Jumpstarting Chapter Four

Introduction

This paper statistically analyses the difference among groups in term of a categorical dependent variable. It compare men and women in terms of their political party affiliation (democrat, republican,). The research aims to understand whether composition of the sample and interpret the data in relation with the population.

Table 1is a contingency table is a showing the items from a population of male and female. The genders are classified according to two characteristics in terms of party identification. The objective is of this table is to analyze the relationship between two qualitative variables i.e. to investigate whether a dependence relationship exists between two variables or whether the variables are statistically independent.

Table 1

Gender data
Party Identification	Males	Females	Total
Democrat	200	700	900
Republican	500	200	700
Totals	700	900	1600

Discussion Question

Transform table into one suitable for task one

Transforming into percentage distribution

A number of factors should be considered when transforming a contingency table for interpretation. According toCreswell (2011), it is important to understand the patternsin order to interpret the contingency table. The value of a cell is the proportion of observation from a particular independent valuable. In this case, male and female genders are the independent valuables. The next step is to convert the observation in the cells into a percentage of the total observations in the column. One must show the total number for each column on which to base the percentageCalifornia State University (2014). The last stage is interpretation. Interpretation involves comparing the percentage across the dependent categories (the rows). In this case, Republican and Democratic parties are the dependent valuables.

Table 5

Gender data
Party Identification	Males	Females	Total  (N)
Democrat	200/900 * 100%	700/900 * 100%	900
Republican	500/700 * 700%	200/700 * 100%	700
Totals	700	900	1600

Table 6

Gender data
Party Identification	Males	Females	Total  (N)
Democrat	22 %	78 %	100 %
Republican	71 %	29 %	100 %

Interpretation in terms of gender

The participants of this research were 700 men and 900 women. Both men were required to declare their party identification. Table 6 shows that out of 900 participants more women, 78% (n = 700), than men (22 %) (n= 200), identify with Democratic Party. Conversely, out of 700 participants, more men 71% (n=500) than women 29 % (n=200) declared their support for Republican Party.

Determine whether the population yielded a fair sample given a population containing roughly equal number of men and women.Critique the data, why? Support your argument utilizing the relationship between population and sample.

Comparison of population and samples can be done by several methods. According to Creswell, the chi-square analysis is best used to analyze independent variables. Chi-squares allow for more than two or more outcomes. It is possible to test the null hypothesis against the research hypothesis with chi-square.

We can do a chi-square for the independent variables. The independent variable in this case are two: gender and party identification. We should test the hypothesis whether there is any difference between gender and party membership.

The following procedures should be followed when computing a hypothesis, according to Engel (2009).

Procedure for testing a hypothesis

1. State the null and alternate hypothesis
2. Select a level of significance.
3. Identify the test statistic
4. Formulate a decision rule and identify the rejection region
5. Determine the value of the test statistic and
6. Make a conclusion.

Step 1. State the null and alternate hypothesis

The null hypothesis

H₀: There is no difference in gender and party membership.

The alternative hypothesis

H₁: There is adifference in gender and party membership.

Step 2.  Select a level of significance

The test level of significance for alpha

We take α = 5% 0r 0.05

Step 3. Identify the test statistic

The test statistic in this case is chi-square.

Notation of Chi-square

The value of such that the area to its right under the chi-square curve is equal to and is denoted by . The value is the point such that the area to its right is . Hence, the area to its left is .

Step 4. Formulate a decision rule and identify the rejection region

For Chi-square;

Test statistic

Rejection region

Step 5. Calculate the value of the test statistic and

Calculating the Proportions

Table 2

Gender data
Party Identification	Males	Females	Total
Democrat	700*900/1600	900*900/1600	900
Republican	700*700/1600	900*700/1600	700
Totals	700	900	1600

Table 3

Gender data
Party Identification	Males	Females	Total
Democrat	393.75	506.25	900
Republican	306.25	393.75	700
Totals	700	900	1600

The x² values represent the accumulated differences between observed and expected cell counts.

Table 4

Observed (o)	Expected (e)	(o-e)	(o-e)2	(o-e)2 /e
200	393.75	-193.75	37, 539.0625	95.3373
500	306.25	193.75	37, 539.0625	122.576
700	506.25	193.75	37, 539.0625	74.1512
200	393.75	-193.75	37, 539.0625	95.3373
			Total	387.4018

Using the Test statistic

X² = 387.4018

The value of X² is observed in the chi-square is 387.4018

We should then compare it with the critical values in chi-square table.

The number of degrees of freedom for a contingency table with  rows and  columns is .

d.f = (2-1) (2-1)

d.f = 1

Critical value (alpha = .05, 1 df) is 3.841

Step 6. Make a conclusion/ decision

Rejection region

387.4018 ˃3.841

• We should reject or fail to accept the null hypothesis H₀
• We should take the alternative hypothesis.
• H₁: There is difference in gender and party membership.

Critique the data, why? Support your argument utilizing the relationship between a population and sample.

The chi-square in this research is used to test for independence of two variables, gender and party identification. The chi-square test proves that there is a difference between gender and party identification.  Gender and party membership are both dependent. Thus, the data is a fair representative sample of the population. It succeeds in providing the association between the dependent and independent variables.

On the opposing side, this method may not give correct results because of the underlying assumptions. According to explorable.com (2014), one of such assumption is that the population from which the sample is obtained has normal distribution. Therefore, the independence test might be misleading. The p-value used is an approximate value for correlation. The same people who participated in the first data might participate in the second one. The above case means that it is possible to obtain two measurement from one participant. Another assumption is that the distribution of deviations of observed and expected frequency counts has a normal distribution.

References

California State University. (2014). Contingency Tables. Retrieved from http://www.csulb.edu/~msaintg/ppa696/696bivar.htm

Creswell, J. W. (2003). Research Design: Qualitative, Quantitative and Mixed Methods Approaches. Second Edition, SAGE. Thousand Oaks. USA.

Engel, R. J. (2009). Fundamentals of Social Work Research. Thousand Oaks. USA.: SAGE.

Explorable.com (Sep 24, 2009). Chi Square Test. Retrieved Sep 03, 2014 from Explorable.com: https://explorable.com/chi-square-test