Statistical Research Techniques using Softwares Revision

Priority and syllabus note

The course has 15 hours for Module 1, 20 for Module 3 and 30 practical hours for Module 4. Module 2 is labelled 10 hours although its sub-unit entries sum to 15. The ESE specifies 2-, 6- and 12-mark theory answers; practical evaluation gives 30 marks for problem-solving and 5 for the record. The practical record minimum is five problems. Priorities follow this evidence rather than guessed topic-wise marks.

Hour discrepancy: please check the intended Module 2 allocation with your lecturer; this material preserves the supplied syllabus figures.

MUST MASTER

Testing procedure and interpretation; the listed z, t, paired t, one-way ANOVA, chi-square and simple non-parametric problems; survey analysis and software skills.

IMPORTANT

Research design, sampling, proposal writing, p-value, power and test assumptions.

QUICK-SCORE

Definitions, hypothesis distinctions, test purpose, error types and conclusion wording.

Scope check

One-way ANOVA only. Sign, median and Wilcoxon ranked tests are limited to simple problems. The supplied syllabus does not specify the Wilcoxon variant.

MODULE 1 · 15 HOURS

Research methodology

10 core concepts

Research question
Research design
Qualitative research
Quantitative research
Data collection
Target population
Sampling technique
Questionnaire
Proposal
Report and interpretation

Key terms

Objective · population · sample · sampling frame · response · variable · questionnaire · descriptive statistics · limitation · communication

Common mistakes: broad questions; leading questions; unclear target population; convenience sample treated as representative; causal claim from survey association.

Expected / Exam-Focused Questions based on the syllabus

2 marks: Define research design; distinguish qualitative and quantitative data; define sampling frame.
6 marks: Outline a research proposal; explain data collection and sampling for a social issue.
12 marks: Plan a social survey on a chosen issue and explain how results would be collected, summarised and reported.

Checklist

I can state a focused research question and objective.
I can distinguish qualitative and quantitative approaches.
I can justify a sampling and data-collection plan.
I can outline and communicate a research proposal/report.
I can identify survey limitations and protect participant information.

MODULE 2 · HOURS TO CONFIRM

Testing of hypothesis

10 core concepts

Parameter
Statistic
Simple hypothesis
Composite hypothesis
Null hypothesis
Alternative hypothesis
Type I error
Type II error
Significance level and p-value
Power and critical region

Key terms and reminders

Null model · test statistic · significance level α · p-value · power 1−β · critical region · reject · do not reject

Do not say a p-value is the probability the null hypothesis is true.

Common mistakes: treating “do not reject” as proof; choosing test direction after seeing data; confusing α with p; calling statistical significance practical importance.

Expected / Exam-Focused Questions

2 marks: define parameter, statistic, p-value or significance level.
6 marks: explain Type I and II errors; distinguish simple and composite hypotheses; outline the testing procedure.
12 marks: explain hypothesis testing from claim to contextual decision, including α, p-value, errors and power.

Checklist

I can write H₀ and H₁ from a research question.
I can distinguish parameter/statistic and simple/composite hypotheses.
I can explain Type I and Type II errors.
I can interpret p-value, α, power and critical region correctly.
I can write a decision and conclusion in context.

MODULE 3 · 20 HOURS

Parametric and non-parametric tests

10 core concepts

One-mean z test
Two-mean z test
One-sample t test
Independent two-sample t test
Paired t test
One-way ANOVA
Chi-square association test
Sign test
Median test
Wilcoxon ranked procedure

Key terms

Standard error · degrees of freedom · paired difference · pooled variance · between-group variation · expected count · rank · critical value · assumption · association

Choose the procedure: one mean → one-sample z/t; two independent means → two-mean z/t; same units twice → paired t; three or more means with one factor → one-way ANOVA; categorical association → chi-square; simple sign/rank/count setting → the matching non-parametric procedure.

Common mistakes: paired observations treated as independent; ANOVA interpreted as proving all means differ; chi-square used with the wrong expected counts; degrees of freedom omitted; assumptions ignored; exact Wilcoxon variant assumed without checking.

Expected / Exam-Focused Questions

2 marks: define degrees of freedom; state the purpose of one-way ANOVA; define expected frequency.
6 marks: distinguish paired and independent t tests; explain the chi-square test for association; outline one-way ANOVA.
12 marks: select and carry out an appropriate listed test for supplied data, stating hypotheses, method, decision and interpretation.
Numerical: compute a z/t statistic; paired differences; ANOVA F components; chi-square statistic; simple sign/median/Wilcoxon-ranked problem.

Checklist

I can select the test based on question, data and design.
I can calculate the listed z and t statistics and identify degrees of freedom.
I can explain what a significant one-way ANOVA does and does not show.
I can build expected counts and calculate chi-square for association.
I know the simple sign, median and Wilcoxon-ranked procedures required by my lecturer.

MODULE 4 · 30 HOURS

Data analysis using software

10 practical skills

Translate an issue into a survey question
Prepare a questionnaire
Define target population and sample
Code and enter data
Check missing or inconsistent values
Calculate descriptive statistics
Make clear diagrams
Prepare geographical representation where applicable
Run a suitable statistical test in R, Python or spreadsheet
Interpret and report the result

Complete at least five practical-record problems as the syllabus requires. The project should document question, sampling, instrument, data, analysis, findings and limitations.

Checklist

I can explain my survey and sample.
I can prepare descriptive tables and diagrams with labels.
I can choose and run an appropriate analysis in the software I use.
I can interpret the output and state its limitations.
I have five or more complete record problems.

Question bank and answer-writing guide

These are expected/exam-focused practice questions based on the syllabus, not actual MGU questions.

2-mark questions

Define a parameter and a statistic.
What is a Type I error?
Define a p-value in the context of a test.
What is a paired t test used for?
What is the purpose of one-way ANOVA?
State the chi-square expected-count formula.
Give one difference between qualitative and quantitative research.
What is a critical region?

6-mark questions

Explain the stages of preparing a research proposal.
Explain null/alternative hypotheses, significance level and p-value.
Compare one-sample t and paired t procedures.
Describe one-way ANOVA and its conclusion.
Explain how to test association of attributes using chi-square.
Describe the steps in a social survey project using spreadsheet, R or Python.

12-mark questions

Develop a research plan for a real social issue, including design, sampling, data collection and reporting.
Explain statistical hypothesis testing, error types, significance level, p-value, power and critical region.
For a supplied research problem, choose an appropriate test from the prescribed list, show the procedure and interpret its result.
Describe a social survey and software-based data analysis project, from questionnaire through descriptive summaries and report.

Numerical and commonly confused practice

Calculate a one-mean z or t statistic from supplied summary data.
Compare two independent means using the procedure and assumptions specified in the question.
Calculate paired differences and a paired t statistic.
Complete a one-way ANOVA table and interpret F.
Find expected cell counts and χ² for a contingency table.
Distinguish paired vs independent samples; p-value vs α; statistical vs practical significance; association vs causation.

Model-answer shape

2 marks: definition plus one distinguishing point.

6 marks: definition, explanation, formula/procedure, small example and interpretation.

12 marks: introduction, hypotheses or research objective, method and assumptions, calculation/table, decision, contextual interpretation and limitation/conclusion.

For a test calculation: Given → hypotheses → assumptions/test choice → α → formula → substitution → statistic and p/critical value → decision → conclusion in context.

7-day revision plan

Day	Focus and output
1	Research design, qualitative/quantitative methods, sampling; outline one proposal.
2	Parameter/statistic, hypotheses, errors, α, p-value, power and critical region.
3	One-mean and two-mean z; one-sample and two-sample t.
4	Paired t, one-way ANOVA and assumptions/interpretation.
5	Chi-square, sign, median and Wilcoxon ranked simple problems.
6	Survey project, descriptive output and software practice; check record minimum.
7	Mixed timed answers, formula recall, correct errors and review conclusion wording.

14-day revision plan

Day	Focus
1	Research question, design and objectives
2	Qualitative/quantitative research and data collection
3	Sampling, questionnaire and proposal/report structure
4	Parameter, statistic and hypothesis types
5	Errors, significance, p-value and power
6	Testing procedure and critical region; short-answer retrieval
7	One-mean and equality-of-two-means z tests
8	One-sample and independent two-sample t tests
9	Paired t and one-way ANOVA
10	Chi-square test for association
11	Sign, median and Wilcoxon-ranked simple problems
12	Survey questionnaire, coding, sampling and descriptive analysis
13	Software analysis, interpretation and record completion
14	Mixed practice, model answer writing and personal error review

Final 24-hour checklist

I can write H₀/H₁ and select a test from the design.
I can state what a p-value and significance level mean.
I can solve at least one representative problem for each listed test.
I can distinguish paired, independent, categorical and multiple-group settings.
I can write a conclusion without overstating the evidence.
My social survey/report and five-problem practical record are prepared as required.

If you can do these things, you are exam ready: frame the question, choose a method, show the procedure, explain the output, and state a careful conclusion.

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