Answer
$ANOVA$
Work Step by Step
$When\:three\:or\:more\:means\:are\:compared,\:$
$the\:technique\:is\:called\:analysis\:of\:variance\:$
$\left(ANOVA\right).The\:ANOVA\:technique\:uses\:$
$two\:estimates\:of\:the\:population\:variance.\:$
$The\:between-group\:variance\:is\:the\:variance\:of\:$
$the\:sample\:means;\:the\:within-group\:variance\:$
$is\:the\:overall\:variance\:of\:all\:the\:values.\:$
$When\:there\:is\:no\:significant\:difference\:among\:$
$the\:means,\:the\:two\:estimates\:will\:be\:$
$approximately\:equal\:and\:the\:F\:test\:value\:will\:be\:$
$close\:to\:1.\:If\:there\:is\:a\:significant\:difference\:$
$among\:the\:means,\:the\:between-group\:$
$variance\:estimate\:will\:be\:larger\:than\:the\:$
$within-group\:variance\:estimate\:and\:a\:significant\:$
$test\:value\:will\:result.$
