5. A 20-year study conducted in Ypsilanti, Michigan, followed the lives of 66 po
ID: 3236726 • Letter: 5
Question
5. A 20-year study conducted in Ypsilanti, Michigan, followed the lives of 66 poor children who attended preschool in the early 1960s, and 57 poor children from the same community who did not attend preschool. The researchers believed that attending preschool would be associated with many desired life events over the next 20 years, including increased high school graduation rates, decreased rates of receiving assistance from government programs such as welfare in early adulthood, decreased arrest rates in adolescence or early adulthood and increased rates of employment. Thus, there was one key EV, which was preschool attendance with two categories (attended/did not attend preschool). And there were four key RVs with two categories each—graduating from high school (yes/no), on welfare at age 19 (yes/no), arrested at least once within the 20-year study window (yes/no) and employed at the end of the study window (yes/no). You will conduct four chi-square tests of independence using the data from the four crosstab tables below. Use = .05 for all tests. a) State the null and alternative hypotheses in words and symbols for each EV/RV combination. The symbols should show expected differences in the rates of each RV between the population of children attending preschool and the population not attending preschool. b) The data file for this problem is uploaded on the course website. Use TAB2 in Stata to generate the four crosstab tables and chi-square statistics. In your TAB2 program, specify the options for the chi-square statistic, row percentages, and expected frequencies (I’m not sure if you generated expected frequencies in lab, so I’ll tell you how to get expected frequencies. Just type the word EXPECTED after you specify the options for the chi-square statistic and the row percentages). The EV for these chi-square tests is the PRESCHOOL variable. The four RVs are named HSGRAD, WELFARE, ARRESTED and EMPLOYED. You will notice that there are four COUNT variables that identify the observed frequencies in each cell for each crosstab table (one COUNT variable for each RV). You will need to include one of these COUNT variables in each of your TAB2 programs using the [freq = ] subcommand in Stata, with the appropriate COUNT variable specified after the = sign. The reason for this is that you are conducting the chi-square tests using a data file that contains the aggregate-level observed frequencies, not the individual-level data. Run the four chi-square tests of independence and paste your output below: c) Do the data satisfy the minimum expected frequency per cell assumption in each of the four chi-square analyses? Explain. d) Write a paragraph in which you interpret the results of the chi-square tests. Be sure to comment on the chi-square, its associated p-value, and whether the RV proportions in the preschool and no preschool groups differ/do not differ significantly. If any differences are significant, describe the magnitudes of the differences. You should write this paragraph carefully because you are summarizing the possible impacts of attending preschool on four RVs, and there might be evidence of impacts of preschool on some RVs but not others.
Explanation / Answer
From the stata , we can see that the tab2 file generates the following results . The commands are highlighted too
tabulate preschool hsgrad
tabulation of preschool by hsgrad
+--------------------+
| Key |
|--------------------|
| frequency |
| expected frequency |
| row percentage |
| column percentage |
| cell percentage |
+--------------------+
| hsgrad
preschool | no yes | Total
-----------+----------------------+----------
no | 29 28 | 57
| 23.6 33.4 | 57.0
| 50.88 49.12 | 100.00
| 56.86 38.89 | 46.34
| 23.58 22.76 | 46.34
-----------+----------------------+----------
yes | 22 44 | 66
| 27.4 38.6 | 66.0
| 33.33 66.67 | 100.00
| 43.14 61.11 | 53.66
| 17.89 35.77 | 53.66
-----------+----------------------+----------
Total | 51 72 | 123
Pearson chi2(1) = 3.8786 Pr = 0.049
. tab2 preschool welfare [freq= countwelf ]
,chi2 row col cell expected
-> tabulation of preschool by welfare
+--------------------+
| Key |
|--------------------|
| frequency |
| expected frequency |
| row percentage |
| column percentage |
| cell percentage |
+--------------------+
| welfare
preschool | no yes | Total
-----------+----------------------+----------
no | 39 18 | 57
| 43.1 13.9 | 57.0
| 68.42 31.58 | 100.00
| 41.94 60.00 | 46.34
| 31.71 14.63 | 46.34
-----------+----------------------+----------
yes | 54 12 | 66
| 49.9 16.1 | 66.0
| 81.82 18.18 | 100.00
| 58.06 40.00 | 53.66
| 43.90 9.76 | 53.66
-----------+----------------------+----------
Total | 93 30 | 123
| 93.0 30.0 | 123.0
| 75.61 24.39 | 100.00
| 100.00 100.00 | 100.00
| 75.61 24.39 | 100.00
Pearson chi2(1) = 2.9768 Pr = 0.084
tabulate preschool arrested
-> tabulation of preschool by arrested
+--------------------+
| Key |
|--------------------|
| frequency |
| expected frequency |
| row percentage |
| column percentage |
| cell percentage |
+--------------------+
| arrested
preschool | no yes | Total
-----------+----------------------+----------
no | 28 29 | 57
| 34.3 22.7 | 57.0
| 49.12 50.88 | 100.00
| 37.84 59.18 | 46.34
| 22.76 23.58 | 46.34
-----------+----------------------+----------
yes | 46 20 | 66
| 39.7 26.3 | 66.0
| 69.70 30.30 | 100.00
| 62.16 40.82 | 53.66
| 37.40 16.26 | 53.66
-----------+----------------------+----------
Total | 74 49 | 123
| 74.0 49.0 | 123.0
| 60.16 39.84 | 100.00
| 100.00 100.00 | 100.00
| 60.16 39.84 | 100.00
Pearson chi2(1) = 5.4018 Pr = 0.020
tabulate preschool employed
-> tabulation of preschool by employed
+--------------------+
| Key |
|--------------------|
| frequency |
| expected frequency |
| row percentage |
| column percentage |
| cell percentage |
+--------------------+
| employed
preschool | no yes | Total
-----------+----------------------+----------
no | 39 18 | 57
| 33.4 23.6 | 57.0
| 68.42 31.58 | 100.00
| 54.17 35.29 | 46.34
| 31.71 14.63 | 46.34
-----------+----------------------+----------
yes | 33 33 | 66
| 38.6 27.4 | 66.0
| 50.00 50.00 | 100.00
| 45.83 64.71 | 53.66
| 26.83 26.83 | 53.66
-----------+----------------------+----------
Total | 72 51 | 123
| 72.0 51.0 | 123.0
| 58.54 41.46 | 100.00
| 100.00 100.00 | 100.00
| 58.54 41.46 | 100.00
Pearson chi2(1) = 4.2761 Pr = 0.039
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