# How to tell if my trend is real?

• kop442000
In summary, the conversation discusses a research project that examines the amount of cosmic rays in a specific region of the sky. Thirteen readings were taken and when plotted, showed a downward trend. The speaker is seeking suggestions on how to quantify the likelihood of this trend being due to fluctuations. They mention the Spearman's Rank Correlation Coefficient as the only relevant statistical test they found. The conversation also highlights the importance of considering all relevant information and creating a probability model in order to find a good solution to real world problems.
kop442000
Hi guys,

I'm working on a research project that looks at the amount of cosmic rays coming out of a particular region of the sky in certain time intervals.

There are 13 readings taken:

9,9,6,6,7,1,6,6,1,6,4,1,0

When this is plotted, it looks like a downward trend - meaning the source could be becoming less active - but it's difficult to say with such small statistics.

I though perhaps I should try to quantify the likelihood of getting such numbers if the source was essentially a constant source - ie the trend is just due to fluctuations.

Could someone please suggest how I might think about doing this?

Thanks in advance for any suggestions!

Browsing the various named statistical tests on the web, the Spearman's Rank Correlation Coefficient is only relevant one I found.

Usually when people state real world problems involving probability they leave out a lot of information. In my opinion, if you want a good answer to a real world problem you should try to make a probability model of it that incorporates most of your knowledge. (For example, you probably know whether those numbers are discrete "counts" from a detector or continouous quantities that have been rounded off, whether there is a reasonable upper limit for the numbers, whether there are other associated known variables that might affect the counts such as the position of the detector and what kind of errors the detector might make.) Think about it as if you were going to write a computer simulation of the process, even if you don't actually do that.

## 1. How do I determine if my trend is statistically significant?

Statistical significance refers to the likelihood that a trend is not due to chance. To determine if your trend is statistically significant, you can perform a statistical test such as a t-test or ANOVA. The result of the test will provide a p-value, which indicates the probability of obtaining the observed trend if there is no real relationship between the variables. Generally, a p-value of less than 0.05 is considered statistically significant.

## 2. What is the difference between correlation and causation?

Correlation refers to a relationship between two variables, where a change in one variable is associated with a change in the other variable. However, correlation does not imply causation. Causation means that one variable directly causes a change in the other variable. It is important to carefully consider the evidence before concluding that a trend is a result of causation.

## 3. How large should my sample size be for my trend to be considered reliable?

The sample size required for a trend to be considered reliable depends on various factors such as the effect size, level of significance, and variability in the data. Generally, a larger sample size is preferred as it increases the power of the statistical test and reduces the likelihood of obtaining a false positive result.

## 4. Can I use visual aids such as graphs and charts to determine the validity of my trend?

Visual aids such as graphs and charts can be helpful in identifying trends and patterns in the data. However, they should not be used as the sole basis for determining the validity of a trend. It is important to also perform statistical tests and carefully consider other factors before drawing conclusions about the trend.

## 5. Is it possible for a trend to appear significant but not be real?

Yes, it is possible for a trend to appear statistically significant but not be real. This is known as a Type I error, where a false positive result is obtained. It is important to carefully consider the evidence and perform multiple tests before concluding that a trend is real.

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