The research on the number of Hispanics persons who were self-employed had a sample (total) of 7,760 and the gender ratio was 64% for men and 36% for women. This translates to 2,102 more men than women. The research also clearly showed that Hispanic women preferred to be self-employed in the service industry, a significant 55% compared to a meager 9% from men. Based on the table provided from the research article, the Chi Square value for the occupation of “operators, fabricators, and laborers is x2=87.99. The chi Square determines whether there is statistical discrepancies between the observed results and expected results in one or more categories. In order to compare the calculated results, the sample must be randomly drawn from a large population; variables must be independent, mutually exclusive, and exhaustive, and data must be reported in raw frequencies (not percentages). According to Polit and Beck (2008), chi square(x2) test is a test used to test hypothesis about the proportion of cases that fall into different categories, as when a contingency table has been created.
The contingency table contains rows and columns values and their totals. Chi Squares analysis utilizes the p value which indicates the level of significance, that is, a point at which you can say with % confidence that the difference is not due to chance alone. From the research article the value of p= (p<0.01) represents the difference between the percentage of men and women who are “operators, fabricators, and laborers.” P<0.01 is indicated on the table and the symbol (***) represents tested statistics for difference between samples; with the expectations of the education variable (Holcomb, 2007).The critical value ( x2) for this occupation is 87.99, inferring that the difference between men and women is statistically significant.
Since the chances of p value being wrong is small, the relationship is statistically significant based on the obtained results that demands rejection of the null hypothesis. All occupation’s x2 values are > than 6.63 implying that there is a significant difference between the data sets. All the differences between the occupations have been found to be statistically significant based on the fact that they were all tested using the value p>0.01.The researcher was attempting to reduce the possibility of committing a type II error, which essentially increased the possibility of a type I error being committed.
According to Munro (2005), with a level of significance, researchers may never know when they have made an error in statistical decision-making, and naturally try to reduce the risk of committing either type of error. Unfortunately, one can never be 100% certain due to a researcher bias, sampling error, problems with reliability and validity, or even the fact that there are too many sources of error to be controlled. The probability level infers the chances of the outcome being within certain vicinity. According to Zuiker et al. (2003) the probability level for the “high school graduate” is p>.10, and the probability level for the “bachelor’s degree or more” is p<.05, which results in the bachelor degree having a greater statistically significance as per the information provided on the graph. A p value of 0.05 means that only 5 percent of variables would have been equal or greater than the x2 value of 5.81.At this time, I don’t feel that I can elaborate further, as other important criteria needs to be provided in order to ascertain the relative importance of the two different samples. I feel that more information is needed determine what coefficients are statistically different between the two samples. The graph only listed three variables, and there is a need for more acculturation variables in order to evaluate the true significance.
The null hypothesis for the difference in the percentages of men and women for “craft, precision, and repair” should be rejected due to significant differences between the sets of data. This can also be categorized as a type I error. Polit et al. (2008) report that whether a null hypothesis is accepted or rejected based on sample data, the hypothesis is used to make inferences about relationships within the population. ”Some college” does not have a chi square value and its difference is therefore not statistically significant as no test was performed. Moreover, the null hypothesis for “immigrated to the united states” should be rejected because more research is necessary to examine this population as the information that is provided in the graph serves only a baseline for investigating the gender differences for Hispanic self employed.
As previously mentioned, there is a chi square testing is less than high school, some college, and immigrated to the United States. With that being said, how will the reader be able to measure the like hood that the observed association between the listed independent variables and the dependent variables (i.e., participants) is caused by chance? There is no threshold to determine statistical significance. The differences in the occupations were not surprising. The large x2 values indicate that the occurrence could not be due to chance alone and sampling errors such as generalizing sample data from the larger population were minimal. The differences between men and women are as well not dramatic. The chi square values for all occupation and education categories are greater than the critical values (tables) which are 6.63 and 2.87 respectively. This implies that the differences were statistically significant and within parameters. Based upon this analysis, the alternative hypothesis leads the reader to believe that Hispanic self-employed women are more likely to have an occupation and educated than men.
References
- Holcomb, Z. (2007). Interpreting basic statistics. (5th ed.). Glendale, CA: Pyrczak Publishing.
- Munro, B. H. (2005). Statistical methods for health care research. (5th ed. P. 588) Chestnut Hill, Massachusetts: Lippincott Williams & Wilkins.
- Polit, D. F., & Beck, C. (2008). Nursing research generating and assessing evidence for nursing practice. (8th ed., p. 600). Philadelphia, PA: Lippincott Williams & Wilkins.
- Zuiker, V. S., Katras, M. J., Montalto, C. P., and Olson, P. D. (2003).Hispanic Self-Employment: Does Gender Matter? Hispanic Journal of Behavioral Sciences, p. 25: 73-94.