# How to find out if a set of daily measurements are random or not?

There is a set of daily measurements. Time and measured values are both discrete. I want to find out whether measured values depend on the day the measurement was taken, or whether measurements are completely random. In other words, I want to find out if it is possible to predict measured values of a certain day or not.

• What subjects of statistics should I study to be able to solve this problem?

Please give me some keywords or direction.

Edit
Some more information. Imagine the following situation. A machine chooses each day a letter (simply a byte) and displays it on a screen. The process which is used to choose daily letter is unknown, but it is clearly algorithmic (not measure the wind speed or count people in the room or similar). Someone collected part of daily letter over a period of time and now wants to understand if it is possible to produce the next (or any) daily letter. Some methods possibly employed by the machine are considered "hard" (or random). For example use a secret key to encrypt the current date (predicting the next letter will be equivalent in most cases to braking the encryption). Other are considered "easy", for example xor of all bytes in date's representation. If the method is random, then there is no hope to produce the next daily letter.

• First graph your data to see if there are any obvious patterns. Do you have any theory suggesting the data might be non-random? That may guide your choice of statistical model. Jul 13 '11 at 1:54
• @Michael: Unfortunately graphing your data doesn't always disclose the "unusual" due to background variability. In trivial cases the human eye is as good as a good statistical program whose focus is separating signal from noise and partitioning the noise into randomness and the exceptional. In non-trivial cases my bet would be on good/superior analytics and not on "tired/confused eyes". Save your eyes ! Use Statistic Methods to do what it was designed to do ! Jul 13 '11 at 14:27
• @Irish I don't think @Michael was suggesting that the analysis be limited to graphing. It would be foolhardy at best to trust the output of "good/superior analytics" without ever looking at the data. Given a choice between some statistical output and a good graph of a dataset (but not both), I will take the graph every time.
– whuber
Jul 13 '11 at 16:03
• @whuber:When one is faced with analyzing/characterizing a large number of problems,one needs to use "productivity aids". Good luck with relying on graphs when one has noisy data with large background variability.In trivial cases where the eye can catch the anomaly one doesn't need to acquire "expensive software" as one can use the human brain/eyesight as a proxy for the "expensive software".Where I come from "human time" is more expensive than software but perhaps lacking software they can use their eyes.Academics are often unable to acquire "better eyes" & that's why they often need glasses. Jul 13 '11 at 16:41
• Are you measuring a single thing, or multiple things each day? (E.g. are you measuring temperature, or are you measuring temperature, humidity, rainfall, etc?) Are you making only one measurement of each thing, or multiple measurements of each thing per day? If you are measuring one thing, you have a univariate time series, otherwise multivariate, for example. Jul 13 '11 at 17:06