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# Statistical Sample Presentation

Lunch and Learn presentation outlining statistical sampling.

by

Tweet## Sthefanie Mckelligan

on 15 April 2013#### Transcript of Statistical Sample Presentation

Sampling is the selection of a subset of

individuals from within a population to

estimate characteristics of the whole. Statistical Sampling Sampling advantages: 1. Reduce Cost

2. Save time since data collection is faster

3. Ensure smaller data sets provide the same or similar results compared to the whole population. Statistical Sample Calculator A statistical sample calculator can be found under the "Improvement Tools" in QI Macros for Excel.

The statistical sample will ensure enough data is included and is adequately represented within an analysis.

Sample criteria can be modified based on desired confidence level and margin of error. Application of Statistical Sample 1. Sampling allows us to make observations which measure one or more properties of the independent objects or individuals in a sample. Sampling Examples Job Applicants:

- Gender

- Age

- Ethnicity Why do we need a statistical sample?

Statistical samples are needed to make sure that the sample size is REPRESENTATIVE of the whole population.

A percentage of the population does not necessarily equal a statistical sample. How much do we sample? We have a bucket with 200 balls and we want to know how many of each color we have. So we decide to take a random sample of 10% which equals to 20 balls.

Our sample results show:

- 10 Green Balls

- 6 Red Balls

- 4 Yellow Balls NOTE: No orange balls were selected in our sample. Statistical Sample Calculator On our previous example we took a percentage of the population to sample in order to know how many balls of each color we have. By using this method we left out the orange balls completely.

By using the statistical sample calculator we discovered that our sample size should be 115 balls instead of 20. By selecting 115 balls we can be fairly certain that all the colors will be selected. 51 Green Balls 44%

32 Red Balls 28%

19 Yellow Balls 17%

13 Orange Balls 11% What if the bucket not only had balls but it had cubes as well? What if we wanted to know what percentage of the objects are blue cubes and what percentage are red balls?

Stratified Statistical Sample is used when the population is not homogeneous. If we take just one sample of the whole population we run the risk of not including enough cubes in our sample.

A stratified sample helps avoid the gaps that can come up if data are collected over a large population where key subgroups of the population are underrepresented. Stratified Random Sample In this case we would get a sample of the balls and a different sample of the cubes.

This way we ensure that both objects are representative of the population Cubes population: 216

Sample size: 120

Blue cubes: 48 - 40%

Red cubes: 34 - 28%

Orange cubes: 27 - 23%

Yellow cubes: 11 - 9% Sampling Results Balls population: 384

Sample size: 158

Blue balls: 56 - 35%

Red balls: 42 - 29%

Orange balls: 35 - 19%

Yellow balls: 25 - 15% Population of objects in the bucket: 600

384 Balls and 216 Cubes

29% of the Balls are red = 111

40% of the cubes are blue = 86 CONCLUSIONS QUESTIONS? The process of preparing and collecting data, can be used as part of a process improvement or similar research projects.

The purpose of data collection is to obtain information to keep on record, to make decisions about important issues, or to pass information on to others.

Quality's Role: To provide information to our business partners that will help them make decisions. Data Collection Data Collection Method that includes only part of the total population Sampling The sample size of a population does not grow at the same rate that the population does.

The actual number of the sample will grow but it will represent a smaller percentage of the whole. Sample Methods Simple Random Sample: The process of choosing individuals from a sample randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process.

Lets assume we have a population of 1,000 students and want to select 212 names for your sample. If we were using the simple random sample we could potentially put their names in a bucket and pull 212 names out. Note that all the names have the exact same chance of being selected. Simple Random Sample Sampling approach that relies on arranging the target population according to some ordering scheme and then selecting elements at regular intervals through that ordered list. This approach consists of the selection of every nth element in a population. Systematic Sampling Is a type of non-probability sampling which involves the sample being drawn from that part of the population which is close to hand. That is, the population is selected because it is readily available and convenient. Accidental Sampling Suppose we wish to sample customer care calls to analyze the customer care representative's behavior If we were to select randomly from a population of calls taken during a whole day, we could end up with calls taken in the morning only. The behavior of the care representatives would probably be of total adherence in the morning, which can potentially wear out towards the end of the day. For this reason we should select every nth call starting at the morning and ending at the end of the shift. That way we ensure that we account for the calls taken in the afternoon, even if the volume is lower than the ones taken in the morning, The branch of applied mathematics concerned with the collection, organization and interpretation of numerical data, especially the analysis of population characteristics by inference from sampling. Statistics An arrangement of values of a variable showing their observed or theoretical frequency of occurrence.

* Normal Distribution

* Binomial Distribution

* Geometric Distribution Statistical Distribution The normal distribution is characterized by two parameters: The mean and the standard deviation. the normal distribution is best suited for data that meets the following conditions:

A. There is a strong tendency for the data to take on a central value.

B. Positive and negative deviations from this central value are equally likely.

C. The frequency of the deviations falls off rapidly as we move further away from the central value. Normal Distribution Is a measure of the expectation that an event will occur or that a statement is true. The higher the probability of an event, the more certain we are that the event will occur. Probability Given a standard die, determine the probability of rolling a 5, when rolling the die one time.

The die has 6 sides and contains the numbers 1- 6. There are a total of 6 outcomes that could occur when we roll the die.

Probability = Number of ways a certain outcome can occur

Total possible outcomes

There is one number 5 on the die, so there is one chance of rolling a 5.

P= 1 = 0.16 probability of rolling a 5.

6 Example

Full transcriptindividuals from within a population to

estimate characteristics of the whole. Statistical Sampling Sampling advantages: 1. Reduce Cost

2. Save time since data collection is faster

3. Ensure smaller data sets provide the same or similar results compared to the whole population. Statistical Sample Calculator A statistical sample calculator can be found under the "Improvement Tools" in QI Macros for Excel.

The statistical sample will ensure enough data is included and is adequately represented within an analysis.

Sample criteria can be modified based on desired confidence level and margin of error. Application of Statistical Sample 1. Sampling allows us to make observations which measure one or more properties of the independent objects or individuals in a sample. Sampling Examples Job Applicants:

- Gender

- Age

- Ethnicity Why do we need a statistical sample?

Statistical samples are needed to make sure that the sample size is REPRESENTATIVE of the whole population.

A percentage of the population does not necessarily equal a statistical sample. How much do we sample? We have a bucket with 200 balls and we want to know how many of each color we have. So we decide to take a random sample of 10% which equals to 20 balls.

Our sample results show:

- 10 Green Balls

- 6 Red Balls

- 4 Yellow Balls NOTE: No orange balls were selected in our sample. Statistical Sample Calculator On our previous example we took a percentage of the population to sample in order to know how many balls of each color we have. By using this method we left out the orange balls completely.

By using the statistical sample calculator we discovered that our sample size should be 115 balls instead of 20. By selecting 115 balls we can be fairly certain that all the colors will be selected. 51 Green Balls 44%

32 Red Balls 28%

19 Yellow Balls 17%

13 Orange Balls 11% What if the bucket not only had balls but it had cubes as well? What if we wanted to know what percentage of the objects are blue cubes and what percentage are red balls?

Stratified Statistical Sample is used when the population is not homogeneous. If we take just one sample of the whole population we run the risk of not including enough cubes in our sample.

A stratified sample helps avoid the gaps that can come up if data are collected over a large population where key subgroups of the population are underrepresented. Stratified Random Sample In this case we would get a sample of the balls and a different sample of the cubes.

This way we ensure that both objects are representative of the population Cubes population: 216

Sample size: 120

Blue cubes: 48 - 40%

Red cubes: 34 - 28%

Orange cubes: 27 - 23%

Yellow cubes: 11 - 9% Sampling Results Balls population: 384

Sample size: 158

Blue balls: 56 - 35%

Red balls: 42 - 29%

Orange balls: 35 - 19%

Yellow balls: 25 - 15% Population of objects in the bucket: 600

384 Balls and 216 Cubes

29% of the Balls are red = 111

40% of the cubes are blue = 86 CONCLUSIONS QUESTIONS? The process of preparing and collecting data, can be used as part of a process improvement or similar research projects.

The purpose of data collection is to obtain information to keep on record, to make decisions about important issues, or to pass information on to others.

Quality's Role: To provide information to our business partners that will help them make decisions. Data Collection Data Collection Method that includes only part of the total population Sampling The sample size of a population does not grow at the same rate that the population does.

The actual number of the sample will grow but it will represent a smaller percentage of the whole. Sample Methods Simple Random Sample: The process of choosing individuals from a sample randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process.

Lets assume we have a population of 1,000 students and want to select 212 names for your sample. If we were using the simple random sample we could potentially put their names in a bucket and pull 212 names out. Note that all the names have the exact same chance of being selected. Simple Random Sample Sampling approach that relies on arranging the target population according to some ordering scheme and then selecting elements at regular intervals through that ordered list. This approach consists of the selection of every nth element in a population. Systematic Sampling Is a type of non-probability sampling which involves the sample being drawn from that part of the population which is close to hand. That is, the population is selected because it is readily available and convenient. Accidental Sampling Suppose we wish to sample customer care calls to analyze the customer care representative's behavior If we were to select randomly from a population of calls taken during a whole day, we could end up with calls taken in the morning only. The behavior of the care representatives would probably be of total adherence in the morning, which can potentially wear out towards the end of the day. For this reason we should select every nth call starting at the morning and ending at the end of the shift. That way we ensure that we account for the calls taken in the afternoon, even if the volume is lower than the ones taken in the morning, The branch of applied mathematics concerned with the collection, organization and interpretation of numerical data, especially the analysis of population characteristics by inference from sampling. Statistics An arrangement of values of a variable showing their observed or theoretical frequency of occurrence.

* Normal Distribution

* Binomial Distribution

* Geometric Distribution Statistical Distribution The normal distribution is characterized by two parameters: The mean and the standard deviation. the normal distribution is best suited for data that meets the following conditions:

A. There is a strong tendency for the data to take on a central value.

B. Positive and negative deviations from this central value are equally likely.

C. The frequency of the deviations falls off rapidly as we move further away from the central value. Normal Distribution Is a measure of the expectation that an event will occur or that a statement is true. The higher the probability of an event, the more certain we are that the event will occur. Probability Given a standard die, determine the probability of rolling a 5, when rolling the die one time.

The die has 6 sides and contains the numbers 1- 6. There are a total of 6 outcomes that could occur when we roll the die.

Probability = Number of ways a certain outcome can occur

Total possible outcomes

There is one number 5 on the die, so there is one chance of rolling a 5.

P= 1 = 0.16 probability of rolling a 5.

6 Example