Exemplar Use-Cases for Training Teachers on Learning Analytics

Abstract

Learning Analytics (LA) provides a rich set of methods, techniques, and tools to analyze learners’ data. However, educators without a background in data analysis and statistical methods experience difficulty comprehending the potentials and pitfalls of learning analytics based pedagogical practices and Engineering Sciences experience this difficulty. This chapter documents a set of exemplars used to demonstrate learning analytics applications in daily classroom activities. These exemplars have been designed and used mainly to train newly recruited teachers on data analysis methods during faculty induction programs. Exemplars demonstrate the application of statistical methods such as hypothesis testing, analysis of variance (ANOVA), correlation analysis, and regression analysis. Each use case’s broad objective is to describe the application’s context so that teachers can apply it in a similar situation. The chapter provides ready-to-use examples for conducting teachers training programs on Learning Analytics.

Appendix: A Primer on Statistical Terms and Definitions

The following are most commonly used terms from Statistics. Here we reproduce their definitions from [17]

• 1. Population It is the set of all possible data for a given context.

• 2. Sample It is the subset taken from population.

• 3. Types of Data A Data can be broadly classified into four categories. These are: (i) Continuous, (ii) Discrete, (iii) Ordinal, and (iv) Nominal. Discrete and continuous data is numeric type data. A continuous random variable such as temperature may take any value from the number space. A discrete random variable such as color can take a fixed set of values. For example, red, blue green etc. An implicit order of hierarchy is understood in case of ordinal type of variable such performance level may be excellent, very good, good and fair. No such implicit order is assumed in case of nominal type of random variable

• 4. Mean is the arithmetical average value of data and is one of the most frequently measures of central tendency. It is defined as:

  $$\mu = \mathop \sum \limits_{i = 1}^{n} \frac{{x_{i} }}{n}$$

• 5. Mode is the most frequently occurring value in the data set. Mode is the only measure of central tendency which is valid for qualitative (nominal) data since the mean and median for nominal data are meaningless. In the bar chart (and histogram), mode is the tallest column.

• 6. Median It is the value that divides the data in to two equal parts, that is the proportion of observations below median and above median will be 50%. Median is much more stable than the mean value that is adding a new observation may not change the median significantly. However the drawback of median is that it is not calculated using the entire data like in the case of mean.

• 7. Variance It is the average of the squared differences from the Mean.

  $${\text{var}} = \mathop \sum \limits_{i = 1}^{n} \frac{{\left( {x_{i} - \mu } \right)^{2} }}{n}$$

• 8. Standard Deviation It is a measurement of how far data is spread out from the mean, or average. The Standard Deviation is a measure of how spreads out numbers are. It is typically defined as

  $$\sigma = \sqrt {\text{var}}$$

• 9. Normal Distribution It is a continuous probability distribution that is symmetrical on both sides of the mean, so the right side of the center is a mirror image of the left side. The area under the normal distribution curve represents probability and the total area under the curve sums to one. It is symmetrical bell-shaped graph as shown in Fig. 6.5.

Fig. 6.5

Normal distribution

• 10. Co-Variance It signifies the direction of the linear relationship between the two variables. By direction we mean if the variables are directly proportional or inversely proportional to each other. Increasing the value of one variable might have a positive or a negative impact on the value of the other variable.

  $$Cov_{x, y} = \frac{{\sum \left( {x_{i} - \mu_{x} } \right)\left( {y_{i} - \mu_{y} } \right)}}{n - 1}$$

• 11. Correlation It is a measure of the strength and direction of relationship that exists between two random variables. It is a measure of association between two variables.

• 12. Pearson Correlation Coefficient measure the strength of the linear association relationship using numerical measure

  $$PCC = \frac{{Cov_{x, y} }}{{\sigma_{x} \sigma_{y} }}$$

• 13. Mean Square Error It measures the average of the squares of the errors i.e., the average squared difference between the estimated values (ŷ) and actual value (y).

  $$MSE = \mathop \sum \limits_{i = 1}^{n} \frac{{\left( {y_{i} - \hat{y}} \right)^{2} }}{n}$$

• 14. t-test is used when the population follows a normal distribution and population standard deviation is unknown. It shows how significant the differences between groups are.

• 15. z-test is a statistical test to determine whether two population means are different when the variances are known and the sample size is large. It can be used to test hypotheses in which the z-test follows a normal distribution.

• 16. Chi-Squared test It is used for testing relationships between categorical variables.