The wordtrendis used with a variety of meanings. The meaning I'd like to look at in this article is that of a regular change in data over time – for example, people talk about upward trends in the stock market or in the consumer price index.In research, the rules for inferring a trend from data are a bit more rigorous than those used in other fields. In this article we'll look at four of these rules.

First, a trend cannot be inferred from two points. If the crime rate drops from one year to the next, that's not evidence of a downward trend in the crime rate. It's unlikely the crime rate is going to be exactly the same from one year to the next. For example, if the crime rate is steady the probability of some drop in it from one year to the next is still effectively 50%. A change in the crime rate is therefore not in and of itself evidence of a trend.

Second, you cannot pick convenient spots for your trend to begin and end. People sometimes will observe that the crime rate has increased, say, for three or four years in a row, and decide that that's a trend. However, since they picked only years when the rate was increasing the main conclusion you can draw is that they're sandbagging.

Similarly, you cannot simply draw a line between the first data point in your series and the last and call that your trend. Any measure includes error, so it is not a completely accurate measure of the variable whose trend you're interested in. You have to fit a trend line with a statistical technique to get a legitimate estimate of the trend.

Finally, no change is a trend until a statistical test says it is. Statistical tests evaluate the likelihood of changes happening and they can tell you pretty quickly how likely the changes in your sample are if there is no trend in the population. They also give you a pretty good idea of how strong the trend is. The statistical techniques to use are founded on statistical correlation, and include regression analysis. Multiple linear regression offers the advantage of being able to separate the effects of elapsed time from other effects correlated with elapsed time.

Even if you never get deeply involved in statistical trend analysis, I hope this brief article has encouraged you to take most public statements about trend with a grain of salt. In particular, I encourage you to be highly skeptical of any "trend" based on three or four points – for example, supposed trends over the last three or four years. The beginning of the trend is usually arbtrarily defined (as the year when the rate started to change), and it is highly unlikely that a statisical test would detect a significant difference over that few points. If the daily high temperature went from 31 Celsius on Monday to 32 on Tuesday and 33 on Wednesday, you wouldn't assume that the high temperature on Thursday was going to be 34. There's usually no more reason to infer trends from any other short series of observations.

What is a Trend? © 1999, 2003, John FitzGerald

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