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Statistical graffiti presentation

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artistic depiction of several statistical concepts

artistic depiction of several statistical concepts

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  • This presentation is being presented in three ways to meet the three different learning styles: Visual, Auditory, and Psychomotor.VISUAL: Each slide has a “written” explanation beneath it in the “Notes” section.AUDITORY: Each slide has an auditory or “sound” icon located at the upper left hand corner indicating this presentation has been prerecorded by the presenter. Click on the icon and “listen” to the presentation for that slide. PSYCHOMOTOR: Each slide has a “Source” reference to allow students to browse the internet for additional information.
  • Everyone nursing student knows the simple definition of basic statistical terms like mean, median, mode, standard deviation, and level of significance. However, conceptualizing these “terms” in relationship to a normal curve can be daunting. A group of senior nursing students at the Texas Tech University Health Science Center were asked to design an artistic mnemonic to help conceptualized and remember this terms.
  • This is their result. They drew a Pirate (head only) and incorporated statistical concepts within the picture:Standard deviation = eyes (1sd) hairline (2sd) ears (3sd)Mean = nosePercentages = teeth (68%) inner hat (95%) outer hat (99%)“feelings about statistics” = skull & cross bones!TEST RESULT: 90% of the nursing students answered the statistic questions correctly on the next test.
  • I found otherartistic representations of statistical concepts in the literature. For example, the normal distribution of “random variables” is represented by this “bean machine”. This machine consists of a vertical board with interleaved rows of pins. Small balls are dropped from the top and then bounce randomly left or right as they hit the pins similar to a pinball machine. The balls are collected into bins at the bottom and settle down into a pattern resembling the Gaussian curve.
  • I found this fun artistic depiction of Pearson’s correlationcoefficient which depicts a linear relationship between two random variables.In the top row, a perfect Pearson’s correlation of -1 or +1 is seen as a line with a positive or negative slope. However, where these is “perfect chaos or randomness” at P=0, there is a perfect circular cluster of scattered data points The middle row depicts “zero” chaos or “noise” in the data. Therefore the relationship is linear with a perfect Pearson’s coefficient. In the center, y=0 and x is increasing with a slope of “0”. The bottom row is a non-linear relationship so P=0.
  • Before class tomorrow, can you think of ways to incorporate these statisticalconcepts into a artistic mnemonic to help conceptualize and remember this terms: Increase the variance, decrease the height: If the variance increases then the density around the mean decreases (ie height of graph decreases)N(μ,σ2) Probability Density FunctionRemember; there are four “moments” or descriptors that define the curve: Mean, SD, skewness, kurtosisThis graph is depicting a “normal distribution” which means Skewness = 0 and kurtosis = 0
  • ASSUMPTION: normal bell curve! Skew=0 and Kurtosis =0In this graph, the relationship between X and Y seems “pure” without external influences that “skew” the normal curve and kurtosis = 0. There are four curves: blue, green, red, & yellow. Each curve has a different variance. The Blue curve has the lowest SD therefore lowest variance. which means the relationship or correlation between the X and Y is strong without a lot of diversity or chaos or randomness or “out-liers”. The Yellow curve has the highest SD which means the relationship between X and Y is more random or loose or has “outliars” I look at the artistic depiction in terms of human relationships: The blue curve represents closest between two happily married people. The orange curve represents two people ready for divorce – their relationship is not close. I added the two “thieves” because I like to remember that variables which are not “tight” or have a lot of variance may have an “external variable” influencing the data set or “steeling” the attention of the sample or variable.
  • This slide depicts the ‘margin of error” for a binominal distribution. Can you come up with an artistic depiction of this concept.The top portion of this graphic depicts probability densities (for a binomial distribution) that show the relative likelihood that the "true" percentage is in a particular area given a reported percentage of 50%. The bottom portion of this graphic shows the margin of error, the corresponding zone of 95% confidence. In other words, one is 95% sure that the "true" percentage is in this region given a poll with the sample size shown to the right. The larger the sample is, the smaller the margin of error is.
  • I remember this concept: The larger the sample is, the smaller the margin of error is.by remembering that the more one shoots a “shotgun”, the more times the pellets hit the target right on.
  • The third moment of a distribution is skewness. A distribution is skewed if one side of the distribution is much more stretched out than the other:A positively skewed distribution has a long-tail to the rightSee if you can come up with an artistic depiction of this concept.
  • I remember the importance of “skewed” curves because it tell me there is a “variable” that is having a “sucking or vacuum” effect on the bell-shape curve. The “outliers” skewed to one side are being sucked away from the mean. These “outliers” are different then thoses who are not being affected by the sucking “external factor” that I failed to take into account. This is an “ah ha!” moment!... And another “I wonder…..” why these outliers are being swayed to one end while the others are not.
  • The fourth moment is kurtosis which measures how sharply the distribution peaks are and how fat the tails are: KEY POINT: HOW FAT THE TAILS ARE!!! Remember that kurtosis is a mathematical description of the ratio between the PEAK and the TAIL. In other words, Kurtosis is a parameter that describes the shape of a random variable's probability density function (PDF). The distribution marked in RED is the most kurtotic.. We are told the K is greater then zero or “positive which means it is Leptokurtic. The distribution marked in GREEN has a zero kurtosis. We are told the K equals zero which means it is Mesokurtic (normal)The distribution marked in BLUE is the leastkurtotic.. We are told the K is less then zero or “negative” which means it is Platykurtic
  • These graphs illustrate the notion of kurtosis. The PDF (probability density function) on the right has higher kurtosis than the PDF on the left. It is more peaked at the center, and it has fatter tails.Which would you say has the greater standard deviation? Graph on the left or the graph on the right???It is impossible to say. The PDF on the right is more peaked at the center, which might lead us to believe that it has a lower standard deviation. BUT it has fatter tails, which might lead us to believe that it has a higher standard deviation. If the effect of the peakedness exactly offsets that of the fat tails, the two PDFs will have the same standard deviation. THIS IS WHERE MOST STUDENTS MESS UP because they try to use their “eyes” to make a conclusion without taking into account the “hard to see” points in the tail which may offset the conclusion.
  • Leptokurtic distributions are represented by a Kangaroo – Kangaroos are tall with deceptive low-lying tails that can be deadly. A graph with a density that is peaked with fat tails have destroyed large corporations who where too focused on the obvious peaks without protecting themselves from the deceptive out of view tails. EXAMPLE: Long-Term Capital Management, a hedge fund cofounded by Myron Scholes, ignored kurtosis risk to its detriment. After four successful years, this hedge fund had to be bailed out by major investment banks in the late 90s because it understated the kurtotic risk of funds that were outliers (powerful Kangaroo tail)of many financial securities underlying the fund's own trading positions. Basically, their own funds fatally tripped them into bankruptcy. Platykurtic distributions are represented by the Platypus – platypuses are predictable and harmless. Although the variance around the mean may be more flat then the leptokurtic distributions, they do NOT have many extreme outliers that can be deadly. EXAMPLE: Dermatology: if a pt has a rash and the EBP shows a Tx intervention distribution curve of k<0, then the “gold standard” tx is safe for most patients with a low risk for problems or failures.
  • This completes my presentation for artistic depiction of statistical concepts also known as “Statistical Graffiti”. There are many statistical humor sites available just by using the internet search engine which I encourage you to peruse for fun ideas. Thank you for celebrating creative nursing education with me.
  • Transcript

    • 1. Statistical Graffiti:
      A creative learning strategy
      NUR 8951
      Susan M Solomon, MSN, CNS, CPNP
      February 1, 2011
      This presentation is presented for three types of learning styles:
      VISUAL: read the note section underneath each slide .
      AUDITORY: click the “sound” icon in the upper left hand corner of each slide and listen to the presenter speak.
      PSYCHOMOTOR:each slide has a reference source to allow the learner to browse the internet
      http://www.workjoke.com/statisticians-jokes.html
    • 2. Normal Curve
      Statistics – a discipline where “truth” is only a probability
      Linear Solutions are often not the best answers
      http://davidmlane.com/hyperstat/humor.html
      http://mvpprograms.com/help/mvpstats/distributions/SkewnessKurtosis
    • 3. Texas Tech University Health Science Center senior nursing students
      Ashcraft, A, (2006). Statistical Graffiti. Journal of Nursing Education, 45(1):44-45
    • 4. Artistic depiction of Random Variables
      The bean machine, a device invented by Francis Galton, can be called the first generator of normal random variables. This machine consists of a vertical board with interleaved rows of pins. Small balls are dropped from the top and then bounce randomly left or right as they hit the pins. The balls are collected into bins at the bottom and settle down into a pattern resembling the Gaussian curve.
      http://mvpprograms.com/help/mvpstats/distributions/SkewnessKurtosis
    • 5. Artist’s depiction of linear correlation between two random variables X, Y
      Top
      (Pearson Coefficien - linear)
      Middle
      (slope)
      Down
      (nonlinear)
      Several sets of (x, y) points, with the Pearson correlation coefficient of x and y for each set. Note that the correlation reflects the noisiness and direction of a linear relationship (top row), but not the slope of that relationship (middle), nor many aspects of nonlinear relationships (bottom). N.B.: the figure in the center has a slope of 0 but in that case the correlation coefficient is undefined because the variance of Y is zero.
      http://mvpprograms.com/help/mvpstats/distributions/SkewnessKurtosis
    • 6. Univariate(“variance” is the second moment of a distribution)
      Out, liars!
      http://mvpprograms.com/help/mvpstats/distributions/SkewnessKurtosis
    • 7. Univariate(“variance” is the second moment of a distribution)
      Out, liars!
      http://mvpprograms.com/help/mvpstats/distributions/SkewnessKurtosis
    • 8. Margin of Error
      The top portion of this graphic depicts probability densities (for a binomial distribution) that show the relative likelihood that the "true" percentage is in a particular area given a reported percentage of 50%. The bottom portion of this graphic shows the margin of error, the corresponding zone of 95% confidence. In other words, one is 95% sure that the "true" percentage is in this region given a poll with the sample size shown to the right. The larger the sample is, the smaller the margin of error is.
      http://www.squidoo.com/statisticshumor
    • 9. Margin of Error
      The larger the sample is, the smaller the margin of error is.
      http://www.squidoo.com/statisticshumor
    • 10. Negatively Skewed Distribution (“skewness” is the third moment of a distribution)
      http://mvpprograms.com/help/mvpstats/distributions/SkewnessKurtosis
    • 11. Negatively Skewed Distribution (“skewness” is the third moment of a distribution)
      http://mvpprograms.com/help/mvpstats/distributions/SkewnessKurtosis
    • 12. Kurtosis(“kurtosis” is the fourth moment of a distribution)
      http://mvpprograms.com/help/mvpstats/distributions/SkewnessKurtosis
    • 13. Kurtosis(“kurtosis” is the fourth moment of a distribution)
      The distribution on the right has greater kurtosis - more peaked, less flat - but it's possible that it has about the same SD as the graph on the left, which is more spread out but is thinner at the tails. Normal distributions are likely have a skew of 0 and a kurtosis of 0.
    • 14. Kurtosis
      Higher kurtosis (leptokurtic) means more of the variance is the result of infrequent extreme deviations, as opposed to frequent modestly sized deviations (platykurtic)
    • 15. Thank you for celebrating our creative nursing education with me