### 11. What is power analysis?

An experimental design technique for determining the effect of a given sample size.

### 12. What is Collaborative filtering?

The process of filtering used by most of the recommender systems to find patterns or information by collaborating viewpoints, various data sources and multiple agents.

### 13. What is the difference between Cluster and Systematic Sampling?

Cluster sampling is a technique used when it becomes difficult to study the target population spread across a wide area and simple random sampling cannot be applied. Cluster Sample is a probability sample where each sampling unit is a collection, or cluster of elements. Systematic sampling is a statistical technique where elements are selected from an ordered sampling frame. In systematic sampling, the list is progressed in a circular manner so once you reach the end of the list, it is progressed from the top again. The best example for systematic sampling is equal probability method.

### 14. Are expected value and mean value different?

They are not different but the terms are used in different contexts. Mean is generally referred when talking about a probability distribution or sample population whereas expected value is generally referred in a random variable context.

For Sampling Data

Mean value is the only value that comes from the sampling data.

Expected Value is the mean of all the means i.e. the value that is built from multiple samples. Expected value is the population mean.

For Distributions

Mean value and Expected value are same irrespective of the distribution, under the condition that the distribution is in the same population.

### 15. What does P-value signify about the statistical data?

P-value is used to determine the significance of results after a hypothesis test in statistics. P-value helps the readers to draw conclusions and is always between 0 and 1.

• P- Value > 0.05 denotes weak evidence against the null hypothesis which means the null hypothesis cannot be rejected.

• P-value <= 0.05 denotes strong evidence against the null hypothesis which means the null hypothesis can be rejected. • P-value=0.05is the marginal value indicating it is possible to go either way.

### 16. Do gradient descent methods always converge to same point?

No, they do not because in some cases it reaches a local minima or a local optima point.

You don’t reach the global optima point. It depends on the data and starting conditions.

### 17. A test has a true positive rate of 100% and false positive rate of 5%. There is a population with a 1/1000 rate of having the condition the test identifies. Considering a positive test, what is the probability of having that condition?

Let’s suppose you are being tested for a disease, if you have the illness the test will end up saying you have the illness. However, if you don’t have the illness- 5% of the times the test will end up saying you have the illness and 95% of the times the test will give accurate result that you don’t have the illness. Thus there is a 5% error in case you do not have the illness.

Out of 1000 people, 1 person who has the disease will get true positive result. Out of the remaining 999 people, 5% will also get true positive result.

Close to 50 people will get a true positive result for the disease.

This means that out of 1000 people, 51 people will be tested positive for the disease even though only one person has the illness. There is only a 2% probability of you having the disease even if your reports say that you have the disease.

### 18. What is the difference between Supervised Learning an Unsupervised Learning?

If an algorithm learns from the training data so that the knowledge can be applied to the test data, then it is referred to as Supervised Learning. Classification is an example for Supervised Learning. If the algorithm does not learn anything beforehand because there is no response variable or any training data, then it is referred to as unsupervised learning. Clustering is an example for unsupervised learning.

### 19. What is the goal of A/B Testing?

It is a statistical hypothesis testing for randomized experiment with two variables A and B. The goal of A/B Testing is to identify any changes to the web page to maximize or increase the outcome of an interest. An example for this could be identifying the click through rate for a banner ad.

### 20. What is an Eigenvalue and Eigenvector?

Eigenvectors are used for understanding linear transformations. In data analysis, we usually calculate the eigenvectors for a correlation or covariance matrix. Eigenvectors are the directions along which a particular linear transformation acts by flipping, compressing or stretching. Eigenvalue can be referred to as the strength of the transformation in the direction of eigenvector or the factor by which the compression occurs.