Understanding Confidence Intervals

Confidence intervals can be an easy way to understand the amount of uncertainty in a sample estimate of a population, like the mean or proportion. This allows you to draw inferences on population values from each sample taken.

Making Estimations

How much your next pay raise will be? Perhaps $3,000 or $5,000? Hmm, it’s extremely difficult to estimate an exact number. You would have more success if you estimated your raise within a range of numbers.

Meaning, if you were to say that your next pay raise would be between $1,000 and $10,000, you would be more confident in your estimate. This is essentially how confidence intervals work.

What is a Confidence Interval?

Confidence Interval (CI) refers to the amount of uncertainty associated with a sample population estimate (the mean or proportion) of a true population.

Say you wanted to determine the average age of victims of robberies in Chicago last year. Now, while there is a true answer, say 30 years old, the best you can do is find an interval that that true answer probably lies in, say, 20-40 years old.

The confidence interval is the sample mean or proportion plus or minus the margin of error (ME), the value used to calculate the upper limit (40) and lower limit (20) of the sample statistic.

Before calculating the CI from a sample mean or proportion, choose either a 90%, 95%, or 99% confidence level (CL). This is the amount of uncertainty in the sampling method. Meaning each time the same sampling method is used, the true population value would be represented in 90%, 95%, or 99% of all the sample estimated CI’s. That also means that 10%, or 5%, or 1% would not contain the true population score.

Calculating CI – Mean

Let’s see how to calculate a confidence interval using the mean.

  1. Identify a population, select a representative sample, and note the number of the sample (n).
  2. Calculate the mean by adding all of the sample values and divide by n.
  3. Select the CL (typically 95%) and locate the corresponding t (z value), which is 1.96 for 95% CI. (NOTE: There are tables of pre-calculated z values for various confidence levels to utilize as a resource).
  4. Calculate the standard deviation (s) by subtracting each value in your sample from the mean, then square each result, then calculate the mean of all of those squared differences. This is known as the variance.
  5. Take the square root of the variance.
  6. Calculate the CI with the following formula:

Note that n uses the degrees of freedom, which is n – 1.

Finally, write out your CI mean ± the margin of error. The CI is between the upper limit (the sample mean plus the margin of error), and lower limit (the sample mean minus the margin of error).

Real World Mean Example

Let’s return to our earlier example. What is the average age of robbery victims in Chicago last year?

  1. Randomly sample 100 police reports of Chicago robberies last year. n = 100
  2. Record the ages of the victims, add them all up all, and divide by 100 to get the mean. Say the mean age in this case is 34.25 years.
  3. Utilizing a 95% CL, which has a standard z value of 1.96; calculate the standard deviation. With a mean of 34.25 and a standard deviation of 10, a margin of error of 8 is calculated with the CI formula.
  4. Your CI is 34.35 ± 8, or 26.35 to 42.35.

You can now say with 95% confidence, that if the true average age of all Chicago robbery victims last year was known, it would fall between 26.35 and 42.35 years of age.

Calculating CI – Proportion

When you’re faced with a population measured by categorical data (ex. gender) you can calculate the CI using a proportion with the following steps and formula:


1. Select an appropriate CL (95% is the most common, which is z*= 1.96).

2. Find the sample proportion by dividing the number of individuals that have the common shared characteristic of interest in the sample and divide that number by the total sample size.

3. Multiply the sample proportion by 1 minus the sample proportion, then divide by the sample size.


4. Take the square root of the result.

5. Multiply the answer by z*(1.96 for 95% CL)

6. Finally use the sample proportion plus or minus the result (margin of error) to give the confidence interval.

Real World Proportion Example

Let’s continue with the theme of robberies. This time, what if you wanted to determine the confidence interval for the percentage of female victims of robberies in Chicago. From the same sample (n=100), let’s say that 57 out of the 100 were female victims.

  • By dividing the number of females by 100 to get 0.57.
  • Using a CL of 95% which gives us a z* of 1.96, you first multiply 0.57 x (1-.57) divided by n = 100 which gives you 0.0025.
  1. Then take the square root of that number which gives you .05.
  2. Multiply .05 x 1.96, which equals .1.
  3. Write out your CI with the margin of error, which in this case would be .57 ±.1.

As a result, with 95% confidence, if the actual percentage of female robbery victims in Chicago was known, it would be between .47 and .67, or between 47% and 67%.

Lesson Summary

When studying a population, it is easier to generalize with a sample rather than studying the entire population. A Confidence Interval (CI) refers to the amount of uncertainty associated with a sample population estimate (the mean or proportion) of a true population. It’s represented by the CI ± the margin of error (upper and lower limits of the value).

To calculate the CI using a mean:

  1. Select the CL (typically 95%) and locate the corresponding t (z value), which is 1.96 for 95% CI.
  2. Calculate the standard deviation (s) by subtracting each value in your sample from the mean, square each result, then calculate the mean of all of those squared differences. This is known as the variance.
  3. Take the square root of the variance.
  4. Calculate the CI with the following formula:

To calculate the CI using a proportion, use:


1. Select an appropriate CL (95% is the most common, which is z*= 1.96).

2. Find the sample proportion by dividing the number of individuals of interest in the sample and divide that number by the total sample size.

3. Multiply the sample proportion by 1 minus the sample proportion, then divide by the sample size.


4. Take the square root of the result.

5. Multiply the answer by z*(1.96 for 95% CL)

6. Use the sample proportion plus or minus the result (margin of error) to give the confidence interval.

Top Ten Ranking for Violent Crimes

This  is a continuum scale ranked from the most violent to the least violent crime based on the severity, amount of force needed to commit the crime and the overall potential rate of victimization.

1. Terrorism

Unlawful, or threatened, use of violence to intimidate or coerce a population or government.

Use of WMD attacks, assassinations, or kidnappings to force changes in policy or gain some type of advantage.


2.  Mass Murder

The killing of 4 or more persons during the same ongoing incident.

Killings occur at the same location, with no cooling off  time between mass incidents, by a single offender.

This differs from spree killing where 2 or more people are killed by the same individual(s) at different times and locations, with no cooling off period.

The third form of mass murder is serial killing where 3 or more people are killed generally by the same person over an extended period of time with a significant cooling off period. (years as opposed to hours).



3. Murder

Taking another person’s life with intentional malice.

Taking another person’s life in commission of a felony.



4. Manslaughter

Voluntary – Causes the death of another person from a sudden, violent, irresistible passion resulting from insufficient provocation.

Involuntary- Causes the death of another without any intention to do so outside of the commission of a felony.



5. Rape

A forcible act of sex against a female .

Or sex with a female less than 10 years of age.



6. Sexual Assault

A person in an authoritative, supervisory, or disciplinary position commits the sexual act without consent.

Nonconsensual sexual contact with intimate body parts for the purpose of sexual gratification.



7. Child Molestation

An immoral or indecent act to, or in the presence of, a minor less than 16 years of age for sexual arousal or gratification.

Transmits images of minors less than 16 involved in immoral or indecent acts for sexual gratification or arousal.



8. Domestic Violence

Physical, verbal, or mental abuse or the threat of abuse, between two intimate partners, roommates, or family members.

Involves at least one person to person crime, or threat of a crime, such as assault, battery, or kidnapping which can occur inside or outside the home.



9. Child Abuse

Parent, guardian, or supervisor of a child under 18 willfully deprives necessary sustenance jeopardizing health or well-being.

Any person that maliciously, or with negligence, causes excessive or cruel mental or physical harm to a child under 18; or intentionally, with knowledge, allows a child to witness or hear crimes or violence.



10. Stalking

Any person that follows, puts under surveillance, or contacts another person without consent with intent to harass or intimidate.

Consists of communication via mail, computer, phone, broadcast or any electronic device at any public or private location occupied by the victim, with the intent to cause emotional distress or fear for safety for the victim or their family.


This is a useful scale when attempting to understand how violent crimes are adjudicated in the courts based on the corresponding punishments ranging from more to less severe.

This scale can also be a general tool to understand the meanings of these crimes and how each one may impact society at large (i.e. large groups of people vs. one person, economic issues).

Finally, it is always a good exercise to contemplate the level of significance placed on some crimes over others. What do you think of this scale? Would you rank some offenses higher or lower on the scale? If so, why?

These are questions that should be contemplated on all types criminal justice issues ranging from theory to community programs.

In upcoming articles in this series, I will touch on how likely individuals are to be victims of these crimes, along with everyday activities that can lead to being a victim of these crimes…These will totally surprise you.


(Ardvarc, FBI, Lexis Nexis)



What’s Your Aversion to Reese’s Peanut Butter Cups?

That question has been posed to a family member for years. Who doesn’t like that rich, chocolaty, peanut butter classic? The family member that has a conditioned taste aversion is who. This is not a life threatening issue, but a rather common occurrence with many individuals that associate a very uncomfortable event to the eating or drinking of a specific food or beverage. After this family member ate this once enjoyable treat, several hours later he became very sick to his stomach. The consequence of that event resulted in this family member feeling nauseous any time he saw, smelled, or even thought about that candy.

A conditioned taste aversion is based off of the psychological principle of classical conditioning. In scientific terms, this occurs when a previously arbitrary stimulus is paired with an unconditioned stimulus, resulting in a new unconditioned response to that original stimulus. Simply put, this phenomenon takes place after a specific food or beverage is consumed, followed by an uncomfortable physical condition, after a random time frame has elapsed.

In this case, the isolated stimulus was the consumed Reese’s candy; the unconditioned stimulus was the physical illness that occurred many hours later, which lead to the future unconditioned response of nausea in the presence of the candy. This principle is unique, in that an association can form with any food or drink. The illness that follows can be directly caused by the food or drink, or have no link at all. That means if you are due to get a stomach flu on the same day you eat your mother’s famous lasagna, you may want to consider skipping family lasagna night. You might just develop a conditioned taste aversion to that good food, for no good reason.

If you are one of the folks that have a taste aversion, it’s not a condition that generally requires counseling. These aversions fade away over time naturally, though the length of time varies based upon how strong this aversion is in the first place.

Interestingly enough this phenomenon has been used by psychologists to help treat alcohol addiction. Addicts with a very serious addiction to alcohol have been known to take a pill, called Antabuse, and then if they decide to drink a beer for example, the addict gets very ill and sick to the stomach. This association is supposed to trigger an aversion to the sight, smell, or taste of alcohol if the addict feels like they need a drink. The true effectiveness has mixed results in the scientific research community,


Article Source: http://EzineArticles.com/?expert=Cleveland_Alexander

@Followme To The Police Station

Local police departments have attempted many citizen outreach, public relation, and collaboration strategies over the past couple of decades for the purpose of creating improved and productive relationships with communities. This philosophy is designed to engage the public on various fronts with the ultimate goal of becoming a trusted, legitimate, and effective partner in crime and safety.

Think back to when you first started seeing bicycle patrols, citizen police academies, neighborhood watch programs, gun collection drives, youth academies, etc… These are all examples of the police attempting to engage the community on a more basic level for the common and beneficial goal of making their cities and towns safer and more stable… which is known as community policing.

Why community policing?

Because citizens are more likely to trust, feel confident in, and collaborate with police, if police are actively providing time, resources, and information in a transparent manner about local issues. Conversely, if the police understand that they have a collaborative and productive relationship with the community, they will come together with the community to help address specific and important crime and disorder issues they both encounter on a daily basis. Just as beat officers can’t be everywhere for everybody, police have also struggled in the past with actively engaging and encountering a large number of citizens for “positive” outreach.

With the innovations provided by internet technology, and the research conducted on the effectiveness of community policing, police have begun to adopt social media as a new form of communication and engagement with the public. Specifically, police departments view Twitter as an easy, fast, and effective means of getting information to the general public on many levels. Furthermore, citizens can reciprocate the kindness by offering information and updates to police from their vantage points. But what does all of this really mean for you?

Think about it… there’s a massive pile-up on a major road you use to get to work… police tweet about it. A prisoner escapes near a school… police tweet about it. There’s a rash of home invasions in your elderly parents’ neighborhood… police tweet about it. And that’s just simple public safety messages.

How about a scenario where there is a youth academy one weekend where police officers educate and mentor middle school children about bullying, but you and your child could not attend. However, the police staff records the event including the Q&A at the end. Then that video, important downloadable information, as well as a link to the police department’s website (where you can sign up and request a police officer to come to your child’s school to talk about bullying) is tweeted out.

Let’s take this one step further. You witness a crime and you get a picture of the culprit, or perhaps a license plate on a vehicle used in the crime, and message that to the police via Twitter.

These are small examples of how Twitter, other social media platforms and the internet can bring citizens and police closer together. Closer in the sense of communication, but also closer as these collaborative back and forth exchanges begin to build a trust and legitimacy factor between citizens and police.

This begins to hit on the big picture, philosophical take away viewed by law enforcement.

Better relationships equal productive relationships equal working relationships… all of which can be cultivated from something as simple as Twitter. And from that, something much bigger and better can begin to take place.

For example:

A major intrinsic problem within a community requires a lot of time, energy, resources and actions. The police-community relationship is such that there is an ample, representative sized advisory committee of individuals, small businesses, churches, outreach centers and police that come together to stage a four point plan over the next 2 to 3 years to deal with this issue. Based on this collaboration, there will be enough resources and entities to successfully tackle a particular issue.

Law enforcement, as well as academia, view this scenario as plausible, and possible, given the right circumstances. But none of that can even be attempted if there is not a sound partnership between police and community. And this type of partnership cannot exist without police first laying a foundation of beneficial, productive, transparent, and collaborative communication and engagement. This also requires civic responsibility and action on the part of the citizen to attempt to reach out to police in order for this progress to begin to take place.

Even if you are not the type of person that gets really involved in civic issues, following your local police department on Twitter can be personally beneficial.

Here are some documented examples of how Twitter has benefited police department followers.

  1. When individuals can see that police are active in the local community, they feel safer.
  2.  There is a 24/7 line of communication with the police.
  3.   When police solicit help from the public on a case, there are that many more individuals that will be alerted and activated to help. (And this case could involve you or someone you know as the victim of a crime that really needs the public’s help).
  4.  This is another resource to get the word out on fund raisers and community awareness initiatives.
  5. Doesn’t everyone want to know the city’s crime reports, or the published sex offender lists.
  6. Everyone can get a good laugh at the end of the day with “dumb crook news”.
  7. Think of alerting 911 to an emergency via a tweet as well as to family and friends at the same time.
  8.  How about getting a GPS link on evacuation routes in a tornado or hurricane areas.
  9.  Amber Alerts.
  10. Counter-terrorism and Homeland Security efforts at the local level.

So with that I say to you, #followmetothepolicestation.


Article Source: http://EzineArticles.com/?expert=Cleveland_Alexander


It All Began By Psyching Myself Out


My journey as a social scientist began when I declared to my parents and family in my senior year in high school that I was going to college to be a….yep you guessed it….a DOCTOR!

8 years later when I earned my Bachelors Degree in Psychology ( no kidding)…that became one of the most expensive but fulfilling journeys of my life.

Social science is unique, fun and interesting because it deals with all aspects of human, and non-human, interaction.  How we think, feel, and comprehend the world around us. The internal and external factors that shapes almost every decision we make and action we take.

While I was going through the first 3 and a half years in college as a pre-med student taking biology, chemistry and physics classes, I really got bogged down in the mundane and endless facts and figures to memorize. Don’t get me wrong, I actually love biology, but I wanted more out of my college experience (and ultimately my long term career) than learning the classification and species name for the sea anemone. So, to the displeasure and everlasting credit of my parents,  I did a complete 180 and turned my studies towards Psychology…with their blessing.

Why psychology you ask? What is it about psychology that is so unique and interesting? There are 3 main reasons.

1. It’s a social science discipline that can easily fit into many diversified “categories” and “careers”.

Psychology is much more than treating mental health concerns as a psychiatrist, being a marriage counselor , or leading group therapy for addictions. Though these are very good and rewarding career options that are greatly needed, psychology embodies so much more to so many other people.

Psychology is ultimately a constant, creative search for the understanding of  how individuals interact with the world around them, and why they are uniquely impacted by specific  people, environments, situations, and circumstances. If that’s not enough fun, then you also get to assess and analyze the findings and outcomes observed from those interactions and influences. As an added bonus, you can then apply innovative solutions and enhancements to similar future occurrences as to help create and manage new and improved outcomes.

All of these roles of a psychology major, or psychology specialist, can carried out in many great and exciting careers that extends to virtually all meaningful parts of society.  Examples include becoming an analyst, advertising salesperson, actor, air traffic controller, manager, supervisor, real estate agent, police officer, detective, investigator, correctional officer, industrial-organizational psychologist, lawyer, marketing manager, occupational health technician, public relations specialist, politician,  photographer, security consultant, teacher, entrepreneur, writer, author, reporter, researcher, school counselor, forensic psychologist, sports psychologist, sports agent, school psychologist, and healthcare administrator to name a few.

So as you can see, not only can psychology lead to an interesting and rewarding career, but you can also become a more interesting person.

2. This social science discipline helps make one a well rounded, and well adjusted individual.

After earning a degree in psychology, you gain some very crucial skills in communication, reasoning, problem solving, understanding different and diverse perspectives, writing, researching, analyzing in-depth information, leadership, motivation, influence, training, and most assuredly understanding the many different mental health issues going on in today’s world.

This occurs based on the wide ranging subject matter that is taught in psychology.           The variety is the spice of psychology after all.

Here are some interesting examples:

Understand the diagnostic criteria for mental health concerns in Abnormal Psychology, apply emotional states to physical fitness in Health Psychology, discover what drives a person to purchase one product over another in Consumer Behavior, create new ways to improve job performance at a multi-million dollar company in Industrial-Organizational Psychology, investigate and analyze if and how a new method of instruction improves graduation rates at a high school through Learning and Cognition Psychology, construct the next poll for a political candidate with Quantitative Research Design, or influence a friend to always lend you money when you ask for it through Social Psychology. But it can’t be all about you, can it?

3. This social science discipline allows one to really help others.

With great knowledge comes great understanding. When someone can take a step back from “life” and realize how or why others act a certain way, or feel something different, or say specific things at specific moments in time, then you are five steps ahead of biology majors when you graduate. All kidding aside. Then you can empathize, sympathize, and help others understand the world around them. Psychology helps you become a type of everyday professional helper.

Based on the large continuum of subjects psychology covers, the individuals immersed this field, or major,  are especially equipped to serve as a link between the everyday world and everyday people. Psychology specialists have the ability to merge theoretical  plans to practical uses. They can transform scientific research findings into applied solutions.  They can analyze complex information gathered from a government agency and provide  “kitchen table” answers to a family of four. All for the greater benefit of others. No matter the many different settings, among vastly different professions, working for a greatly diverse populous; a psychology specialist is a rare class of person that can truly make meaningful change for many people.

So I’ll say it again, I psyched myself out of memorizing the difference between a radius and an ulna…and into my current role as a social science consultant helping others with important scholarly research, article creation, research design, thesis formation, background investigation, surveys, and report writing to name a few.

***To all of the potential psychology majors, college students, academics, instructors, businesses, or interested parties, I hope you enjoyed a brief introduction to Psychology 101, and Careers in Psychology.***

To gain a greater understanding of my personal story and biography I invite you to read more at www.socialsciencepro.com