Solved – Proving an upward trend in line graphs with inconsistent increase

trend

Do you think this trend is increasing? I want to know if the proficiency test affects the performance of participants throughout the years.

How about this one?

If you think the trend is increasing, how do i prove it?

Best Answer

Your data can be represented as years (explicit) and ranks (1 $=$ lowest) allowing calculation of rank correlation.

  +-----------------------+
  | year   first   second |
  |-----------------------|
  | 2009       .        1 |
  | 2010       .        4 |
  | 2011       2        2 |
  | 2012       1        3 |
  | 2013       3        6 |
  | 2014       4        5 |
  | 2015       5        7 |
  +-----------------------+

A Spearman (or separately a Kendall) rank correlation can be regarded as measuring how far the data trace out a monotonic increase (always rising) or decrease (always falling). Always rising implies rank correlation of exactly 1. I get Spearman correlations of 0.90 and 0.86 for these series, which match strong tendencies to increase, as are visually apparent. Some might want to decorate with observed significance levels or P-values. Given the preconception of increase, a one-tail test is arguably applicable if any is.

It's a judgment call on whether such small datasets showing simple patterns need or much benefit from even this extra analysis. Conversely, more insight might be gained from any substantive knowledge of events or factors influencing the outcome.

Related Solutions

Solved – a trend line

A trend line is an expression, in mathematical form, of the relationship between your data - lets say in your case, knowledge and income. The assumption is there is some mathematical relationship between the two - lets say for every increase of $100 in annual income, your score on a hypothetical test goes up by one. Now that's not what you'll see in the actual data, because there's some random variation in the data. What a trend line does is tries to fit the data as best it can to give you an idea what the actual relationship is.

The difference between various trendlines comes from what shape the line is allowed to take. For example, a linear trendline must be a straight line - you're saying there is a linear relationship between your variables. An exponential line is a little more flexible, as it says that the relationship of one variable is found with some exponent of the other variable - that exponent can be 1, where you get a straight line, or it could be something else.

If you are simply trying to summarize your data, and give the viewer of the graph some idea of the relationship that exists between them, a linear or exponential trendline should be fine. For questions beyond that, it would be useful to know what you'd like to say about the two variables, but at that point, you may be well served by going to talk to someone in your department who works more heavily with statistics.

Solved – Trend test for ratios

you may not need this answer anymore, but I'm doing a series of trend analyses I think are similar looking at rates of antibiotic resistance in different populations over time. I'm using prop.trend.test to proxy for Cochran-Armitage test (seems VERY similar if not exactly the same). This tests whether or not there is a significant trend, but doesn't speak to the shape.

To test the linearity and direction of the trend, you can use lm...since our rates vary over time I add a quadratic term (our trend is clearly non-linear). I'm using this format:

> fit<-lm(m$prop ~ m$score + I(m$score^2))

where prop are the proportions and score is a 1:n count by year. Allows you to test the linear and quadratic terms at once.

I'm following the methods used in a previous paper but working a bit blind; would like to hear if I'm wrong!

Best of luck.

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Solved – a trend line

Solved – Trend test for ratios

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