Introduction to Statistics

1. Introduction to Statistics Do I have to??

2. Why we “do it” "What we really want to get at [in health care research] is not how many reports have been done, but how many people's lives are being bettered by what has been accomplished. In other words, is it being used, is it being followed, is it actually being given to patients—... What effect is it having on people—" Rep. John Porter (R-IL), retired chairmanHouse Appropriations Subcommittee on Labor, Health and Human Services (HHS), and Education

3. Is Statistics Important? • Statistics is important because we can use it to find out whether something we observe can be applied to new and different situations. • Knowing this allows us to plan for the future, and to make decisions about how to allocate our scarce resources of money, energy, and ultimately life. • We use the term generalizable: can what we know help to predict what will happen in new and different situations?

4. Why Statistics • Scientific knowledge represents the best understanding that has been produced by means of current evidence. • Research design, if used properly, strengthens the objectivity of the research. • Statistical methods allow us to compare what is actually observed to what is logically expected.

5. Why Statistics (cont’d) • Knowledge of statistics . . . • Useful in conducting investigations • Helpful the preparing and evaluating research proposals. • Vital in deciding whether claims of a researcher are valid • Keep abreast of current developments. • Effective presentations of the findings.

7. Evils of Pickle Eating • Pickles are associated with all the major diseases of the body. Eating them breeds war and Communism. They can be related to most airline tragedies. Auto accidents are caused by pickles. There exists a positive relationship between crime waves and consumption of this fruit of the cucurbit family. For example

8. Evils of Pickle Eating (cont’d) • Nearly all sick people have eaten pickles. 99.9% of all people who die from cancer have eaten pickles. • 100% of all soldiers have eaten pickles. • 96.8% of all Communist sympathizers have eaten pickles. • 99.7% of the people involved in air and auto accidents ate pickles within 14 days preceding the accident. • 93.1% of juvenile delinquents come from homes where pickles are served frequently. Evidence points to the long-term effects of pickle eating. • Of the people born in 1839 who later dined on pickles, there has been a 100% mortality.

9. Evils of Pickle Eating (cont’d) • All pickle eaters born between 1849 and 1859 have wrinkled skin, have lost most of their teeth, have brittle bones and failing eyesight-if the ills of pickle eating have not already caused their death. • Even more convincing is the report of a noted team of medical spe­cialists: rats force-fed with 20 pounds of pickles per day for 30 days de­veloped bulging abdomens. Their appetites for WHOLESOME FOOD were destroyed.

10. Evils of Pickle Eating (cont’d) • In spite of all the evidence, pickle growers and packers continue to spread their evil. More than 120,000 acres of fertile U.S. soil are devoted to growing pickles. Our per capita consumption is nearly four pounds. • Eat orchid petal soup. Practically no one has as many problems from eating orchid petal soup as they do with eating pickles. EVERETT D. EDINGTON

13. Types of Statistics • Descriptive Statistics • enumerate, organize, summarize, and categorize • graphical representation of data. • these type of statistics describes the data. • Examples • means and frequency of outcomes • charts and graphs

14. Types of Statistics • Inferential Statistics • drawing conclusions from incomplete information. • they make predictions about a larger population given a smaller sample • these are thought of as the statistical test • Examples • t-test, chi square test, ANOVA, regression

16. Variables J.D. Bramble, Ph.D. Creighton University Medical Center Med 483 -- Fall 2006

17. Types of Data • Qualitative • data fall into separate classes with no numerical relationship • sex, mortality, correct/incorrect, etc. • Quantitative • numerical data that is continuous • pharmaceutical costs, LOS, etc.

18. Parameters and Statistics • Parameters • characteristics of the population • calculating the exact population parameter is often impractical or impossible • Statistics • characteristics of the sample • represent summary measures of observed values

19. Types of Variables • Variables are symbols to which numerals or values are assigned • e.g. X and Y are variables • Dependent (Y’s), that which is predicted • Independent (X’s), that which predicts • Extraneous (Confounding or Control) • statistical models “adjust” for their influence

20. Independent variables • Independent variables are the presumed cause of the the dependent variable • The variable responsible for the change in the phenomena being observed • Nothing is for sure, so avoid the word ‘cause’ and think in terms of independent and dependent variables

21. Dependent variables • Also referred to as the outcome variable • The outcome of the changes due to the independent variables • Example: y = a + bx

22. Confounding variables • Additional variables that may effect the changes in the dependent variable attributed to the independent variables. • These variables are controlled by measuring them and statistical methods adjust for there influence. • Sometimes referred to as control variables

23. Active vs. attribute variables • Active variables are those variables under the control of the researcher • controlled experimental studies • e.g., amount of drug administered • Attribute variables can not be manipulated by the researcher • quasi-experimental studies • e.g.,sex or age of subject; blood pressure; smoker

24. The Wrong data Leads to Migraines

25. Levels of Measurement • Categorical Variables • Nominal Scale • Ordinal Scale • Continuous Variables • Interval Scale • Ratio Scale

26. Continuous Variables • Continuous variables are measured and can take on any value along the scale • quantitative variables • measured on a interval or ratio level • Examples • Age, income, number of medications

27. Categorical Variables • Categorical variables are measured as dichotomous or polytomous measures • qualitative variables • measured on a nominal or ordinal level • Examples • sex; smoking status; ownership • Categorizing continuous variables

28. Nominal measurement scale • Used for qualitative data • Two or more levels of measurement • The name of the groups does not matter • Examples • Sex (Male/Female) • Smoker (Yes/No) • Political Party (Rep, Dem, Ind)

29. Ordinal measurement scale • All the properties of nominal plus . . . • The groups are ordered or ranked • Intervals between groups are not necessarily equal • Example: • Income (low, med, high) • Disease severity • Likert scales

30. Interval measurement scale • All properties of nominal and ordinal plus . . . • A scale is used to measure the response of the study subjects • The intervals scale’s units are equal; however arbitrary (e.g., a relative scale) • Examples: • Temperature on Fahrenheit scale

31. Ratio measurement scale • All properties of the previous scales plus . . . • An absolute zero point • Can perform mathematical operations • Highest level of measurement • Examples • Income, age, height, weight

32. Summarizing Data Measures of Central Tendency and Variation

33. Mean • Arithmetic mean • the balance point sum all observations • sum all observations • divide the sum by the number of observations

34. Median • Divides the distribution into two equal parts. • Considered the most “typical” observation • Less sensitive to extreme values

35. Calculating Medians • To find the median value: q(n+1) 41, 28, 34, 36, 26, 44, 39, 32, 40, 35, 36, 33 order data in ascending order 26, 28, 32, 33, 34, 35, 36, 36, 39, 40, 41, 44 Apply the median location formula: 0.5(12+1) = 6.5 Note: this is ONLY the location of the median

36. Quantiles • Quantiles are those values that divide the distribution into n equal parts so that there is a given proportion of data below each quantile. • The median is the middle quantile. • Quartiles are also very common (25, 50, 75) • If we divided the distribution into 100 then we have percentiles.

37. Mode • The observation that occurs most frequently • Graphically it is the value of the peak of the distribution. • Frequency often may be bimodal--two modes. • If values are all the same--no mode exists

38. Single Modal

39. Bimodal Example

40. Symmetrical: The relationship between the Mean, Median, & Mode mean median mode

41. Positive Skew: The relationship between the Mean, Median, & Mode Mean Mode Median

42. Negative Skew: The relationship Between the Mean, Median, & Mode Mode Mean Median

43. Summarizing Data • Frequency distributions • Measures of central tendency • The tendency of data to center around certain numerical and ordinal values. • Three common measures: • mean, median, & mode • Measures of variation • standard deviation

44. Five Figure Summary • Median • Quartiles • Maximum • Minimum • Can be shown in a box and whisker plot

45. Which Measure? • Mean • numerical data • symmetric distribution • Median • ordinal data • skewed distribution • Mode • bimodal distribution • most popular

46. Variation • Must also report measures of variation • Measures of variability reflect the degree to which data differ from one another as well as the mean. • Together the mean and variability help describe the characteristics of the data and shows how the distributions vary from one another.

47. Example of Variation • Take the following three sets of data: 1) 10, 8, 5, 5, 2; 2) 5, 6, 6, 7, 6; 3) 6, 6, 6, 6, 6 • In all three cases the mean is 6, • the variability is a lot of variability in set 1 • No variability in set 3. • We will discuss three measures of variability: 1) the range; 2) the standard deviation; and 3) variance

48. Measures of Variation • Range • the value between the highest and the lowest observations • Range = xmax - xmin • limited usefulness since it only accounts for the extreme values • can also report the inter-quartile range (q3 – q1)

49. Standard Deviation • most widely used & preferred measure of variation. • represented by the symbol s or sd • the square root of the variance (s2) • larger values = more heterogeneous distribution • 75% of the observations lie between x-2s and x+2s • if the distribution is normal (bell shaped) • 67% = • 95% = • 99.7% =

50. Variance and Std Deviation Variance Standard Deviation