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How do you determine if the percent growth between two time periods is statistically significant? For example, the total population in 2000 was 180,000. It grew to 220,000 ten years later. How do you determine if this 22% growth was significant? Similarly, group A (6,000 people) earned £50,000 last year. Group B (9,000 people) earned £65,000. Are Group B's 50% earnings over Group A statistically significant?

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    $\begingroup$ What is the null hypothesis? That the population sizes are the same? I don't need a statistical test to see that the null is false. Do you mean testing whether the population growth is exponential, or..? With the second example, are you asking about whether the average income has increased? In that case, a $t$-test would work (possibly log transforming the values since incomes are known to be highly skewed). $\endgroup$ – Macro Jul 4 '12 at 15:30
  • $\begingroup$ Thanks for replying. For the second question how would you set up a t-test when you only have two values and the population? Would this be a difference in proportions hypothesis test? For the first the null would be less than .20. $\endgroup$ – cehua Jul 4 '12 at 15:41
  • $\begingroup$ you need an estimate of the variance to do a $t$-test. Do you have that? Better yet, do you have the data or just the averages? $\endgroup$ – Macro Jul 4 '12 at 15:43
  • $\begingroup$ If it helps to clarify my first question I am looking at population and housing census data for subsets of the population. I am just comparing one variable at two points in time and want to know if the change is significant. We have a computer program to do it, but I would like to learn by hand. I am able to do this for large groups of data but lost when looking at one percent change involving two time periods. $\endgroup$ – cehua Jul 4 '12 at 15:47
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    $\begingroup$ If you're viewing the census data as a 100% sample of the population then there's no statistical hypothesis to be tested. If there's a difference, then the null hypothesis is not true. When people statistically analyze census data, they are often viewing the outcomes as draws from a theoretical infinite population, in which case, you'd treat it as you normally would treat a sample. $\endgroup$ – Macro Jul 4 '12 at 15:52
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I think you are confusing "statistically significant" with the common sense of the word "signficant" which means "important" or "material". I always try to avoid that use of the word around statistics, and generally opt for "material" instead. "Statistically significant" is short hand for "statistically significant evidence against the null hypothesis". Statistical significance only matters when you are conducting some kind of inference; not when you are just describing census data.

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Think if you have a historical data (sufficiently large) for YoY growth rates, you can spread them out and see what are the chances of the growth rate happening. If the data is large then you may normalize the data by subtracting the mean and dividing by the standard deviation, now plot the distribution and see if it lies towards a tail. Ex: It may well happen that it takes a bell shape and your value lies in a tail.

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  • $\begingroup$ Although this describes a way of assessing whether growth is apparent, it does not address the question about statistical significance. What hypothesis test do you propose to apply here? $\endgroup$ – whuber Nov 6 '14 at 15:06

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