Some more practice with tables

For your analysis section, for each table you need to do three things.

l. Describe the pattern.

2. State the null and alternative/research hypothesis.

3. Interpret the chi-square statistic.

Table 1.

1. Table description is usually a paragraph or so. Here is just one model. The “bits” don’t have to be in this order but they should all be there.

LEAD IN: NOTE THE USE OF THE TOTAL COLUMN TO SET THE STAGE. IT GIVES A POINT OF REFERENCE FOR WHAT IS BIG OR SMALL IN THIS PARTICULAR TABLE.	High poverty is defined as a 10 percent or higher poverty rate in a tract, and according to this classification, some 35.1 percent of all MA tracts reported a high poverty rate to the census in 2000. Poverty was not evenly spread across the state, however. Rather, it appears to have been concentrated along racial and ethnic lines.
FIRST, SOME GENERAL DESCRIPTION OF WHAT THE TABLE SHOWS. NOTE THE DIFFERENCE BETWEEN A POSITIVE AND NEGATIVE RELATIONSHIP.	Consider Table 1. It documents a positive relationship between the proportion of African-Americans in tracts in Massachusetts, 2000, and poverty levels in those tracts. That is, as the proportion of African-Americans increases, so does the poverty rate.
Follow with a more SPECIFIC STATEMENT ANCHORED IN ACTUAL NUMBERS. COMPARE ACROSS CATEGORIES OF THE INDEPENDENT VARIABLE. I USe THE HIGH POVERTY CATEGORY BECAUSE THAT IS WHAT IS OF INTEREST IN THIS PARTICULAR PROBLEM. If comparing TABLES, EX. for Blacks and Hispanics AS IN LAB 3, you would have to describe the PATTERN in each table first, and then compare the tables.	Comparing high poverty tracts, note that nearly 89 percent of tracts where the African-American population was 50 percent or higher reported high rates of poverty, and 79.2 percent of tracts where African-Americans constituted between 7 and 50 percent of the population fell into the high poverty category. In sharp contrast, among non-black tracts – that is, tracts that had 7 percent or fewer African-Americans – only 24.6 percent fell in the high poverty category.

2. Stating the null and the research/alternative hypotheses usually occurs prior to the description and analysis of the pattern in the table. In your final project, it should grow out of your more general discussion of residential concentration by race, i.e., the big ideas and also be connected to your discussion of measurement and variables.

Research/alternative hypothesis: I hypothesize that there is a positive relationship between the minority composition of a census tract and the poverty level of that tract. That is, I expect to find that tracts with a higher proportion of African-Americans report higher rates of poverty than tracts with lower proportions of African-Americans.

Null hypothesis: There is no association between the proportion of African-Americans and the rate of poverty in MA census tracts in 2000; any observed difference in poverty rate between high and low minority tracts is due to chance.

3. Interpreting the chi-square output. Here you need to mention the observed test statistic, the expected test statistic, and your alpha level. You read only the first line of the SPSS output. The rest is boilerplate that does not apply to us. NOTE: I assume that you have already selected alpha at .05.

The observed chi-square statistics of 292.034 is much higher than the expected value for chi-square of 9.488 for a table with 4 degrees of freedom at the .05 level. Indeed, the probability of attaining such a high observed chi-square statistic is less than one thousandth of one percent. On this basis, I reject the null hypothesis of no association between poverty rate and the minority composition of census tracts in MA in the year 2000. Instead, I find a statistically significant relationships between race and poverty at the tract level; the more African-Americans in a tract, the higher the reported poverty rate is likely to be in that tract.