CHI-SQUARE TEST 4

Chi-SquareTest

Chi-SquareTest

Instatistics, Chi-square is mostly used in comparing observed data towhat was expected from the specific hypothesis (Eck& Ryan, 2015).It can be used in cases where primary and secondary means of datacollection is used (The Statistic, 2015). Whentesting Chi-square for independent, the method of sampling must be asimple random, and the variables which are under study ought to becategorical. Further, in case where contingency table is used todisplay sample data, the expected frequency should be at least fivefor each cell.

Considera case where opinion poll is used to survey 1000 voters. Therespondents are to be classified according to their gender (female ormale) as well as according to their voting preferences (independent,republicans or democrat). These parameters form the independent andthe dependent variables StatTrek, 2016).

Inthis case, the alternative and null hypotheses become:H_{a}:Gender and voting preferences are not independent

H_{0}:Gender and voting preferences are independent (StatTrek, 2016)

Asindicated above, the use of chi-square would be very appropriate whencarrying out this study, since simple random sampling is used and thevariables are categorical. The expected frequency for each table isabove five on the contingency table as indicated by the sample resulttable below.

Gender |
Voting Preferences |
Row Total |
||

Independent |
Republican |
Democrat |
||

Male |
50 |
100 |
300 |
450 |

Female |
100 |
300 |
150 |
550 |

Total |
150 |
400 |
450 |
1000 |

Bythe use of 0.05 as the significance level, one is able to indicatethe disparity between the voting preferences between genders. Forinstance, if p-value is 0.003, then the null hypothesis is reject asit is far less than 0.05 (the significance level) and the vice-versa.

Part2

Simplesize is related to statistical study test and study in that itdetermines the hypothesis to be used and the method of analysis to beemployed such as Chi-square among others. Planning sample sizedetermines the method of analysis to be used.

References

Eck,D. & Ryan, J. (2015). *TheChi Square Statistic.*Available at http://math.hws.edu/javamath/ryan/ChiSquare.html

StatTrek (2016). *Chi-SquareTest for Independence.*Available at

__http://stattrek.com/chi-square-test/independence.aspx?Tutorial=AP__

The Statistic (2015). Available at

__http://www.stat.wmich.edu/s216/book/node114.html__