the percentage of values at or below a given score.
There are three common measures of central tendency: mean, median, and mode. The mean is the average value found by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently. Each measure provides a single number to represent the central or typical value in a data set.
This document discusses measures of central tendency (mean, median, mode) and measures of spread (range, variance, standard deviation). It provides formulas and examples to calculate each measure. It also presents two problems, asking to calculate and compare various descriptive statistics for different data sets, such as milk yields from two cow herds and weaning weights of lambs from two breeds. A third problem asks to analyze and compare price data for rice from two markets.
Group 3 measures of central tendency and variation - (mean, median, mode, ra...reymartyvette_0611
This document discusses various measures of central tendency and variation. It defines central tendency as indicating where the center of a distribution tends to be, and mentions that measures of central tendency answer whether scores are generally high or low. It then discusses specific measures of central tendency - the mean, median, and mode - and how to calculate each one for both ungrouped and grouped data. It also discusses other measures of variation like range and standard deviation, and how to compute standard deviation for ungrouped and grouped data.
Organizing test scores for statistical analysisneliababy
This chapter discusses organizing test scores for statistical analysis through ordering, ranking, and frequency distribution. Ordering refers to arranging scores numerically in ascending or descending order. Ranking determines the relative position of scores by assigning serial numbers from highest to lowest, with the highest score ranked 1. Tied scores are given the average of their serial numbers. Frequency distribution and stem-and-leaf plots are also examined as ways to organize test scores.
Mean, Median, Mode: Measures of Central Tendency Jan Nah
There are three common measures of central tendency: mean, median, and mode. The mean is the average value found by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently. Each measure provides a single number to represent the central or typical value in a data set.
This document discusses different measures of central tendency including the mode, median, and mean. It provides examples of how to calculate each measure using both raw and grouped data. The mode is the most common value, and is appropriate for qualitative or nominal level data. The median is the middle value when data is ordered from lowest to highest, and is used for ordinal or interval level data. The mean is the average and is calculated by summing the product of each value and its frequency, divided by the total number of values. It requires interval level data. The appropriate measure depends on the level of measurement and research objective.
This document provides information about frequency distributions and constructing frequency distribution tables. It defines a frequency distribution as a representation of data in a tabular format showing the number of observations within intervals. It then outlines the general process for constructing a frequency table which includes determining the range, number of classes, class width, and recording the frequencies in a table. An example is provided of constructing a frequency table from data on the ages of 50 men who died from gunfire using 7 classes. Guidelines for constructing frequency tables are also listed.
This document discusses measures of central tendency, variation, and dispersion in statistical data. It explains that measures of central tendency alone are not enough to understand differences between data sets. Measures of variation such as range, variance, and standard deviation provide additional important information. The document uses an example of returns on stocks to illustrate this point, defining key terms like rate of return. It states that the variation or dispersion in historical returns can help predict future performance beyond just average returns.
Mode of Grouped Data - Math 7 (4th Quarter)Carlo Luna
This document discusses the concept of mode in grouped data. It provides examples of calculating the mode of different data sets. The mode is the value that occurs most frequently in a data set. For grouped data, the mode is calculated using a formula that considers the lower boundary of the modal class, the frequency of the modal class, and the frequencies of neighboring classes. Worked examples demonstrate applying this formula to frequency distributions to determine the modal value.
This document discusses various measures of central tendency including arithmetic mean, median, and mode. It provides definitions and formulas for calculating each measure along with examples using raw data and grouped data. The three main points covered are:
1. Measures of central tendency (mean, median, mode) calculate the central or typical value in a data set and are used to describe data distributions.
2. The arithmetic mean is the sum of all values divided by the number of values, the median is the middle number when values are arranged in order, and the mode is the most frequent value.
3. Formulas and methods are provided for calculating each measure using both raw ungrouped data as well as grouped frequency distribution data
Measures of Variability of Grouped and Ungrouped DataJunila Tejada
Here are the scores of the three students in their Mathematics quizzes:
Student A: 75, 80, 85, 90
Student B: 70, 72, 78, 82
Student C: 65, 68, 73, 77
Range of Student A: 90 - 75 = 15
Range of Student B: 82 - 70 = 12
Range of Student C: 77 - 65 = 12
Mean Deviation of Student A: |75 - 82.5| + |80 - 82.5| + |85 - 82.5| + |90 - 82.5| = 17.5
Mean Deviation of Student B: |70 - 76| + |72 - 76| + |
This document discusses different measures of variability in data, including range, interquartile range, standard deviation, and variance. It provides examples calculating each measure using students' quiz scores. Range is the distance between the highest and lowest values, while interquartile range describes the middle 50% of scores. Standard deviation and variance measure how dispersed all values are from the mean by taking the average of squared deviations from the mean. Standard deviation is the square root of variance and is commonly used in inferential statistics.
This document discusses descriptive statistics concepts including measures of center (mean, median, mode), measures of variation (range, standard deviation, variance), and properties of distributions (symmetric, skewed). Frequency tables are presented as a method to summarize data, including guidelines for construction and different types (relative frequency and cumulative frequency). Common notation and formulas are provided.
Central tendency refers to measures that characterize the middle or center of a data set. The three most common measures of central tendency are the mean, median, and mode. The mean is the average value found by dividing the sum of all values by the number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently in the data set. These measures help analyze and understand data in a statistical analysis.
This document provides information about various statistical measures of central tendency including the median, mode, and quartiles. It defines each measure and provides examples of how to calculate them from both grouped and ungrouped data sets. Formulas are given for calculating the median, quartiles, deciles, and percentiles for grouped data. The mode is defined as the value that occurs most frequently in a data set, and a formula is provided for calculating it from grouped frequency distributions.
Presentation on methods to analyse student's performance. The presentation includes - Measures of central tendencies (Mean, Median, Mode), Percentile and Percentile rank, Standard scores - Z and T scores
This document discusses analyzing and interpreting test data using various statistical measures. It describes desired learning outcomes around measures of central tendency, variability, position, and covariability. Key measures are defined, including:
- Mean, median, and mode as measures of central tendency
- Standard deviation as a measure of variability
- Measures of position like percentiles and z-scores
- Covariability measures the relationship between two variables
Examples are provided to demonstrate calculating and interpreting these different statistical measures from test data distributions. The appropriate use of measures depends on the level of measurement (nominal, ordinal, interval, ratio). Measures reveal properties like skewness and help evaluate teaching and learning.
This document discusses calculating quartiles of a data set. It begins by defining key terms like quartiles, data, ungrouped data, and measures of position. It then explains how to find the quartiles using the Mendenhall and Sincich method, which involves arranging data in order and using a formula to determine quartile positions. The document provides examples of calculating the lower and upper quartile differences for different data sets. It concludes by generalizing the process and evaluating example problems of finding individual quartiles and their sum.
The document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the average and is calculated by adding all values and dividing by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently in the data set. Examples are provided to demonstrate calculating each measure using both raw and grouped data.
1. The document discusses various statistical methods for organizing and summarizing score data, including talligrams, ranking, score frequency distribution, and graphical presentation.
2. A talligram is a process of tallying scores in a table to show the frequency and distribution of scores. Ranking involves ordering scores from highest to lowest and assigning them consecutive numbers.
3. Score frequency distribution creates a table showing how often each score occurred. Graphical presentation such as histograms and frequency polygons can depict the distribution of scores visually.
Standard deviation (SD) is a measure of variability or dispersion of data from the mean. It is calculated as the square root of the average of the squared deviations from the mean. The t-test is used to determine if there is a statistically significant difference between the means of two groups, and requires calculation of the standard error of the difference between the means. There are different procedures for the t-test depending on whether the samples are independent or correlated, large or small. The null hypothesis of no difference between means is tested against the alternative hypothesis at a chosen significance level.
This document provides an overview of key concepts in statistics and probability. It discusses descriptive statistics, which includes techniques for summarizing and describing numerical data through tables, graphs and charts. It also covers inferential statistics, which allows generalization from samples to populations through hypothesis testing and determining relationships. Key terms are defined, such as data, population, sample, and variable. Common statistical measures like the mean, median and mode are also introduced.
Non-parametric Statistical tests for Hypotheses testingSundar B N
A complete guidelines for Non-parametric Statistical tests for Hypotheses testing with relevant examples which covers Meaning of non-parametric test, Types of non-parametric test, Sign test, Rank sum test, Chi-square test, Wilcoxon signed-ranks test, Mc Nemer test, Spearman’s rank correlation, statistics,
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This document discusses the collection and classification of data. It defines primary and secondary data, with primary data being first-hand data collected by an enumerator through surveys or tests, and secondary data being previously collected data from sources like reports. It also describes different modes of collecting primary data like personal interviews, questionnaires, and phone interviews. Methods of collecting primary data include census/complete enumeration and sampling techniques like random and non-random sampling. Data can be classified in different ways like chronologically, spatially, quantitatively, or qualitatively. Ungrouped raw data can be arranged and grouped data is presented in frequency distribution tables with class intervals. Classification of data is important for comparing tests, students, systems, and making predictions
This document provides information about constructing and administering objective tests. It discusses terminology related to testing such as test, marks, item, analysis, scoring, and reports. It also covers administering a test, scoring methods, types of scores like raw scores, percentile ranks, and standard scores. The document discusses grading systems, methods of grading tests, and item analysis to select appropriate test items. Finally, it describes different types of objective tests including true/false, matching, multiple choice, identification, and completion tests and provides guidelines for constructing each type of objective test.
Mathematics 7 Frequency Distribution Table.pptxJeraldelEncepto
The document provides instructions for constructing a frequency distribution table using test score data from 60 students. It explains how to determine the number of class intervals, calculate the class width, tally the scores within each interval, and record the frequencies. The steps include finding the range of scores, dividing the range by the number of intervals, establishing the class limits, and populating the frequency table with tallies and counts.
This document discusses analyzing and interpreting test data using measures of central tendency, variability, position, and co-variability. It defines these statistical measures and how to calculate and apply them. Key points covered include calculating the mean, median, and mode of a data set; measures of variability like standard deviation; and how these measures can be used to analyze test scores and interpret results to improve teaching. Formulas and examples are provided to demonstrate calculating and applying these statistical concepts to educational test data.
There are four primary types of measurement scales: nominal, ordinal, interval, and ratio. Nominal scales assign numbers or symbols to objects for identification purposes only, while ordinal scales indicate relative position or rank. Interval scales represent equal distances between scale values, and ratio scales allow for meaningful comparisons using ratios. Common scaling techniques include paired comparisons, rank ordering, constant sum, and various rating scales like Likert scales that assign values along a range of agreement levels. Non-comparative techniques involve direct ratings on continuous or itemized scales to measure attributes or characteristics of objects.
This document defines and explains several key statistical concepts:
- Statistics is the study of collecting, analyzing, and presenting quantitative data. It involves planning data collection through surveys and experiments.
- The mean is the average value of a data set, calculated by summing all values and dividing by the number of values.
- The median is the middle value when data is arranged in order. For even data sets, the median is the average of the two middle values.
- The mode is the most frequently occurring value in a data set.
- Standard deviation measures the variation or dispersion of data from the mean. It involves subtracting the mean from each value, squaring the differences, summing them, and taking the square
The document provides details about conducting an item analysis of a test. It discusses the key steps in item analysis which include: 1) arranging student answer sheets in order of performance and dividing them into high and low groups, 2) calculating the difficulty level and discrimination power of each item, and 3) using the results to select items to keep, modify, or eliminate from the test. The item analysis helps evaluate the quality of individual test items and identify areas for improving the test and future item writing.
The document discusses organizing and presenting data through descriptive statistics. It covers types of data, constructing frequency distribution tables, calculating relative frequencies and percentages, and using graphical methods like bar graphs, pie charts, histograms and polygons to summarize categorical and quantitative data. Examples are provided to demonstrate how to organize data into frequency distributions and calculate relative frequencies to graph the results.
The document discusses statistical concepts used in analyzing assessment data. It defines statistics as the science of collecting, organizing, summarizing, and interpreting data. Descriptive statistics are used to describe data through measures of central tendency like the mean, median, and mode, while inferential statistics make predictions about a larger data set based on a sample. The document outlines steps for constructing frequency distributions and calculating the mean, including determining class limits and sizes. Graphs like histograms and frequency polygons can be used to visually represent grouped assessment data.
Frequency distribution, central tendency, measures of dispersionDhwani Shah
The presentation explains the theory of what is Frequency distribution, central tendency, measures of dispersion. It also has numericals on how to find CT for grouped and ungrouped data.
Similar to Analyzing and using test item data (20)
2. It refers to the process of examining
the students response to each item
in the test.
3. Purposes and Elements of Item Analysis
1. To select the best available items for the final form of the
test
2. To identify the structural defects in the items
3. To detect learning difficulties of the class as a whole; and
4. To identify the areas of weaknesses of the students in
need of remediation
4. Characteristics of an item
Desirable characteristics can be
retain for subsequent use
Undesirable characteristics is either
to revised or rejected
5. Three main Elements in an Item-
Analysis
1.Difficulty level of the items
2. Discrimination power of each item
3. Examination of the effectiveness of
distracters
6. Difficulty index - refers to the
proportion of the number of students
in the upper and lower groups who
answered an item correctly.
Therefore it can be obtain by
adding the proportion in the upper
and lower groups who got the item
right and divide it by 2.
7. Index of Discrimination- it is the
percentage of high-scoring
individuals responding correctly vs.
the number of low-scoring
individuals responding correctly to an
item.
8. • Maximum Positive Discriminating
Power of an item – it is indicated by an
index of 1.00 and is obtain when all the
groups answered correctly and no one in
the lower group did.
• Zero Discriminating power – is obtain
when an equal number of students in both
groups got the item right
• Negative Discriminating Power of an
item – it is obtain when more students in
the lower group got the item right than in
the upper group.
9. Measures of attractiveness.
To measure the attractiveness of
the incorrect option in a multiple
choice test, we count the number of
the students who selected the
incorrect option in both the upper
and lower groups. The incorrect
options should attract less of the
upper group than the lower group.
10. PREPARING DATA FOR ITEM ANALYSIS
1. Arrange test scores from highest to lowest.
2. Get one-third of the papers from highest
scores and the other one-third from the
lowest scores.
3. Record separately the number of times each
alternative was chosen by the students in
both groups.
4. Add the number of correct answer to each
item made by the combined upper and
lower groups.
11. 5. Compute the index of difficulty for each item,
index of difficulty = No. of students responding correctly to an item x 100
Total no. of students in the upper and lower groups
6. Compute the index of discrimination
index of discrimination=Upperncr – Lowerncr
No. of students per group
12. Difficulty of a test item can be interpreted with the
use of...
Range Difficulty Level
20 & below very difficult
21-40 difficult
41-60 average
61-80 easy
81-above very easy
13. Discrimination Index
Range Verbal Description
0.40 and above very good item
0.30-0.39 good item
0.20-0.29 fair item
0.09-0.19 poor item
14. CORRELATING TEST SCORES
CORRELATION- the relationship
between two or more paired-factors
or two or more sets of tests scores
CORRELATION COEFFICIENT- a
numerical measure of the linear
relationship between two factors on
sets of scores
15. Obtained Correlation coefficient
can be interpreted with the use of….
Correlation Coefficient Degree of Relationship
0.00-0.20 negligible
0.21-0.40 low
0.41-0.60 moderate
0.61-0.80 substantial
0.81-1.00 high to very high
16. Pearson’s Product-Moment Correlation
1. Compute the sum of each set of scores (SX.SY).
2. Square each score and sum the squares (SX2
,SY2 ).
3. Count the number of scores in each group (N).
4. Multiply each X score by its corresponding Y
score.
5. Sum the cross product of X and Y (SXY).
6. Calculate the correlation, following the formula:
17. Spearman Rho
1. Rank the scores in distribution X,
giving the highest score a rank of 1.
2. Repeat the process for the scores in
distribution Y.
3. Obtain the difference between the
two sets of ranks (D).
4. Square each of these differences
and sum up squared differences
(SD2 )
18. 5. Solve for Rho following the formula:
Rho=1-{6 SD2 }
{N3 –N}
Where: rho= rank- order correlation
coefficient
D= difference between paired ranks
SD2 = sum of squared differences
between paired ranks
N= No. of paired ranks
19. Organizing Test Scores for
Statistical Analysis
1.Organizing test scores by ordering
2.Organizing test scores by ranking
3.Organizing test scores through a
stem- and leaf plot
4.Organizing data by means of a
frequency distribution
20. Preparing Single Value Frequency
Distribution
1. Arrange the scores in descending order.
List them in the X column of the table.
2. Tally each score in the tally column.
3. Add the tally marks at the end of each
row. Write the sum in the frequency
column.
4. Sum up all the row total tally marks
(N=___).
21. Shapes of the frequency Polygons
1. Normal- bell- shaped curve.
2. Positive skewed- most scores are
below the mean and there are
extremely high scores. (mean is
greater than the mode)
3. Negatively skewed- most scores are
above the mean and there are
extremely low scores. (mean is
lower than the mode).
22. 4. Leptokurtic- highly peaked and the
tails are more elevated above the
baseline.
5. Mesokurtic- moderately peaked
6. Platykurtic- flattened peak
7. Bimodal curve- curve with two peaks
or mode.
23. 8. Polymodal curve- curve with three or
more modes
9. Rectangular Distribution- there is no
mode
24. Skewness- degree of symmetry of
the scores
kurtosis – degree of peakness or
flatness of the distribution curve
25. Sk= 3( M –Md)
SD
K= Q
(P90 – P10)
• Normal distribution – 0.263
• Platykurtic - > 0.263
• Leptokurtic - < 0.263
27. Organizing Test Scores By
Ordering
Ordering refers to the numerical
arrangement of numerical
observations or measurements.
There are two ways of ordering:
1. Ascending Order
2. Descending Order
28. the following are the scores obtained
by 10 students in their quizzes in
English for the first grading students.
A B C D E F G H I J
110 130 90 140 85 87 115 125 95 135
30. Organizing test scores by
ranking
Ranking is another way by which test
scores can be organized.
It is process of determining the
relative position of scores, measures
of values based on magnitude,
worth, quality, or importance,
31. Steps in ranking test scores:
Arrange the test scores from highest
to lowest
Assign serial number for each score.
Assign the rank of 1 to the highest
score and the lowest rank to the
lowest score.
In case there are ties, get the
average of the serial numbers of the
tied scores.
R= ( SN1 + SN2 + SN3 .... SN N)
32. Example: Rank the following scores
obtained by 20 ist year high school
students in spelling.
15 the rank of 12, 8,7, and
Find 14 10 9 8
8 7 6 2 4
4 8 7 8 10
9 14 12 4 6
33. Organizing Test Scores Through A
stem and Leaf Plot
It is a method of graphically sorting
and arranging data to reveal its
distribution.
It is a method of organizing a scores,
a numerical score is separated into
two parts, usually the first one or
two digits and the other digits.
The stem is the first leading digit of
the scores while the trailing digit is
the leaf
35. Procedures:
Split each numerical score or value into
two sets of digit. The first or leading set
of digits is the stem, and the second or
trailing set of digits is the leaf
List all possible stem digits from lowest
to highest.
For each score in the mass of data,
write down the leaf numbers on the line
labelled by the appropriate stem
number
36. Illustrate the stem and leaf plot on
the following periodical test results
in biology.
30 74 80 57 32
31 77 82 59 90
33 46 65 49 92
42 50 68 48 57
37. Organizing Data by means of
frequency distribution
Preparing Single value Frequency
Distribution
1. Arrange the scores in descending
order. List them in the x column of
the table.
2. Tally each score in the tally column.
3. Add the tally marks at the end of
each row. Write down the sum in the
frequency column.
4. Sum up all the row total tally marks
38. Prepare a single value frequency
distribution for the spelling test
scores of grade 3 pupils
14 2 6 8 8 6 6 9 8 6
4 2 14 9 4 6 2 4 14 4
5 6 3 6 6 10 10 4 3 8
39. Preparing Group Frequency
Distribution
Steps
Find the lowest and the highest score.
Compute the range.
Determine the class interval
Determine the score at which the
lowest interval should begin.
Record the limits of all class interval
Tally the raw scores in the appropriate
class interval
Convert each tally to frequency.
40. Setting the class boundaries and
class limits
Class boundary is the integral limit of
a class. These integral limit should
be apparent or real.
• The apparent limits of a class are
comprised of an upper and lower limit
Class mark is the midpoint of a class
in a grouped frequency distribution.
• It is used when the potential score is to
be represented by one value if other
measures are to be calculated
41. Derived Frequencies From
Grouped Frequency Distribution
Relative frequency distribution
indicates what percent of scores falls
within each of the classes.
RF = ( F/N) 100
.
42. Computation of relative
frequency
Class frequenc Relative
interval y Frequen
cy
75-77 1 2.5
72-74 3 7.5
69-71 5 27.5
66-68 12 30
63-65 11 25.5
60-62 8 20
40 100
43. Cumulative Frequency distribution indicates the
number of scores that lie above or below a class
boundary
Types:
1. <cf- are obtained by adding the
successive frequencies from the bottom
to the top of the distribution
2. >cf- are obtained by adding the
frequencies from top to bottom
46. 1. MEAN
It is often called arithmetic average.
47. 2. Median
It is the score that occurs at a point
on the scale below which 50 % of the
scores fall and above which the other
50 % of the scores occur.
48. 3. Mode
It is the most recurring score in a set
of test scores
49. Measure of Dispersion
To determine the size of the
distribution of the test scores
or the portion of it.
50. Range
It is the simplest and the easiest
measure of dispersion.
It simply measure how far the
highest score from the lowest score
It is considered as the least
satisfactory measure of dispersion
For ungrouped data we have:
R= Hs - Ls
51. Example
Determine the range of the test
score of nine students in a
community development course test.
Sol: R = 43-19 = 24
53. Compute the range of the following
frequency distribution of the test
scores in Math
Class interval Frequency
60-64 1
55-59 5
50-54 4
45-49 5
40-44 7
35-39 8
30-34 4
25-29 3
20-24 2
15-19 1
58. Compute the inter quartile range of
the following frequency distribution
of the test scores in Math
Class interval Frequency
60-64 1
55-59 5
50-54 4
45-49 5
40-44 7
35-39 8
30-34 4
25-29 3
20-24 2
15-19 1
60. The quartile Deviation
It devides the difference of the 3rd
and 1st quartile into two.
It is the average distance from the
median to the two quartiles
QD = Q3- Q2
2
61. Example
Determine the quartile deviation of
the test score of nine students in a
community development course test.
Sol: 15 / 2 = 7.5
62. Compute the quartile deviation of
the following frequency distribution
of the test scores in Math
Class interval Frequency
60-64 1
55-59 5
50-54 4
45-49 5
40-44 7
35-39 8
30-34 4
25-29 3
20-24 2
15-19 1