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CHAPTER THREE

METHODOLOGY

3.0 Introduction

This chapter outlines the research approach, data collection methods, and analytical techniques used in the study. It covers the research design, study area, data sources, processing methods, analysis techniques, and potential limitations.

3.1 Research Design

The study adopts a quantitative research approach, utilizing structured secondary data from the Ministry of Health records to ensure reliability and validity.

3.2 Data Sources

Data will be extracted from databases, records, publications, and journals within the Ministry of Health.

3.3 Data Processing and Analysis Techniques

Data Processing

• Editing: Checking for errors and omissions.
• Coding: Organizing data into meaningful patterns.
• Model Specification & Software: Using statistical tools for tabulation, processing, and report compilation.

Data Analysis

• Descriptive Statistics: Summarizing data through tables and graphs.
• Time Series Analysis: Examining trends and seasonality in HIV prevalence.
• Statistical Interpretation: Aligning findings with research objectives and questions.

3.3.1 Descriptive Analysis

Provides a summary of key trends in the dataset.

3.3.2 Time Series Analysis

Given the time-dependent nature of the data, the study focuses on trend and seasonality in HIV prevalence.

Model Assumption: Multiplicative model

Yt=Tt×StYt​=Tt​×St​

Where:

• YtYt​ = Mortality series
• TtTt​ = Trend component
• StSt​ = Seasonal component

Analytical Techniques:

1. Graphical Presentation
   • Plotting YtYt​ against time.
2. Non-Parametric Tests for Trend
   • Runs Test (Bradley, 1968): Determines if data follows a random process.
     • Hypotheses:
       • H0H0​: HIV prevalence series is stationary.
       • HAHA​: HIV prevalence series is non-stationary.
     • Test Statistic:

       Z=R−μRSRZ=SR​R−μR​​

     • Decision Rule: Reject H0H0​ if Z>Zα/2Z>Zα/2​ at $\alpha =0.05$.
3. Test for Seasonality
   • Kruskal-Wallis Test: Non-parametric alternative to ANOVA.
     • Hypotheses:
       • H0H0​: No seasonality.
       • HAHA​: Presence of seasonality.
     • Test Statistic:

       H=12N(N+1)∑i=1kRi2ni−3(N+1)H=N(N+1)12​i=1∑k​ni​Ri2​​−3(N+1)

     • Decision Rule: Reject H0H0​ if H>χα(k−1)2H>χα(k−1)2​.

3.3.3 Autoregressive Integrated Moving Average (ARIMA)

The Box-Jenkins (ARIMA) model will forecast HIV prevalence in children under 15.

Key Steps:

1. Identification:
   • Determine $p$ (autoregressive terms), $d$ (differencing order), and $q$ (moving average terms).
   • Assess stationarity via correlogram plots.
2. Estimation:
   • Use nonlinear estimation for model parameters.
3. Diagnostic Checking:
   • Verify residuals for white noise; refine model if necessary.
4. Forecasting:
   • Apply exponential smoothing and regression techniques.

Forecast for 2016:

• Regress HIV prevalence against time.

Regional & Residential Analysis (ANOVA):

• Model:

  Yt=β0+β1DR+β2DC+β3DN+β4DEYt​=β0​+β1​DR​+β2​DC​+β3​DN​+β4​DE​

Where:

• YtYt​ = HIV prevalence
• DRDR​ = Dummy for Rural
• DCDC​ = Dummy for Central
• DNDN​ = Dummy for North
• DEDE​ = Dummy for East

3.4 Ethical Considerations

• Respondents will be informed of the study’s academic purpose.
• Data will be handled confidentially.
• Ministry of Health and other stakeholders will be acknowledged appropriately.