# Statistical Analysis for our project

## Main Question or Discussion Point

I actually have no idea on how would we conduct our statistical analysis for our design project. We will be creating a digital alarm clock with an improvised sensor and we will also be conducting series of tests for it. Now our teacher is looking for the statistical analysis.

Our testings are as follows:
1. Accuracy of digital alarm clock - we will set the alarm clock to a specific time and wait for it to alarm. If it alarms at the set time, then the criterion is considered successful, otherwise, it is not.

2. Relay response - Once the alarm clock starts ringing, several appliances will also start to act differently (e.g. the lights will turn on or off depending on the status of the sensor & alarm clock).

3. Accuracy of the improvised sensor - since this sensor is a crucial part of the alarm system, the amount of switches that's turned on must agree with the amount of switches the researchers set.

I know what is Z-test, T-test and chi-squared test. But I don't know if they're the right one (well, if they're, then I don't know which is which) to use. So please help me.

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General test measure: For time accurate to the nearest minute, assume the existence of a perfect random alarming clock. The probability that in any given minute the alarm is correctly alarmed is 1/(24*60). Run simulations where the run length equal to the # of tests on the real alarm clock. Apply test to the differences in successes or probability of success (which is precisely known for the random alarming clock).

For relay response or improvised sensor construct appropriate random clock performance statistics. Compare to your real efforts.

Note, to the extent that your clock is pure junk, it behaves more closely to the random clock, and becomes statistically indistinguishable.

More meaningful for some, compare the performance of your clock to an existing similar functioning clock for a given number of large trials.

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Stephen Tashi
Now our teacher is looking for the statistical analysis.
You should find out whether the teacher expects statistical "hypothesis tests" or statistical "estimation".

The tests you gave propose to answer yes-or-no questions (e.g. the clock does or does-not alarm at the correct time. To me, it makes more sense to estimate the precision with which the clock alarms. (A real clock would probably never alarm at exactly the correct instant of time and you can't measure the exact instant with infinite accuracy anyway.)

General test measure: For time accurate to the nearest minute, assume the existence of a perfect random alarming clock. The probability that in any given minute the alarm is correctly alarmed is 1/(24*60). Run simulations where the run length equal to the # of tests on the real alarm clock. Apply test to the differences in successes or probability of success (which is precisely known for the random alarming clock).

For relay response or improvised sensor construct appropriate random clock performance statistics. Compare to your real efforts.

Note, to the extent that your clock is pure junk, it behaves more closely to the random clock, and becomes statistically indistinguishable.

More meaningful for some, compare the performance of your clock to an existing similar functioning clock for a given number of large trials.
Is testing the accuracy of the time to the nearest minute necessary? I find it unnecessary (I'm considering its removal from the testing) since we'll be using DS1307 which ticks approximately one second (compared to the analog one), and it is also, I believe, the one that is being used on almost all digital alarm clocks.

Or I just don't get what you're saying?

Also, what do you mean by random clock performance statistics and real efforts? Do you mean the real efforts is by just allowing manual contacts (by pressing) of the conductors? And the random clock performance is by passing a high logic output signal from the system itself?
You should find out whether the teacher expects statistical "hypothesis tests" or statistical "estimation".

The tests you gave propose to answer yes-or-no questions (e.g. the clock does or does-not alarm at the correct time. To me, it makes more sense to estimate the precision with which the clock alarms. (A real clock would probably never alarm at exactly the correct instant of time and you can't measure the exact instant with infinite accuracy anyway.)
Hypothesis test or statistical estimation, its all up to us. Hypothesis test is about accepting and rejecting hypotheses (Ha and Ho), and statistical estimation is for calculating the average of a certain data, am I right?

Anyway, based on what I know about those two, I believe statistical estimation would be enough.

I have been hearing about Analysis of Variance but as I take a look and try to analyze how it would be performed, my data does not suffice the needed for the variables for this ANOVA.

I am not really fond of Statistics that's why I'm asking too much. I am sorry.

Stephen Tashi
Hypothesis test or statistical estimation, its all up to us. Hypothesis test is about accepting and rejecting hypotheses (Ha and Ho), and statistical estimation is for calculating the average of a certain data, am I right?
Estimation is about estimating any parameter of a probability distribution. It is often the mean ( the "average") that we want to estimate.

Anyway, based on what I know about those two, I believe statistical estimation would be enough.
From your project description, I agree.

I have been hearing about Analysis of Variance but as I take a look and try to analyze how it would be performed, my data does not suffice the needed for the variables for this ANOVA.
ANOVA is used to analyze how many aspects of situation affect the outcomes of it. I don't don't think it is relevant to your project. If you were comparing 5 or 6 different designs of clock, it would apply. If your clock behaves very differently under different situations (temperature, humidity, battery voltage, etc.) ANOVA might apply, but you haven't mentioned that you are expected to collect such data.

Approaching your problem as estimation, you should read about "confidence intervals for the mean" ( to use in estimating things such as the mean error of the time at which the clock alarms).

To evaluate such things as whether the clock activates the right switches, you should look at the topic of "reliability" and perhaps "mean time to failure" since that is often given as an engineering specification. I'm not an expert in such things. If your clock works well, you might test whether it threw the right number of switches 100 times and it would work every time. I'm guessing that the theory of reliability would allow to make some technical statement about the probability of failure being small even if you never have a failure in your tests.