Consider　a　one-way　layout　with　three　treatments　with　unknown　means,　and,　and　a　common　unknown　variance.　The　practical　equivalence　of　the　three　treatments　can　be　concluded　if　the　range　of　the　three　means　is　small　in　comparison　to　their　standard　deviation　σ.　This　implies　that　the　range　Δ　of　the　three　reciprocal　coefficients　of　variation,　is　less　than　a　specified　amount.　In　this　article,　it　is　shown　how　to　construct　an　upper　confidence　bound　for　Δ　for　possibly　unbalanced　data　sets.　Small　values　of　this　upper　bound　allow　practical　equivalence　to　be　established　in　an　efficient　manner.　Examples　of　the　implementation　of　this　procedure　are　provided,　and　comparisons　are　made　with　other　approaches.　R　code　to　implement　the　procedure　is　available.　©　Grace　Scientific　Publishing,　LLC.