Statistics Essentials For Dummies (54 page)

Watch for situations in which the time axis isn't marked with equally spaced jumps. This often happens when data are missing. For example, the time axis may have equal spacing between 1971, 1972, 1975, 1976, 1978, when it should actually show empty spaces for the years in which no data are available.

Histograms

Histograms graph numerical data in a bar-chart type of graph (seen in Chapter 3). Items to watch for regarding histograms:

Watch the scale used for the vertical (frequency/relative frequency) axis, especially for results that are exaggerated or played down through the use of inappropriate scales.

Check out the units on the vertical axis, whether they're reporting frequencies or relative frequencies, when examining the information.

Look at the scale used for the groupings of the numerical variable on the horizontal axis. If the groups are based on small intervals (for example, 0-2, 2-4, and so on), the data may look overly volatile. If the groups are based on large intervals (0-100, 100-200, and so on), the data may give a smoother appearance than is realistic.

Biased Data

Bias in statistics is the result of a systematic error that either overestimates or underestimates the true value. Here are some of the most common sources of biased data:

Measurement instruments that are systematically off, such as a scale that always adds 5 pounds to your weight.

Participants that are influenced by the data-collection process. For example, the survey question, "Have you ever disagreed with the government?" will overestimate the percentage of people unhappy with the government.

A sample of individuals that doesn't represent the population of interest. For example, examining study habits by only visiting people in the campus library will create bias.

Researchers that aren't objective. Researchers have a vested interested in the outcome of their studies, and rightly so, but sometimes interest becomes influence over those results. For example, knowing who got what treatment in an experiment causes bias — double-blinding the study makes it more objective.

No Margin of Error

To evaluate a statistical result, you need a measure of its precision — that is, the margin of error (for example "plus or minus 3 percentage points"). When researchers or the media fail to report the margin of error, you're left to wonder about the accuracy of the results, or worse, you just assume that everything is fine, when in many cases it's not. Always check the margin of error. If it's not included, ask for it! (See Chapter 7 for all the details on margin of error.)

Nonrandom Samples

A random sample (as described in Chapter 12) is a subset of the population selected in such a way that each member of the population has an equal chance of being selected (like drawing names out of a hat). No systematic favoritism or exclusion is involved in a random sample. However, many studies aren't based on random samples of individuals; for example, TV polls asking viewers to "call us with your opinion"; an Internet survey you heard about from your friends; or a person with a clipboard at the mall asking for a minute of your time.

What's the effect of a nonrandom sample? Oh nothing, except it just blows the lid off of any credible conclusions the researcher ever wanted to make. Nonrandom samples are biased, and their data can't be used to represent any population beyond themselves. Check to make sure an important result is based on a random sample. If it isn't, run — and don't look back!

Missing Sample Sizes

Knowing how much data went into a study is critical. Sample size determines the precision (repeatability) of the results. A larger sample size means more precision, and a small sample size means less precision. Many studies (more than you would expect) are based on only a few subjects.

You might find that headlines and visual displays (such as graphs) are not exactly what they seem to be when the details reveal either a small sample size (reducing reliability in the results) or in some cases, no information at all about the sample size. For example, you've probably seen the chewing gum ad that says, "Four out of five dentists surveyed recommend [this gum] for their patients who chew gum." What if they really did ask only five dentists?

Always look for the sample size before making decisions about statistical information. Larger sample sizes have more precision than small sample sizes (assuming the data is of good quality). If the sample size is missing from the article, get a copy of the full report of the study or contact the researcher or author of the article.