7.4 Tips, Formulas and Definitions of Terms

Question 1

As you get started, it is important to stop and ask what might be the most basic - and most important - questions in the use of data: 'have we found the correct number?' and 'what event or events are most appropriate to answer the question posed?' For example, we will examine data concerning abuse reports and 'founded' abuse reports. Which of these is the most appropriate data to look at and report on? It depends on the question that is being asked and requires a good working knowledge of the data, the intent of the question and the definition of the data. The issue of what data to use to respond to a question will resurface again and again.

A percent tells you how many out of 100. The way to calculate percent is to write a fraction whose denominator (the number on the bottom) is the number after the word of and whose numerator (the one on the top) is the other number and then multiply by 100. Frequently you are dividing the smaller number by the larger number.

A comparison examines two or more items to establish similarities and dissimilarities.

Question 2

Percents may be used to show a change--either an increase or decrease-- in an amount, quantity or value. To calculate PERCENT CHANGE, use the following formula:

(Most Recent Number - Previous Number) * 100 = Percent Change
Previous Number.......................................

When comparing percentage change across entities, it is important to use the same time period.

Rate tells you frequency of occurrence A critical issue in attempting to compare data is knowing that the data are really comparable. In many instances, simply knowing the number of events is not sufficient. For example, we know that there will be more abuse in the State as a whole than in Cascadia - one of its Counties. In order to make the raw data comparable, statisticians calculate rates. Rate means that the number of events that occurred is compared to the population for which that event could have occurred. The figure is then standardized to some number (such as 100, 1,000 or 10,000.) In fact, when you calculate the percentage, you standardize to the number 100. (Remember that percent tells how many out of 100. You also could have standardized to some other number, for example, the number of abused children in the county compared to the number in the state.)

To calculate RATE PER 1000, use the following formula:

% * 10 = Rate per 1000

Question 3

Small numbers can cause large fluctuations in statistics that can render them virtually meaningless. When confronted with a situation like this, report actual numbers.

Question 4

Since all numbers with a % sign represent a rate per 100, the % numbers within a single data set can be added, subtracted, multiplied or divided as you would other numbers. For example, 2 people + 5 people =7 people and 2% of people +5% of people =7% of people.

A cumulative percent is a summing of all data or values related to a percent

Question 5

While anecdotes and personal experience often help provide richness and depth to supplement data, too often they can be misleading and do not actually represent the true nature of the phenomenon being studied.

A trend is a general line of direction.

Question 6

The major questions which need to be asked in a situation where there are new categories for a variable are…'what is the impact on other categories?' Is it a subset? Is it pulling numbers from one or more of the other categories?

7.5 Table 1: Abuse Reports - Statewide

7.6 Table 2: Abuse Reports - Cascadia

7.7 Table 1: Abuse Reports - Statewide

Table 2: Abuse Reports - Cascadia

Formula: (Most Recent Number - Previous Number) * 100
Previous Number

7.8 Table 3: Abuse and Neglect Fatalities

Formula: (Most recent number - previous number) * 100
Previous number

Calculations:
State change 1996 to 1997: (34 - 17)/ 17 * 100= 100%
Statewide change 1997 to 1998 (17 - 34)/ 34 *100 = -50%

Cascadia change 1996 to 1997 (1-1)/1 * 100=0%
Cascadia change 1997 to 1998 (4-1)/1 * 100 = 300%

7.9 Table 4: Age of Victims - Statewide and Cascadia

*Percentages don't add to 100% because of rounding.

7.10 Table 5: Alleged Perpetrator of Substantiated Abuse, State

Table 6: Alleged Perpetrator of Substantiated Abuse, Cascadia County

Table 7: Alleged Perpetrator of Substantiated Abuse - 1998

7.11 Table 8: Type of Maltreatment, Statewide

Table 9: Type of Maltreatment, Cascadia County

7.12 Table 9: Type of Maltreatment, Cascadia County

7.13 Sample Report to the Commissioner

TO: Commissioner Smith

FROM: Jane Jones, Program Administrator, Cascadia

Stan Leon, CPS Supervisor, Cascadia

This memo responds to your questions concerning a perceived rise in child abuse in Cascadia County, especially in cases where the mother's boyfriend is the perpetrator and where substance is a factor. It also addresses the comment that Cascadia County had a 300% increase in the number of abuse and neglect cases last year.

We found no data to substantiate a 300% increase in abuse and neglect cases. There was a 300% increase in fatalities in Cascadia, but that large percent increase was caused by an large increase in a small number of fatalities (from 1 to 4 between 1997 and 1998) which, in our opinion, does not indicate a trend.

There is no data to support the statement that substance abuse is a factor in child abuse cases in Cascadia. The only data available are statewide, not county specific.

Finally the research shows that both statewide and in Cascadia County mothers, not boyfriends, are the perpetrators listed most often in substantiated child abuse reports. Data on abuse by the mother's boyfriend isn't collected.

More specifically, the research shows the following.

• Overall Cascadia has had a steady decrease in child abuse since 1992 and the County consistently has a better track record than the state.
• Cascadia has had a steady decrease in the number of CPS reports during the past five years from 1309 reports in 1994 to 1105 in 1998. The actual figures are: 1994=1309 reports, 1995=1224; 1996=1199; 1997=1158 and 1998=1105.
• The number of substantiated reports decreased in each of the past five years except in 1996. The figures are: 1994=257; 1995=235; 1996=244; 1997=230 and 1998=217.
• Growth in CPS reports since 1992 has been slower in Cascadia than in the state, at 10.28% and 44.15%, respectively.
• When compared with the state, Cascadia County had a lower percent of substantiated reports in 1998 (19.6%) compared with the state's (23.7%).
• From 1992-1998 substantiated reports in Cascadia went down 3.13% whereas the state saw an increase of 2.70% over the same period.
• The fatalities in the state were 17 in 1996; 34 in 1997 and 17 in 1998. In Cascadia in 1996 there was one fatality; in 1997 there was one and in 1998 there were four. The yearly percentage change in the state was 100% between 1996 and 1997 and between 1997 and 1998 the percent change was -50%. In Cascadia in between 1996 and 1997 the percent change was 0% and between 1997 and 1998 it was 300%. Since the number of fatalities is so small, it causes large fluctuations in the percent change figures.
• About a quarter of child abuse victims in both Cascadia and the State were age 10 and over but a more significant percent were under the age of 10 and a significant percent were under the age of one. Children age 10 and older represent about a quarter of child abuse victims - less than 22% statewide and less than 27% in Cascadia.
• About three-quarters of child victims are under the age of 10 - 78.03% statewide and 70.18 percent in Cascadia. Statewide 12.26% of child abuse victims are under the age of one, while in Cascadia 9.14% of victims are under age one.
• Statewide and in Cascadia, parents are the two most likely perpetrators in child abuse cases. Statewide last year mothers were the abusers in 42.0% of all substantiated reports, while fathers abused in 25.5% of substantiated cases (A total of 67.5% together). In Cascadia last year, abuse percentages for parents were similar with mothers abusing in 41.9% of cases and fathers in 23.3% (a total of 67.2% together). Total relative abuse, statewide = 86%; in Cascadia it's about the same at 85%.
• The top three type of abuse in Cascadia and the state in 1994 and 1995 are physical abuse, neglect, and sexual abuse and exploitation. In 1996 Threat of Harm was added as a category and in both the state and Cascadia it became the number one type of abuse, followed by physical abuse and neglect.

In summary, the data available show that child abuse in Cascadia is decreasing and compares favorably with the state, based on measures that include total number of CPS reports and substantiated reports. Child victims are more likely to be under the age of ten and many of those are under the age of one. The most common perpetrator of abuse is most likely to be the mother or father or at least a relative of the victim.

To locate the missing data that has been requested (how often boyfriends are the perpetrators and how often substance abuse plays a role in abuse cases in Cascadia), the Commissioner would have to collect additional data, perhaps by reading cases or doing a survey.

The information in this report was obtained from the State Office for Services to Children and Families (SCF) WebPages.

If we can be of any further assistance, please let us know.

7.14 Interpreting Data

Interpret the data on the sample reports. Can you make any conclusions using these figures? Can you see any trends? Do these numbers surprise you? Do you think these figures could be misleading in any way?

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