How to conduct test analysis to improve learning
By now we know that the most important assessment is the school- based one, otherwise known as formative assessment, conducted by the classroom teacher. It is not only critical to mark and discuss the test outcomes with the class, but also to analyse the test marks and understand what they tell you.
Classroom assessment is conducted using different formats and instruments. Thus, in computing end of term marks for reporting to the stakeholders, it should incorporate all the marks obtained using other formats of assessment, such as practicals, performance, oral, to give a true reflection of what the learner knows and can do.
Although analysis of terminal examinations administered by an external body is important, it however provides the least information to the teacher and school for improvement because the results are reported as grades.
Irrespective of the assessment format used, the extent to which the learner possesses the knowledge, skills or attitude can be quantified. It is this quantification which enables us to carry out the analysis. The most commonly conducted analysis includes the mean, median and mode, which are collectively called the central tendency of a test. The central tendency measure is a summary measure that attempts to describe a whole set of marks with a single value that represents the middle or central location The mean is the average score of the class. It is calculated by dividing the sum of all values in a data set by the number of values. A high mean indicates that generally, learners have scored high marks hence mastered the subject content. The reason every parent sends his/ her child to school is to learn and it is the desire of every learner to learn and they are capable. Thus for classroom assessment, it is the ultimate goal of all learners to master the content.
Although the mean is most used and considered the best measure of the central tendency, it is however, affected by outliers ( those scores at the extreme ends) which might significantly increase or decrease its value since all test scores are used in its calculation. For example, if one learner scores 5percent and the next lowest mark is 40percent , then 5percent is considered an outlier, because it tends to lower the mean when it is included in the calculation.
In such situations, the median would be the most appropriate central tendency measure to use since it is less affected by the outliers and skewed data. The median is the middle score in the class scores arranged from lowest to highest, as such it is a positional average. It is also preferred when there are some missing scores, for example if one or two learners did not write the test.
When dealing with categorical data, such as gender, colour, breed, the mode is the best choice to compute. The mode is the most appearing mark in a set of test scores. Sometimes the test scores may contain multiple modes and in some cases, it may not contain any mode at all. Like the median, it is not affected by extreme scores.
It should be noted that the mean, mode and median are exactly the same in an evenly spread marks across the spectrum, what is normally called a symmetrical or normal distribution. For optimal information, the three measures of central tendency are best used in combination with each other because they have complementary strengths and limitations.
In addition to calculation of central tendency, the other important measure to calculate is the dispersion of the marks. This is simply determination of how the scores are spread. The three commonly analysed measures of dispersion are the range, quartile and standard deviation. The range is the difference between the highest and the lowest score. The higher the value of the range, the higher the spread in data, which shows that there is a great difference amongst learners in understanding the subject content. This implies that there will be need for remedial intervention for those scoring lower marks.
The standard deviation measures the distance of each mark from the class mean. Low standard deviation means scores are clustered around the mean, and high standard deviation indicates that scores are more spread out. The closer the marks to the mean the better because it tells you that learners understanding of the topic is almost the same. As such, in most cases, the reporting of the mean is accompanied by the standard deviation. Standard deviation is related to the range in that the smaller the range the smaller will be the standard deviation.
On the other hand, quartiles are the values that divide a list of marks into three quarters. The quartile is achieved by ordering data from smallest to largest and divide it into four equal sections. While the median breaks the data into two sections, the quartile divides it into four. Quartiles are used to calculate the interquartile range, which is a measure of variability around the median, as much as the standard deviation is variability around the mean. The interquartile range is simply calculated as the difference between the first and third quartile.
Generally, measures of dispersion are important for describing the spread of the data, or its variation around a central value. Two distinct test scores may have the same mean or median, but completely different levels of dispersion ( range, standard deviation and quartile), or vice versa.
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