Dr Iain Weir, Dr Rhys Gwynllyw, Dr Karen Henderson
Background
The Business Decision Making module comprises a single semester course covering statistical methodology
in far greater depth than had been taught previously and modernised to include analyses using the statistical
software SPSS rather than by hand calculations.
Over the twelve-week semester, the Statistics staff deliver a one-hour lecture and a one-hour computer practical
to students each week. Concurrently, Business School staff supply relevant context to each of the statistical
topics taught through a one-hour tutorial per week.
E-exams comprise 50% of the assessment of the module and are run as three in-class tests sat under controlled conditions.
These are equally spaced throughout the teaching delivery period and assess students' statistical competency.
The content of the material assessed in the in-class tests prepares students for the subsequent uncontrolled element of the assessment
which the Business School staff are responsible for. This comprises a 1,200 word report which students complete in their own time, also worth 50%.
For this piece of coursework, students are given access to a large questionnaire data set in response to a business question.
They are required to find something of interest in this data set in order to demonstrate one of the statistical techniques taught in the module.
Here we showcase the first of the three in-class tests which is taken in week 5 and concerns a single sample
test for central tendency. The weekly teaching for the previous four weeks is then presented together with the
key skills e-Assessments that are the main learning tool for the first in-class test.
Please note that the following e-Assessments are catalogue versions of individual questions.
Full Dewis features are available when any of these questions are embedded into an assessment.
In-class test 1(Sat in Week 5)
The first in-class test is taken under controlled conditions in week 5 of teaching.
The following describes various facets of the e-Assessment and by pressing the button you may try it.
INCLASS1
The first in-class test relates to the data dependent choice of the application of either the one-sample t-test or Wilcoxon signed rank test.
The following design features are coded into the question:
Data of random sample size is supplied each time the test is accessed;
The null hypothesised average is random each time the test is accessed;
Data is randomly generated so that with equal chance students would experience both tests and significant or nonsignificant results.
The basic statistical analysis tasks tested are the ability to;
Transfer data from CSV format to SPSS;
Perform an exploratory data analysis for summary statistics, graphics and assumption testing;
Identification of appropriate statistical test (parametric or nonparametric equivalent);
Interpretation and reporting of test output.
There are, in total, 22 numerical/dropdown entries and each entry is worth one mark if answered correctly. There are a further three marks available for the correct choice of test to report; this weighting acknowledges the complexity of a decision based upon taught guidelines that consider sample size, skewness and normality.
We shall now consider the prior 4 weeks of lectures and computer labs that prepare the students for the first in-class test.
Week 1
In the Illustrative and descriptive statistics lecture students are introduced to some of the most common ways of accurately describing and summarising large datasets through graphs, tables and summary statistics. This is achieved through considering the SPSS output from a profiling exercise of a multivariate data set concerning customers at a coffee shop.
The lecture PowerPoint slides deliberately do not contain any SPSS instruction so that students can focus merely on SPSS output and its
interpretation. The students are supplied with a pdf of supporting notes that do however contain SPSS instruction.
In the computer lab the students watch two SPSS instructional videos that relate to the lecture's coffee shop example:
Introduction to SPSS: Entering and coding data and saving a file;
Reproducing the coffee example SPSS output.
These videos allow students to self-learn the basics of SPSS at a pace that suits them and frees up staff to talk to students about specific concerns.
It is explained to the students that Dewis is employed on the module for both summative (the 3 in-class online tests)
and formative assessments (weekly key skills exercises). It is also mentioned that staff can monitor engagement each week through
the Dewis reporting system as well as having the highest attempt at any one key skill updated to Blackboard.
The following e-Assessment introduces the students to the basics of how the Dewis
system works and provides staff with an engagement register for this week and baseline statistics knowledge scores for the cohort.
STATSCORE
This e-Assessment is the first experience students have of the Dewis system and is independent of the taught material.
Introduces the students to the mechanics of the Dewis system, e.g. inputs, submission, feedback;
Gives staff an engagement register for Week 1 and an insight to the cohort's statistics knowledge.
Week 2
The lecture introduces students to the Normal distribution and in doing so covers the following topics:
Distribution shapes;
Normal distribution;
One/two/three SD rule;
Symmetry, negative skewness and positive skewness;
Skewness and Kurtosis evaluation via their coefficients and standard errors;
Shapiro-Wilk normality test.
In the computer lab students use the following key-skill e-Assessment which build upon the previous week's lecture material.
BAR_PROFILE
This Dewis key skill concerns SPSS use for an exploratory data analysis of a random sized data set comprising five variables
of various measurement levels; 2 x scale, 2 x nominal and 1 x ordinal.
The following learning objectives are covered:
Downloading data to CSV file and then importing into SPSS;
Setting SPSS Variable View appropriately for each of the variables
(i.e. Decimals, Labels, Values and Measure);
Introduction to embedded Help pages;
Obtaining and interpreting various illustrative and descriptive statistics.
The 'Report' section of The Feedback indicates, with colour coded marking, what the student has answered correctly (green) or incorrectly (red).
In this and future computer labs there are also questions that require the students to download and complete
pre-written analysis Word templates. Students are required to populate the
templates with SPSS output, numerical values and make interpretation decisions.
As an example, for this week students explore a subset of the Living Costs and Food Survey (LCF), 2013.
The template is
here
and the completed template looks like
this.
Note:
Templates are more challenging as they generally assume knowledge of SPSS commands;
Templates allow students to learn the mechanics of importing various forms of SPSS output into Word;
The set of saved completed templates are beneficial for students to refer back to when they are required to conduct their own statistical report writing.
Week 3
In the lecture students are introduced to performing an appropriate single sample test for an average;
i.e. the one-sample t-test or its non-parametric equivalent the Wilcoxon signed rank test.
In the computer lab students use the following six key-skill e-Assessments which build upon the previous week's lecture material.
The relevant SPSS output for these key skills come from the single SPSS command Explore
and comprise the components of a thorough exploratory data analysis (EDA) of a data set.
BOXPLOT
Students are made aware throughout the module that boxplots are a very powerful graphic for
not only graphically summarising data but for also gaining a gut feel for an impending analysis.
Many of the subsequent Dewis key skills display boxplot(s) at the beginning of a question to
stimulate immediate interest relating to the question posed. For instance, two side by side
boxplots for the independent t-test for comparing two means can reveal the likely test outcome
as well as a quick visual check of the test assumptions of normality and equal variance.
This key skill covers the following learning objectives:
Mild and extreme outlier detection;
Evaluating distribution shape (approximate symmetry and negative/positive skewed);
Estimating the median.
This is the only Dewis key skill that requires subjective judgement and as such the students are warned to not be too worried if they sometimes got different answers. The Feedback does give the actual values of the skewness coefficient and the median to help the student self-evaluate their choice.
NORMAL
This e-Assessment concerns visualisation of the normal distribution via 1, 2 and 3 standard deviation rule.
MEANS
The e-Assessment concerns using a 95% confidence interval for the mean to infer about a change to a hypothesised population value.
This e-Assessment sets the style for many of the subsequent e-Assessments:
Posed question includes a graphic to allow immediate curiosity;
Data download link supplying CSV file to read into SPSS;
Data transfer check;
Embedded Help pages giving SPSS commands and interpretation advice;
Instructions on numerical value reporting accuracy;
Practice in the formal reporting of statistics;
Marking scheme;
The 'Report' section indicates, with colour coded marking, what the student has answered correctly (green) or incorrectly (red).
It is also worth noting that in the feedback there is a pictorial representation of the confidence interval included along with accompanying text in blue that provides extra feedback information with the aim of aiding students' understanding of the correct inference to the question posed.
SKEWKURT
The e-Assessment concerns assessing for normality using skewness and kurtosis.
SPSS use to gain skewness and kurtosis output and its subsequent interpretation;
Using the skewness coefficient/standard error to check for symmetry or positively/negative skewness;
Using the kurtosis coefficient/standard error to check for similar or heavier/lighter tails than a normal distribution;
Using both skewness and kurtosis exploration for an overall assessment for normality.
The identification of skewness is used in the decision rule for the main test choice in in-class test 1.
SHAPIROWILK
The e-Asessment concerns the application of the Shapiro-Wilk Normality test which makes students aware of:
The null and alternative hypotheses;
SPSS use to gain output and its subsequent interpretation;
Formal reporting of the statistical test.
The identification of normality is used in the decision rule for the main test choice in in-class test 1.
PVALUES
The e-Assessment was written after staff witnessed the difficulties that some students had in comparing whether a p-value is less than or bigger than .05.
As an alternative, ignoring the decimal point in the p-value and comparing the resulting number to 50 instead appeared to work for some of these students.
There is a template for students to complete that concerns EDA and the normality of a data set.
Week 4
In the lecture students cover Probability and Decision trees. These topics do not have a follow up computer lab in the subsequent week as that is when the
first in-class test takes place. However, the Business School tutorial in the following week expands upon the material taught in this lecture.
In the computer lab students use the following three key-skill e-Assessments which build upon the previous week's lecture material and
comprise the main topic for the in-class test held in the subsequent week.
ONESAMPLET
The e-Assessment concerns the application of the one-sample t-test and makes students aware of:
The null and alternative hypotheses;
SPSS use to gain output and its subsequent interpretation;
Formal reporting of the statistical test.
WILCOXON
The e-Assessment concerns the application of the Wilcoxon signed rank test which makes students aware of:
The null and alternative hypotheses;
SPSS use to gain output and its subsequent interpretation;
Formal reporting of the statistical test.
WHICHTEST
This e-Assessment concerns the decision of whether to perform the one-sample t-test or the Wilcoxon signed rank test.
Students are expected to use the guidelines that they have been taught that consider the following:
Sample size;
Skewness;
Normality test.
There are templates for students to complete for both statistical tests.
Access to a practice test is available immediately after the corresponding PC class held this week. The practice test is exactly the same
format as the in-class test and remains available until midnight the day before the in-class test is scheduled.
During its availability period, students are allowed unlimited attempts at the practice test getting different data (and hence analysis outcomes)
for each attempt together with full feedback.
