gm.general mathematics – Control & Experimental Group Selection Methodology using STDEV and T-Test Methodology?

I would like to know if my methodology was ‘correct’:

I am trying to conduct an experiment on my stores.
I would like to find out the effect of a marketing campaign on the number of transactions.

Only about 20% of the stores are participating in the marketing campaign.

The original methodology was to use the entire 20% as the experimental group and the remaining 80% as the control group. Unfortunately, these two groups are incomparable in terms of number of transactions.
when plotted as box and whisker plots next to each other, their distributions are incomparable (mean, median, quartlies, min, max, etc).

So what I did was filter out the ‘outlier stores’ at each end until the box and whisker plots for each group were practically identical. I then ran a t-test on the filtered groups, we failed to rej the null (meaning that these groups are statistically the same prior to the promotion).

Now that we have 2 comparable groups for time -1, we run the promotion for a month.
after promotion month is over, we take the number of transactions from each group and run another t-test.
We Rejected the null in favor of the alternate Hypo, which is that these 2 groups are now statistically different with an alpha of 0.05.

My first question is: is this methodology okay ?

My second question is: alternatively from using box and whiskers and removing outliers until both groups’ descriptive stats are similar, can i use a normal distribution and STDEV to remove outliers and create comparable groups within my population ?
The box and whisker method worked to get a comparable groups as confirmed by the t-test, but is very manual. So i would like to create an automated method and was wondering if using a normal distribution and removing outliers by STDEV would be plausible ?

Sorry for the long read.
Thank you

gm.general mathematics – Need suggestion in writting equation in a simple mathematical way

I have a equation given by
begin{align}
1+F(K_{1},K_{2};beta)=0
end{align}

This equation is needed to solve for $beta$‘s ($beta_1,beta_2,beta_3…..beta_n$) for given value of $K_{1}$ and $K_{2}$. Both $K_{1}$ and $K_{2}$ can take values $epsilon$ and $frac{1}{epsilon}$, corresponding to this four different equation can be obtained. From each of this equations we have get ($beta_1,beta_2,beta_3…..beta_n$), correspondingly we can construct a function called $g(x;beta_{1}),g(x;beta_{2})….g(x;beta_{n})$ for each set.

Table showing different combinations of K_1 and K_2

using these $g(x;beta_{1}),g(x;beta_{2})….g(x;beta_{n})$ for each set I am interested in constructing one final equation called.
begin{align}
W(x)=sum_{i=1}^{n}c_{i}g_{i}(x;beta_{i})+sum_{i=1}^{n}d_{i}g_{i}(x;beta_{i})+sum_{i=1}^{n}e_{i}g_{i}(x;beta_{i})+sum_{i=1}^{n}f_{i}g_{i}(x;beta_{i})
end{align}

So the question now is how to write in $W(x)$ in an elegant manner and how to generalize this procedure for when $1+F(K_{1},K_{2}….,K_{n};beta)=0$, then I will be having $2^n$ combinations.

gm.general mathematics – Is the solution to this trig function known to be algebraic or transcendental?

This largest solution to this gorgeous equation is the first local extremum on a function related to the Fibonacci sequence:

$$x^2 cdot sin left(frac{2pi}{x+1} right) cdot left(3+2 cos left(frac{2pi}{x} right) right) = (x+1)^2 cdot sin left(frac{2pi}{x} right) cdot left(3+2 cos left(frac{2pi}{x+1} right) right)$$

This is as simplified as I could get it. The largest solution to this equation is around $x = 2.1392.$

It appears there is no closed-form solution for this; is there any way to prove if the solution is algebraic or transcendental?

gm.general mathematics – Mass supply for a Customer

A customer would like to buy with an amount of 10,000,000 € 2 Kind of Products in a relation of 1 to 3

Whereas the product he wants least of is the Food and the product he wants most are the Potions.

  • 3x Food Costs 12 Thousand
  • 3x Potions Costs 20 Thousand

How much of each Product must be produced in a relation to 1:3 (Food:Potions)

gm.general mathematics – Need help calculating timing sequence based on a specific rate

could use some help with a problem I need to solve. I have a main line conveyor belt that is 156.5 ft long. There are 7 conveyor lanes that merge packages onto the main line conveyor. The 7th lane which is the most downstream is 102.5 ft from the start of the main line conveyor. Lane 6 is 88.5 ft from the start, and Lane 1 is 12.25 ft from the start. I send a release signal to each lane when they are clear to merge their package onto the main line. The release signal is equal to length of the package. The release signal is set at the start of the main line conveyor, so based on speed, I know how long it will take the head end position of each lines signal to reach its lane. The head end of the release signal is basically the head end position of the package. Lane 7 will take 15.375sec, Lane 6 13.28sec, Lane 1 1.83sec.

If I send a signal to lane 7 every 15.375sec, the release rate will be much lower than desired. If I send the signal to Lane 1 every 1.83 seconds the rate is much higher. The solution I need to come up with is based on the number of active lanes, I need to ensure each lane has an equal (or close to) release rate.

Known info: Each lane has a min cycle time of 1.189sec, the means that it will take 1.189sec for the head end of the package to reach the exit of the lanes conveyor.The time it takes the package to exit the lane conveyor is added to this value. Using a 20″ package, +.25sec will = 1.1439 sec. So in theory every 1.439 secs a package can be released. This time will go up based on length of package. min 6″ = .075sec max 60″ = .75sec.

Release signal for each lane is = the length of the package. Min time between release signals is based on a desired gap. So if Lane 7 and 6 package length is 20 inches and desired gap = 9 inches, then release signal for lane 7 will be .25secs, then after .11sec the release for lane 6 will be sent. This will result in 9 inches of space between two packages once they end up on the main line.

Main Line conveyor = 156.5ft or 1878 inches. Runs at a constant speed of 400 ft/min or 80 inc/sec
Lane 7 = 1230 inches from start of main line takes 15.375 sec to travel 1230 inches.
Lane 6 = 1063 inches, 13.28sec
Lane 5 = 711 inches, 8.88sec
Lane 4 = 603 inches, 7.53sec
Lane 3 = 448.5 inches, 5.6sec
Lane 2 = 292.5 inches, 3.65sec
Lane 1 = 147 inches, 1.83sec

I cant figure out how to come up with a formula that will come close to ensuring each lane is allowed equal release times. The length of the package is determined upstream of the merging conveyor. So the release signal can be sent before staging on the lane merge conveyor. The attached pic shows the layout of the conveyor. For the length of the main line, the values I provided is longer that what is shown. This is due to the my programming logic. I create a virtual belt of the actual belt. I increased the length of this virtual belt to include the curve length, and + 120″. This makes my programming make Lane 1 logic the same as the other lanes.

gm.general mathematics – Determine sample size when averaging over sensor data

I was not too sure where to post this if in either stackoverflow or mathoverflow. Im not too sure how to approach this problem.

I have a accelerometer which I use to calculate angles currently I’m averaging over 14 samples of data (the sensor samples at 1600Hz) and I see a lot variance in my measurements. If I keep my sensor at a stable angle it varies for each calculation around 2-4 degrees.

I thought this might be a statistics problem perhaps, I need to somehow find how many samples of data I should average over inorder to reach atleast +-1 degree accuracy