What test to use

Question

I have a data of 13 months. What I am trying to do is compare total value in current month with past 12 months data. If there is significant difference In current months data to past data.

i tried chi sq where i took current month as observed and average of past 12 months as expected.

is there a better way to do this or a better test? Not sure if ANNOVA is a good fit.

TIA

Answer 1

Nish,

I am not sure a statistical inference test is appropriate for a time series data set. These tests are meant to determine whether a sample is comparable to an underlying population (one that does not evolve over time) or to compare samples between each other.

A Chi Square test is used to determine the relationship (or independence) between two or more categorical variables (are people who buy an SUV more likely to buy a black SUV?). This does not seem to be the case here.

Typical business KPIs are YoY, QoQ, or MoM growth, so you would compare December 2019 with December 2018, or Q4 2019 with Q4 2018.

The closest you can get with statistical inference is a regression (which you should not use to extrapolate data, only to interpolate it); if you are looking at one month beyond a 12 month series, a regression may be appropriate (but remember babies do not grow 9 feet tall, nor do trees grow to the sky!).

I would recommend testing different forecast models against your historical data (trend & seasonality, exponential smoothing, or other) and determine which would be a best fit, and check for any deviation from the forecast.

Answer 2

You have the data from the 13th month. You can decide based on whatever criteria you choose whether it’s significantly different from any other number.

I think that you need more information in order to answer this question properly. Also if you have the data for the completed 13th month, the current month is month 14.

This does not appear to be a Chi square problem. You would have to check assumptions and requirements. Without any statistical inference tests, you could do a boxplot of your 13 data points and see if the 13th belongs in the set or not. Is it an outlier? Is it outside of the IQR?