Administration, Scoring & Analysis of Test

Test administration 

• Introduction : Test administration procedures are developed for an exam program in order to help reduce measurement error and to increase the likelihood of fair, valid, and reliable assessment. Specifically, appropriate standardized procedures improve measurement by increasing consistency and test security.
• Issues of test administration include selection of the computerized test delivery sites, computer test software and hardware considerations, test security provisions, time limits, administration frequency, cost concerns, and test program support

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• Typical guidelines related to the test administration locations state that all the sites should be comfortable, and should have good lighting, ventilation, and handicap accessibility. Interruptions and distractions, such as excessive noise, should be prevented
• A test administrator is responsible for observing and monitoring the students during examinations and related assessments. Test administrators discuss the procedures and rules before the test, responding to any inquiries and concerns the examinees may have.

STEPS OF TEST CONSTRUCTION�

• Planning.
• Writing items for the test.
• Preliminary administration of the test.
• Reliability of the final test.
• The validity of the final test.
• Preparation of norms for the final test.
• Preparation of manual and reproduction of the test.
• PLANNING:

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• Test specifications usually include a test description component and a test blueprint component. The test description specifies aspects of the planned test such as the test purpose, the target examinee population, the overall test length, and more
• It is most important for a teacher and student, that regular forms of testing should take place. ... In order to plan and give instructions that are appropriate for an individual situation, it is necessary to understand all the factors that influence the students in your class.

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• The fundamental principles of test construction are such as (a) Validity, (b) Reliability (c) Standardisation (d) their evaluation. 
• The steps include specifying the construct of interest, deciding the test's function (diagnosis, description of skill level, prediction of recovery), choosing a method (performance, behavioral observation, self-report), designing item content, evaluating the reliability and validity of the test, and modifying the test .

Consideration on administration test

• Checking the testing tools
• Clear directives
• Sitting arrangements
• Unbiased invigilation
• Creation of appropriate environment
• Controlling of cheating
• Delivery of needed materials
• Collection of answer sheet

Scoring of Test

• After construction of test, test are administered and then scored for evaluating the test so it is for evaluation purpose
• Objective scoring is based on observable qualities not affected by other things where as subjective scoring relies on private & personal criteria that are not open to observation
• A raw score is simply the number of question answers by the students correctly for a test

Steps in scoring

• Prepare an answer key
• Check the answer key
• Score blindly
• Check machine-scored answer sheets
• Check scoring
• Record score

Scoring of Subjective Test

• Evaluate all answers to one question before going to next question
• Point scoring method (definition, explanation, examples, conclusion….)
• Grouping method (excellent, very good, good, average, below average, bad, very bad….)
• Avoiding personal bias in scoring
• Scoring more than one examiner

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Scoring of Objective Test

• Objective test is scored on the basis of answer-key which are already developed
• Hole method for correct answer can also be developed by making hole on right answers
• Scoring by hand
• Scoring machine can also be used
• Correction for guessing i.e. penalty for guessing plan can be developed

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• In True-false question, scoring=right-wrong
• In MCQ, S=R+O/N where; R=right answer, O= omitted items, N= no of choices (for prize)
• In MCQ, S= R-W/(N-1) where W=wrong answer (for penalty) OR
• S=T-N/(N-1)*(W-O) where T= total items

Statistical analysis of test scores

• Statistics is considered as a science of collecting, summarizing, analyzing and interpreting numerical facts & figures
• It is a body of mathematical techniques or processes for gathering, organizing, analyzing & interpreting numerical data
• To select the appropriate statistical method, one need to know the assumption and conditions of the statistical methods, so that proper statistical method can be selected for data analysis.

Why in education?

• To find individual difference of the students, institutions & Provide feedback
• To present education related data scientifically
• To compare different scores among each other
• To select, admit & categorize the students
• To provide all round individual achievements
• To find conclusion on different educational aspects
• To update educational records correctly

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Methods of analysis

• Many methods are used but only some methods which are frequently used in education are:
• Tabulation
• Frequency distribution
• Graphical presentation
• Measures of Central tendency
• Measures of Dispersion
• Others bi-variate & multivariate analysis tools

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Frequency distribution

• A frequency distribution is an overview of all distinct values in some variable and the number of times they occur. That is, a frequency distribution tells how frequencies are distributed over values. Frequency distributions are mostly used for summarizing categorical variables.
• In statistics, a frequency distribution is a list, table or graph that displays the frequency of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval

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• A frequency distribution is a representation, either in a graphical or tabular format, that displays the number of observations within a given interval. The interval size depends on the data being analyzed and the goals of the analyst. ... Frequency distributions are typically used within a statistical context
• A frequency distribution is a tabular representation of a survey data set used to organize and summarize the data

Graphical presentation

• Line graph (single, double, multiple…..)
• Bar graph (simple, multiple, sub-divided, histogram …..)
• Pie chart

Bar graphs/Bar-diagrams

• A graphical display of categorical data in which values are shown as horizontal & vertical bars
• A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a column chart
• A bar chart is orientated horizontally, whereas a column chart is arranged vertically. Sometimes “bar chart” refers to both forms. These types of charts are usually used for comparison purposes

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Subdivided bar-diagram

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Multiple bar-diagram

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Pie chart

• A pie chart is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice, is proportional to the quantity it represents
• Pie charts are used in data handling and are circular charts divided up into segments which each represent a value. Pie charts are divided into sections (or 'slices') to represent values of different sizes. For example, in this pie chart, the circle represents a whole class.

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• So A Pie Chart is a type of graph that displays data in a circular graph. The pieces of the graph are proportional to the fraction of the whole in each category. In other words, each slice of the pie is relative to the size of that category in the group as a whole
• A circle graph/pie chart is a way of summarizing a set of categorical data or displaying the different values of a given variable

Central tendency

• In statistics, a central tendency is a central or typical value for a probability distribution. It may also be called a center or location of the distribution. Colloquially, measures of central tendency are often called averages
• Central tendency is a descriptive summary of a dataset through a single value that reflects the center of the data distribution. Along with the variability (dispersion) of a dataset, central tendency is a branch of descriptive statistics

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• There are three main measures of central tendency: these measures describes a different indication of the typical or central value in the distribution
• Mean (Average): Represents the sum of all values in a dataset divided by the total number of the values.
• Median: The middle value in a dataset that is arranged in ascending order (from the smallest value to the largest value). ...
• Mode: Defines the most frequently occurring value in a dataset

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Mean

• The mean is the average or the most common value in a collection of numbers. In statistics, it is a measure of central tendency of a probability distribution along median and mode. It is also referred to as an expected value
• For a data set, the arithmetic mean, also known as average or arithmetic average, is a central value of a finite set of numbers: specifically, the sum of the values divided by the number of values

Median

• In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value
• The median formula is {(n + 1) ÷ 2}th, where “n” is the number of items in the set and “th” just means the (n)th number. To find the median, first order the numbers from smallest to largest. ... For example, the middle for this set of numbers is 5, because 5 is right in the middle: 1, 2, 3, 5, 6, 7, 9

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Continuous series

Mode

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• If the maximum frequency is in first & last
• If there is no concentration of frequency around maximum frequency &
• If there are more than two maximum frequency, then mode is calculated by developing grouping table & analysis table as in next slide

So

Measure of Dispersion

• Dispersion is the measure of the variation between items.
• A measure of dispersion indicates the scattering of data. It explains the disparity of data from one another, delivering a precise view of their distribution. The measure of dispersion displays and gives us an idea about the variation and the central value of an individual item.
• Standard deviation (SD) is the most commonly used measure of dispersion. It is a measure of spread of data about the mean.

Examples of dispersion measures �

• Standard deviation.
• Interquartile range (IQR)
• Range.
• Mean absolute difference (also known as Gini mean absolute difference)
• Median absolute deviation (MAD)
• Average absolute deviation (or simply called average deviation)
• Distance standard deviation.

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Standard Deviation

• Standard deviation: Standard deviation is the square root of the arithmetic average of the square of the deviations measured from the mean. The standard deviation is given as,
• σ = [(Σi (yi – ȳ) ⁄ n] ½ = [(Σ i yi 2 ⁄ n) – ȳ 2] ½
• Apart from a numerical value, graphics methods are also applied for estimating dispersion.
• SD is the most commonly used measure of dispersion. It is the square root of sum of squared deviation from the mean divided by the number of observations.

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