Posted by: rcieri | November 24, 2008

Math Tools for Journalists: Abridged Version

Polls and Surveys

Polls and surveys are both common and commonly misused, which is why it is a reporter’s job to help the public understand them.

Poll (n.) – estimate of public opinion on a single topic or question based on a representative sample

Survey (n.) – an estimate of public opinion based on the answers of multiple questions by a representative sample

Polls are most frequently used for political means. To evaluate their validity, it is important to for reporters to consider a variety of factors including the organization that created the poll, how the poll was paid for, the time the poll was taken, the wording of the questions, the size and type of sample used, the margin of error, and the relationship of the poll to any event that could have had an effect on its outcome.

The sample size is extremely important to take into consideration because it must be large enough (usually at least 400 responses) to accurately represent the population. There are several formulas for selecting sample size. A census samples every person in the population; a cluster involves sampling people from a specific place or region; a multistage sample selects smaller and smaller subgroups until it has reached to optimal size; a systematic random sample selects a number; like 10, and samples every tenth person; a quota selects the sample based on known demographic characteristics; and probability sampling involves a random drawing of a certain percentage of the population.

In considering the validity of a poll, one must take into consideration margin of error and confidence level. The margin of error shows how accurate the results are based on the norm. It is expressed as a percentage based on the sample size, and it decreases as the sample becomes larger. The confidence level is exactly as the name describes, and it is expressed as a percentage. The formal definition calls it the probability of getting a given result by chance. This means a confidence level of 93 percent indicates that there is a seven percent chance of the results being obtained by chance. As the confidence level goes up, the margin of error gets larger and vice versa. Confidence level should always be reported with the results of a poll in order to help readers understand the validity.

The U.S. Census provides national statistics through short forms sent to five out of six households collecting social, economic, financial and housing information. The results can be adjusted on unadjusted. Adjusted figures have been modified to compensate for missing data because statisticians have determined that undercounts tend to occur in predominantly black areas, while overcounts tend to occur in predominantly white areas. The unadjusted figures are used to create congressional districts, but the formula allows smaller states to gain congressional seats more easily. Adjusted and unadjusted results are predicted to vary from one to four percent.

It is important for journalists to understand z and t scores because they are often used in the results of studies. A z score or “standard score” indicates how much a figure differs from the mean. The standard deviation is used as the unit of measure in the z score, and the mean becomes zero. A t score is similar to a z score and used when the sample size is 100 or fewer. To learn more about a t score, a journalist should consult a statistics text book.

Z score = (raw score – mean) / standard deviation

 

Business

Business reporting involves some of the most math of any beat, which is why it is important for journalists to understand where the numbers come from in the business world. Many of these numbers come from quarterly and annual reports published by companies and corporations.

Financial statements are formal documents that disclose quantitative statements about a company’s business transactions that usually include a profit and loss chart. Profit and loss statements are extremely important documents because they reveal whether or not the company is making money. In this statement, expenses are subtracted from the income.

To understand these documents, it is important to understand some key terms:

Cost of goods sold – the expenses directly related to making or buying the product sold
Overhead – expenses not directly related to the product (ex: employee salaries, insurance)
Gross margin – difference between the cost of goods sold and the selling price
Net profit – the profit minus the cost of goods sold and overhead. Also called net income or net earnings.

It is sometimes useful to calculate EBITDA, the earning before interest, taxes, depreciation and amortization to determine how much cash a company brings in before its expenses that are unrelated to business.

A balance sheet is a written statemnt of a company’s assests, liability and equity that indicates the financial stability of the company. The assets side of the balance sheet always equals the liabilities and equity side.

Assets – real estate, equipment, cash – things that give the company value
Liabilities – the company’s debt
Equity – the company’s real worth

Ratio analysis is used to evaluate a company’s financial situation with factors like cash, profitability, operating efficiency and market value to examine trends over time and compare it to other companies. To give readers context of these numbers, include industry standards as well. The current ratio examines the company’s ability to meet its liabilities, and it is found through dividing the current assets by the current liabilities. The quick ratio shows the company’s ability to meet its liabilities with the cash it has on hand. Other ratios include:

Debt-to-asset ratio = total debt/ total assets
Debt-to equity ratio = total debt/ equity
Return on assets = net income / total assets
Price earnings ratio = market price /earnings

Stocks and Bonds

Stocks are a way for corporations to raise cash through sales to investors, who become partial owners of the company. Stock prices rise and fall over time based on demand. Mutual funds allow investors to buy funds that will be used to invest in stocks. Journalists should be sure to learn to read stock charts that report earnings and losses at the end of each business day.

Bonds are a way for corporations and governments to raise money by selling bonds, a small loan to the organization with a fixed interest rate. The face value of the bond is typically what the buyer pays for it, and the buyer will get this money over an allotted number of years. The value of this money, however, fluctuates with the market. Some bonds are tax-exempt, yielding a slightly higher return. Bonds are tracked by indexes like the J.P. Morgan Government Bond Index and the Dow Jones Corporate Bond Index.

Current yield = (interest rate x face value) / price

Readers may be interested to know how much bonds will cost a particular local government, so reporters should know the following formula to find this number:

Bond cost (interest) = amount x rate x years

Market indexes are used by analysts to measure changes on stock exchanges, tracking indexes on groups of stocks to give investors a broad overview of the markets. The Dow Jones Industrial Average divides the total value of one share each of 30 prominent stocks by a number called the divisor.  This number changes daily and is determined by certain corporate actions. The NASDAQ stands for the National Association of Securities Dealers Automated Quotations, and it is monitored by the Securities and Exchange Commission. It reports on trading of domestic stocks and bonds not listed in most markets.

Property Taxes

Property taxes are the largest single source of income for the national and local governments, meaning that they will be important to news consumers. These taxes are determined by the amount of money the government needs and divided among all property owners, depending on how much property they have. These taxes are measured in units called mills, which are 1/10 of a cent. One mill per dollar would be 10 cents for every $100 dollars. The taxes are also applied to the assessed value of property, a percentage of the market value.

Assessed value = appraisal value x rate

This is determined differently by every state and local government. It is important to remember that some areas are taxed by multiple governing bodies and some are not.

To calculate the mill levy, use this formula:
Mill levy = Taxes to be collected by the governing body / assessed valuation of all property in the taxing district

To calculate how much a particular property owner owes, use the following formula:
Tax owed = tax rate x (assessed value of the property/ 100)

Practice Problems

1.      If the confidence level of researchers in a particular study is 92 percent, what is the probability that the score was obtained by chance?

2.      A particular stand buys Vanity Fair magazine for $3.50 and sells it for $3.95. What is the gross profit for the stand on each issue?

3.      If Smith Jackson paid $700 for a $900 bond with an interest rate of 6 percent, what is the current yield on his bond?

4.      Find the mill levy if the Town of Elon needs to collect $230,400 and the assessed value of all property in the town is $50,890,800.

Answers:

1.      8 percent

2.      $0.45

3.      7.7 percent

4.      0.0045

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