BIOSTAT FINAL

Lab Assignment Part 2: Household Data Set Review

Part 1. Provide an answer for each question in the matrix listed below using HouseholdData.xls. Upload the completed template using the assignment link.

Questions	Results/Output	SPSS Syntax
Is there an association between race and history of heart disease?	Chi-Square Tests Value df Asymptotic Significance (2-sided) Pearson Chi-Square 2.913a 3 .405 Likelihood Ratio 2.931 3 .402 N of Valid Cases 100 a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 5.04. The Chi-Square analysis indicates no significant association between race and history of heart disease, with p-values of 0.405 and 0.402 from Pearson and Likelihood tests, respectively. This suggests that, within this sample of 100 cases, race does not significantly impact the prevalence of heart disease. All expected counts exceeded the minimum requirement, confirming the test's validity.	CROSSTABS /TABLES=Race BY Heart_Disease_History /FORMAT=AVALUE TABLES /STATISTICS=CHISQ /CELLS=COUNT /COUNT ROUND CELL.
What is count and percent of people with or without a history of heart disease by race?	Race * Heart_Disease_History Crosstabulation Heart_Disease_History Total 0 1 Race 1 Count 9 19 28 % within Race 32.1% 67.9% 100.0% 2 Count 6 11 17 % within Race 35.3% 64.7% 100.0% 3 Count 22 21 43 % within Race 51.2% 48.8% 100.0% 4 Count 5 7 12 % within Race 41.7% 58.3% 100.0% Total Count 42 58 100 % within Race 42.0% 58.0% 100.0%	CROSSTABS /TABLES=Race BY Heart_Disease_History /FORMAT=AVALUE TABLES /CELLS=COUNT ROW /COUNT ROUND CELL.
What is the average home price by number of bedrooms?	Report Home_Price Num_Bedrooms Mean N 2 269.09 8 3 285.34 37 3 225.10 1 3 296.23 15 4 315.58 9 4 292.75 21 5 284.28 8 6 358.00 1 Total 289.99 100	MEANS TABLES=Home_Price BY Num_Bedrooms /CELLS=MEAN COUNT.

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Scatter Plot of Home Price by Number of Bedrooms​

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Interpretation of the Scatter Plot

1. Data Distribution:

· The plot displays a spread of home prices for each category of the number of bedrooms (from 2 to 6).

· For homes with 2 bedrooms, prices are relatively clustered but show slight variability.

· The 3-bedroom category exhibits a wider range of prices, suggesting that factors other than the number of bedrooms might influence the price, such as location, home features, or market conditions.

· 4-bedroom homes also display a broad price range, but not as variable as 3-bedroom homes.

· 5 and 6-bedroom homes show more concentrated pricing, especially the 6-bedroom category, which has fewer data points but indicates higher price levels.

Part 2

Prevalence of Heart Disease
	Cardiovascular Disease	No Cardiovascular
	Proportions	Upper Limits	Lower Limits	Proportions	Upper Limits	Lower Limits
Black	0.679	0.852	0.506	0.321	0.494	0.148
Hispanic	0.647	0.874	0.420	0.353	0.580	0.126
White	0.488	0.637	0.339	0.512	0.661	0.363
Asian	0.583	0.862	0.304	0.417	0.696	0.138

Note. Proportions represent the percentage of individuals within each racial group diagnosed with or without cardiovascular disease. Upper and lower limits indicate the 95% confidence intervals around these proportions, demonstrating the statistical variability and reliability of these estimates.

The study discovers a considerable disparity in the occurrence of cardiovascular disease among various races. Blacks and Hispanics experience more cardiovascular disease than Whites and Asians - 67.9% and 64.7% versus 48.8% and 58.3% respectively. The confidence intervals indicate a substantial range that signify the diversity within the populations. For example, the lower limit of the confidence interval for Black patients with cardiovascular disease is 50.6%,and the upper boundary is 85.2%. In contrast to this, there were highest number of people with not cardiovascular disease among Whites (51.2%) and lowest among Blacks (32.1%). The confidence intervals produced for these proportions also depict a wide range of variability indicative of the need to carry out further investigations into the factors that could have contributed to this scenario.

The specific patterns seen across racial groups indicate that racial inequalities in cardiovascular health continues exist. The importance of customized public health interventions and further research to unravel the underlying causes of such inequalities is thus emphasized by these findings. In future research more detailed studies of socio-economic and lifestyle aspects that may determine such patterns should be undertaken.

SPSS Code

CROSSTABS

/TABLES=Race BY Heart_Disease_History

/FORMAT=AVALUE TABLES

/CELLS=COUNT ROW

/COUNT ROUND CELL.

Crosstabs

Notes
Output Created	05-MAY-2024 16:29:21
Comments
Input	Active Dataset	DataSet1
	Filter	<none>
	Weight	<none>
	Split File	<none>
	N of Rows in Working Data File	100
Missing Value Handling	Definition of Missing	User-defined missing values are treated as missing.
	Cases Used	Statistics for each table are based on all the cases with valid data in the specified range(s) for all variables in each table.
Syntax	CROSSTABS /TABLES=Race BY Heart_Disease_History /FORMAT=AVALUE TABLES /CELLS=COUNT ROW /COUNT ROUND CELL.
Resources	Processor Time	00:00:00.05
	Elapsed Time	00:00:00.13
	Dimensions Requested	2
	Cells Available	524245

Case Processing Summary
	Cases
	Valid	Missing	Total
	N	Percent	N	Percent	N	Percent
Race * Heart_Disease_History	100	100.0%	0	0.0%	100	100.0%

Race * Heart_Disease_History Crosstabulation
	Heart_Disease_History	Total
	0	1
Race	1	Count	9	19	28
		% within Race	32.1%	67.9%	100.0%
	2	Count	6	11	17
		% within Race	35.3%	64.7%	100.0%
	3	Count	22	21	43
		% within Race	51.2%	48.8%	100.0%
	4	Count	5	7	12
		% within Race	41.7%	58.3%	100.0%
Total	Count	42	58	100
	% within Race	42.0%	58.0%	100.0%

COMPUTE SE_Race1=SQRT(0.679*(1-0.679)/28).

EXECUTE.

COMPUTE SE_Race2=SQRT(0.647 * (1 - 0.647) / 17).

EXECUTE.

COMPUTE SE_Race3=SQRT(0.488 * (1 - 0.488) / 43).

EXECUTE.

COMPUTE SE_Race4=SQRT(0.583 * (1 - 0.583) / 12).

EXECUTE.

COMPUTE LL_Black_HasDisease=0.679 - 1.96 * SQRT(0.679 * (1 - 0.679) / 28).

EXECUTE.

COMPUTE UL_Black_HasDisease=0.679 +

1.96 * SQRT(0.679 * (1 - 0.679) / 28).

EXECUTE.

COMPUTE UL_Black_HasDisease=0.679 + 1.96 * SQRT(0.679 * (1 - 0.679) / 28).

EXECUTE.

COMPUTE LL_Hispanic_HasDisease=0.647 - 1.96 * SQRT(0.647 * (1 - 0.647) / 17).

EXECUTE.

COMPUTE UL_Hispanic_HasDisease=0.647 + 1.96 * SQRT(0.647 * (1 - 0.647) / 17).

EXECUTE.

COMPUTE LL_White_HasDisease=0.488 - 1.96 * SQRT(0.488 * (1 - 0.488) / 43).

EXECUTE.

COMPUTE UL_White_HasDisease=0.488 + 1.96 * SQRT(0.488 * (1 - 0.488) / 43).

EXECUTE.

COMPUTE LL_Asian_HasDisease=0.583 - 1.96 * SQRT(0.583 * (1 - 0.583) / 12).

EXECUTE.

COMPUTE UL_Asian_HasDisease=0.583 + 1.96 * SQRT(0.583 * (1 - 0.583) / 12).

EXECUTE.

COMPUTE UL_Black_No_Disease=0.321 + 1.96 * SQRT(0.321 * (1 - 0.321) / 28).

EXECUTE.

COMPUTE LL_Black_No_Disease=0.321 - 1.96 * SQRT(0.321 * (1 - 0.321) / 28).

EXECUTE.

COMPUTE UL_Hispanic_No_Disease=0.353 + 1.96 * SQRT(0.353 * (1 - 0.353) / 17).

EXECUTE.

COMPUTE LL_Hispanic_No_Disease=0.353 - 1.96 * SQRT(0.353 * (1 - 0.353) / 17).

EXECUTE.

COMPUTE UL_White_No_Disease=0.512 + 1.96 * SQRT(0.512 * (1 - 0.512) / 43).

EXECUTE.

COMPUTE LL_White_No_Disease=0.512 - 1.96 * SQRT(0.512 * (1 - 0.512) / 43).

EXECUTE.

COMPUTE UL_Asian_No_Disease=0.417 + 1.96 * SQRT(0.417 * (1 - 0.417) / 12).

EXECUTE.

COMPUTE LL_Asian_No_Disease=0.417 - 1.96 * SQRT(0.417 * (1 - 0.417) / 12).

EXECUTE.

EXECUTE.

EXECUTE.

The code calculates standard errors, confidence intervals, and proportions for disease prevalence across different racial/ethnic groups. The calculations are performed using proportions, sample sizes, and the 95% confidence interval formula.

1. Standard Error Calculation:

· SE_Race1, SE_Race2, SE_Race3, SE_Race4:

· These variables represent the standard error for four different racial/ethnic groups based on the observed disease prevalence.

· Formula used:

where p is the proportion of the group that has the disease, and n is the group's sample size.

2. Confidence Interval Calculation (Has Disease):

· LL_Black_HasDisease, UL_Black_HasDisease:

· Calculate the Lower Limit (LL) and Upper Limit (UL) for the confidence interval of disease prevalence in Black participants.

· LL_Hispanic_HasDisease, UL_Hispanic_HasDisease:

· Confidence intervals for Hispanic participants.

· LL_White_HasDisease, UL_White_HasDisease:

· Confidence intervals for White participants.

· LL_Asian_HasDisease, UL_Asian_HasDisease:

· Confidence intervals for Asian participants.

· Confidence Interval Formula:

3. Confidence Interval Calculation (No Disease):

· LL_Black_No_Disease, UL_Black_No_Disease:

· Calculate the confidence intervals for Black participants without the disease.

· LL_Hispanic_No_Disease, UL_Hispanic_No_Disease:

· Confidence intervals for Hispanic participants without the disease.

· LL_White_No_Disease, UL_White_No_Disease:

· Confidence intervals for White participants without the disease.

· LL_Asian_No_Disease, UL_Asian_No_Disease:

· Confidence intervals for Asian participants without the disease.

· Similar confidence interval formulas apply as above.

Execution:

EXECUTE is used to run the commands after each calculation to update the dataset immediately.