Ask Ghassem - Recent activity in general

How do I compare the count of a value in each year while having a different sanple size each year.

Wed, 08 Jun 2022 10:32:33 +0000

How do I accurately compare between the number of something a survey measure from my employees each year with a varying umber of survey engagement and employee size?

If I was measuring the satisfaction of my employees over the years by collecting a survey from my them each year by asking them wether they are satisfied or not, and then comparing yes’s over the years but the number of employees who answer is not the same each year and the number of employees increases every year. How do I correctly compare this throughout each year?

In other words, how do I remove the effect of the survey engagement rate when calculating the results?

Using aggregate data to generate observation-level data statistically sound?

Tue, 11 Jun 2019 22:04:01 +0000

Context: In the realm of Paid Search Marketing. Current reporting does not provide event level data only aggregate totals with different segments. Want to compare distributions/test statistical significance of A/B test results. Did not want to assume that data followed normal distribution or know STDEV for data so came with this approach.

My Question: I am going to use the average "CPA" or "CTR" for a date range, and generate an observation for each conversion based off the average for a time range. Is this statistically sound way if I want to generate raw data? Would I have wonky distributions because of the multiple averages? Just want a gutcheck if I'm completely off base.

My Aggregate data looks like below:

Day	Cost	Acquisition	CPA or CTR
1	40	2	$20
2	75	3	$25

Observation data I generate looks like below:

Day	Acquisition
1	$20
1	$20
2	$25
2	$25
2	$25

I really appreciate your help with this question! An important project to me at work.

Answered: What will be probability for the data items within mean +- 1, +-2, +-3 standard deviation?

Fri, 30 Nov 2018 21:17:20 +0000

Probobality mean for +-1 standard deviation is 0.68.
Probobality mean for +-2 standard deviation is 0.95.
Probobality mean for +-3 standard deviation is 0.997.

Answered: What is the rule that determines percentages with the mean +- 1,2 or 3 standard deviations?

Sat, 17 Nov 2018 19:04:26 +0000

The Empirical Rule, which is used for normal distribution. The notes about the rule can be found in the slides.

Answered: How much percentage of data items are consumed within mean +-1 , +-2, +-3 standard deviation?

Wed, 14 Nov 2018 15:05:54 +0000

For mean +-1 standard deviation, 68% of data items.

For mean +-2 standard deviation, 95% of data items.

For mean +-3 standard deviation, 99.7% of data items.

What is a test statistic in hypothesis testing and how does it relate to the p-value?

Tue, 13 Nov 2018 00:51:11 +0000

Answered: What is sampling error?

Tue, 13 Nov 2018 00:48:25 +0000

Sampling error occurs when using a sample mean to estimate a population mean. Usually the sample mean is quite close to the population mean, but it is important to understand that there will be some level of sampling error.

Answered: In the first week of November 2003.... What is the expected number of homicides per week in the GTA?

Fri, 02 Nov 2018 19:36:25 +0000

If there are 78 per year then the expected value or mean for a week is 78 homicides/52.1429 weeks which is 1.496 per week.

Answered: In statistics, whats the difference between contingency and frequency tables?

Tue, 30 Oct 2018 11:38:10 +0000

Contingency table associates two categorical variables whereas frequency table associates one categorical variable

Answered: Define measures of center (Median and Mode) ?

Sat, 27 Oct 2018 14:06:42 +0000

Median

The median is the middle score for a set of data that has been arranged in order of magnitude. The median is less affected by outliers and skewed data. In order to calculate the median, suppose we have the data below:

We first need to rearrange that data into order of magnitude (smallest first):

Our median mark is the middle mark - in this case, 56 (highlighted in bold). It is the middle mark because there are 5 scores before it and 5 scores after it. This works fine when you have an odd number of scores, but what happens when you have an even number of scores? What if you had only 10 scores? Well, you simply have to take the middle two scores and average the result. So, if we look at the example below:

We again rearrange that data into order of magnitude (smallest first):

Only now we have to take the 5th and 6th score in our data set and average them to get a median of 55.5.

Mode:

The mode is the most frequent score in our data set. On a histogram it represents the highest bar in a bar chart or histogram. You can, therefore, sometimes consider the mode as being the most popular option. An example of a mode is presented below:

Normally, the mode is used for categorical data where we wish to know which is the most common category, as illustrated below:

We can see above that the most common form of transport, in this particular data set, is the bus. However, one of the problems with the mode is that it is not unique, so it leaves us with problems when we have two or more values that share the highest frequency, such as below:

Retagged: Calculate IQR(Inter Quartile Range) of {18, 24, 19, 16, 21}?

Tue, 16 Oct 2018 11:59:59 +0000

Answered: How do you tell a permutation problem from a combination problem?

Mon, 15 Oct 2018 17:15:22 +0000

The key is finding out if the order of items are important or not. If the order does matter, it will be permutation, otherwise it is combination.

In these two examples, we should think about context of the words "Groups" and "Lists". For Groups, the order is NOT important, but because Lists comes with the index, and the order does matter. So, the first question is combination and the second one is permutation.

Combination:

1. How many different groups of 4 students can be made from a class of 40?

Answer: $C(40,4) = \binom{40}{4} = \frac{40!}{4!(40-4)!} $

Permutation:

2. How many different lists of 4 students can be made from a class of 40?

Answer: $P(40,4) = \frac{40!}{(40-4)!} $

Reshown: What is the probability of getting a King of Hearts?

Mon, 15 Oct 2018 02:53:32 +0000

What is the probability of picking a King of Hearts in a standard 52 card deck?

Answered: If x is the number that comes up when you roll a 20 sided die. What is the expected value of x?

Sun, 14 Oct 2018 04:22:54 +0000

Assign a number to each of those events (having 1 as outcome, having 2 as outcome, ..., having 20 as outcome) which is the job of Random Variable. For this specific example, we can assign the same numbers. The Expected Value equation is $\mu = \sum x.p(x)$. Now you have $x = {1,2,...,20}$, and if you have $p(x)$, you can easily calculate expected value.

In this case that we have a fair die with 20 sides, probability of each side is $\frac{1}{20}$. Now, we can calculate it in this way:

$\mu = \sum x.p(x) = \sum_{x=1}^{20} x.\frac{1}{20} = \frac{1}{20} \sum_{x=1}^{20} x = \frac{1}{20} \frac{20\times21}{2} = 10.5 $

(note: $\sum_{x=1}^{n} x = \frac {n\times(n+1)}{2}$)

Answered: What is a discrete random variable?

Sat, 13 Oct 2018 01:23:29 +0000

https://revisionmaths.com/advanced-level-maths-revision/statistics/discrete-random-variables

A discrete variable is a variable that can only take a finite number of values. The variable is said to be random if the sum of the probabilities is 1.

Answered: What is the difference between permutation and combination?

Sat, 13 Oct 2018 01:20:38 +0000

https://towardsdatascience.com/difference-between-permutation-and-combination-9e12b6763ee1

Permutation is when the order matters on the selection of objects, whereas Combination is the number of combinations that can be performed on a set of n objects

Answered: What is the difference between Qualitative and Quantitative data?

Sat, 13 Oct 2018 01:16:53 +0000

Qualitative data is not a number, and is typically a text value, whereas Quantitative data is a number (which is then divided into sub-groups: Discrete and Continuous).

Answered: What is binomial experiment and when do we use it?

Fri, 12 Oct 2018 22:30:50 +0000

A binomial experiment is a probability experiment where a same process is repeated for certain number of times.

So we use binomial experiment when we know that the events are independent of each others and has only 2 possible outcomes. For example, tossing a coin has 2 outcomes head or tail. Success is denoted as p while failure is denoted as 1- p .

What is "Random Sampling"?

Fri, 12 Oct 2018 22:26:06 +0000

Define random sampling

Answered: When should we use permutation and combination?

Fri, 12 Oct 2018 22:22:57 +0000

Permutations are used when we need to arrange things in a specific order. For example, lets assume there are 10 people and we have to assign them medals. So order is important here as 1st person gets gold while 2nd gets silver. In this case, we use permutations.

Combinations are used when we need to make groups where order doesn't matter. For example, if we need to give 3 tin cans to 8 people, order doesn't matter here for the way we pick people. In this case, we use combinations.

Answered: What do population, parameter, census and sample mean in statistics?

Fri, 12 Oct 2018 21:57:50 +0000

Population is a set of similar items or events. It can be a group of any existing objects.

Parameter is an very important component of population. It is a numerical quantity which features population or some aspect in it.

Census is a survey which is conducted after a complete observation belonging to any population.

Sample generally refers to a set of observations. Here, it refers to a set of observations drawn from a population.

Answered: Question for Discrete random variable

Fri, 12 Oct 2018 21:07:12 +0000

μ, of a random variable x is $\mu = \sum x.P(x)$ for all values of x

Here we will subtract the second value as it is in loss.

$\mu = (0.60)(20000) - (0.40)(25000)$

$\mu = 2000$

Answered: Sample question of permutation and combination.

Fri, 12 Oct 2018 20:52:42 +0000

Here the order of the r elements does not matter, so we will use combination formula:

= $\frac{n!}{r!\left(n-r\right)!}$

= $\frac{5!}{2!\left(5-2\right)!}$

= 10

Answered: {1.75, 1.63, 1.55, 1.92, 1.81, 1.79, 1.81}. Determine the mean, the median, and the 20th percentile?

Fri, 12 Oct 2018 20:37:02 +0000

Mean = (1.75 + 1.63 + 1.55 + 1.92 + 1.81 + 1.79 + 1.81) / 7 = 1.751

Median = Arrange the values in ascending order, if the total number of values in data set is odd the middle value is median

1.55, 1.63, 1.75, 1.79, 1.81, 1.81, 1.92

Percentile = 1.55, 1.63, 1.75, 1.79, 1.81, 1.81, 1.92

A = (nk)/100

= (7 x 20)/100 = 1.4

=> 2nd value in data set, which is 1.63

Answered: What is difference between discrete numerical variable and continuous numerical variable?

Fri, 12 Oct 2018 19:28:25 +0000

A discrete numerical variable can be determined by counting a quantity or variables that can only take on a finite number of values are called "discrete variables."

Variables that can take on an infinite number of possible values are called continuous numerical variable.

What is the difference between Combination and Permutation?

Thu, 11 Oct 2018 17:25:28 +0000

As an example:
Calculate the possible permutations for a rubik's cube?

Why is it not, calculate the possible combinations for a rubik's cube?

Answer selected: What is the difference between qualitative and quantitive data?

Thu, 11 Oct 2018 17:17:35 +0000

Qualitative data is data that cannot be measured numerically.

For example:

How hungry you are
The color of the sky

Quantitative is data that can be measured numerically.

For example:

The number of goals scored in a hockey game
Your age

Reshown: Six devices (A,B,C,D,E, F) are each assigned one of three IP addresses...how many different assignments are possible?

Mon, 08 Oct 2018 23:58:52 +0000

Six devices (A,B,C,D,E, F) are each assigned one of three IP addresses (IP#1, IP#2, IP#3). If three
devices are assigned IP#1, two devices are assigned IP#2, and one device IP#3, how many different
assignments are possible?

This is question 4 from lecture 3A.

Commented: How many different ways are there to deal four 13 card hands to four players from a standard deck of 52 cards?

Mon, 08 Oct 2018 20:56:04 +0000

Yes thanks. I just learnt about the Basic Counting Rule(BCR) from the textbook too which made this even more clearer. BCR says that if there are r actions with the first action having m1 possibilities and second having m2 possibilities and so on, then the total number of possibilities is m1*m2... *mr. So with your simplified example, the number of actions (r) is 2 for disturbing to 2 people
For the first person or action there are 6 possibilities (m1) for distributing 4 cards
For the second person or action there is only 1 possibility (m2) for distributing the remain 2 cards.

By the BCR the total number of possibilities is(m1*m2) 6*1 which is 6.

This applied to my original question means the answer I found is correct! Thanks again.

Answer selected: A standard deck of 52 cards is shuffled and a single card is drawn. What is the probability that this card is a Joker

Fri, 05 Oct 2018 22:15:03 +0000

In a standard deck of cards, as shown in the image that you have included, does not contain any Jokers.

J is for Jack.

Answered: What is the difference between the mean and the median? Calculate both for the following number set {18, 24, 19. 16. 21}

Fri, 05 Oct 2018 20:26:57 +0000

The mean is all of the numbers in a data set, divided by the number of numbers. Another word for mean is average.

The median is the middle number in an ordered set of numbers. If there is an even number of numbers (ie. 4), then take the two middle numbers, and divide them by 2.

Both calculations are meant to find the number that represents the data set (and the range of ts numbers) the best.

The mean (or average) in this case is: 18 + 24 + 19 + 16 + 21 / 5 = 19.6

The median in this case is: {16, 18, 19, 21, 24} = 19

Commented: What is the difference between a bar plot and a histogram?

Tue, 02 Oct 2018 15:44:29 +0000

Great explanation. Thanks.