Ratio Statistical Analysis With IBM SPSS

Introduction

In business, an appraisal is a key activity in evaluating the well-being of a business. The truth is this cannot be done without having historical pieces of information on the business. Well, this still takes us back to analysis! Ratio Statistical Analysis is one of the quickest and most precise analysis approaches for business appraisal!

A statistical ratio analysis is a means to show relative size between two or more values. The values are not the actual values of either, but rather a means to show how the values are related.

We shall perform a statistical ratio analysis on property assessment data to observe the region due for appraisal.

What are Ratio Statistics, and what are they used for?

The Ratio Statistics process is done to extract while describing a complete list of summary statistics of two variables with scalar type data.

For businesses, ratios serve as benchmarks. Within an industry, they assess the stocks. They assess a company's current performance in comparison to its past results.  

In most circumstances, it is also crucial to comprehend the factors influencing ratios because management has the freedom to occasionally change its approach to improve the stock and business ratios.

Data

Property_assess_data compiles data on house sales and appraisals.

Variables name	Description	Values
propid	Property ID	Scale
town	Township	Eastern, Central, Southern, Northern, Western  (Nominal)
assessor	Assessor	Scale
saleval	Sale value of house	Scale
lastval	Value at last appraisal	Scale
time	Years since last appraisal	Scale

 

Business Task

With the above data, we are required to Analyze the property values of an asset in a given region of study so that the management can determine fair property values to calculate property taxes across the county accurately.

However, the resources for maintaining current evaluations are few, so it is crucial to know the various house appreciation rates in various communities.

Running Analysis: Ratio statistics are used to help assess property values.

Ratio Statistics Using Ratio Statistics to Aid Property Value Assessment, Firstly, download the dataset from the above link as CSV, and import the data appropriately.

Then Go to the Variable View in the SPSS Widow code the measure and Values of Township as Shown in figure 1.

Figure 1: Recoding the measure and values of the data

Secondly, go to the data view, then from the menus, choose: Analyse => Descriptive Statistics => Ratio

Figure 2: Descriptive Statistics and Ratio

Thirdly, select value at last appraisal as the numerator variable, the Sale value of a house as the denominator variable, and then, most importantly, Select Township as the grouping variable. Then Click Statistics.

 

Figure 3: Ratio statistics of data last appraisal and sales value.

From Figure 4, after Statistics have been Selected, you may uncheck both Median in the Central Tendency group, the PRD and check the Median centered COV in the Dispersion group.

After the above stated in figure 3 has been achieved, Input 0.8 [AC1] as the Low Proportion and 1.2 as the High Proportion. Click Add.

Doing the same thing for In the concentration Index, Input 20[AC2]  in the percentage of the median textbox. Click Add. Click Continue. Click OK in the Ratio Statistics dialogue then SPSS does the magic!

Figure 4: selecting the dispersion and central tendencies statistics

 

 

Summary Statistic and Interpretation

The summary statistics you requested are shown in this table for each category identified by the grouping variable.

This is the five (5) region property percentages by region from the observation collected with Eastern and northern have the list and most property assets of 17.8% and 22%, respectively.

Case Processing Summary
		Count	Percent
Township	Eastern	177	17.7%
	Central	187	18.7%
	Southern	205	20.5%
	Northern	220	22.0%
	Western	211	21.1%
Overall		1000	100.0%
Excluded		0
Total		1000

Table 1: township and region Size by percentage

The Median, a statistic of central tendency, provides information on the "usual" relationship between the most recent assessed value and the sale price. The township whose housing values have changed the most can be identified by contrasting the median ratios for each township.

Group	Median	Coefficient of Dispersion	Coefficient of Concentration
			Percent between 0.8 and 1.2 inclusive	Within 20% of Median inclusive
Eastern	.867	.128	67.2%	78.5%
Central	.904	.118	75.9%	81.8%
Southern	.747	.199	36.1%	58.5%
Northern	.963	.070	95.9%	95.9%
Western	.816	.118	55.5%	84.8%
Overall	.873	.141	66.3%	75.7%

Table 2: Ration statistics for the last appraisal/sale value of a house

From table 2, because its median ratio is closest to 1, the typical value of a Northern township house has changed the least. Contrariwise, Southern township's housing values have changed the most.

The variability in the ratios is often measured by the coefficient of dispersion (COD). Greater variability is indicated by higher COD levels. With a COD of 1.99[AC3] , southern township ratios exhibit the most variation.

Although the within a percent of median coefficient of concentration (COC) also assesses variability, it is simpler to understand because it just shows the proportion of values that are within a certain fraction of the Median. Less variability is indicated by this statistic's larger values.

The within 20% COC confirms that the ratios in Northern township had the least variability.

The business is particularly interested in updating the assessments for homes whose value has changed by more than 20% of the last appraised value.

Though the Median, COD, and within 20% COC are helpful measures of the distribution of ratios, they cannot help you determine how many homes are "of interest" to the business.

The percentage between the coefficient of concentration (COC) is a flexible measure that allows us to determine the percentage of ratios that fall within an arbitrary interval.

 

By requesting the COC for the interval between 0.8 and 1.2, you will be able to determine the percentage of homes in each township whose values have changed by less than 20% of the last appraised value.

In Northern Township, less than 20% of recent property transactions had house values that had increased or decreased by more than 96% since the previous assessment. As a result, the clerk's office only interests 4.1% of the properties. It is usually fine to postpone the reappraisal of properties in that municipality until later.

Conclusion

Using the Ratio Statistics procedure, we have found that the value ratio at last appraisal to the Sales value of a house differs greatly across townships in terms of  central tendency and dispersion.

Moreover, we found that the percentage between the coefficient of concentration gives us a more directly useful number than the other statistics. Thus, it is recommended that you focus more on the COC.

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