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# Introduction to Statistics

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Introduction to Statistics
Do I have to??

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 chairman House Appropriations Subcommittee on Labor, Health and Human Services (HHS), and Education

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?

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.

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.

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

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.

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.

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

Types of Statistics Descriptive Statistics Examples
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

Types of Statistics Inferential Statistics Examples
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

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

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

Parameters and Statistics
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

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

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

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

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

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

The Wrong data Leads to Migraines

Levels of Measurement Categorical Variables Continuous Variables
Nominal Scale Ordinal Scale Continuous Variables Interval Scale Ratio Scale

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

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

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)

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

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

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

Measures of Central Tendency and Variation
Summarizing Data Measures of Central Tendency and Variation The mean is our usual concept of an overall average - add up the items and divide them by the number of sharers (100 candy bars collected for five kids next Halloween will yield 20 for each in a just world). The median, a different measure of central tendency, is the half-way point. If I line up five kids by height, the median child is shorter than two and taller than the other two (who might have trouble getting their mean share of the candy). A politician in power might say with pride, "The mean income of our citizens is \$15,000 per year." The leader of the opposition might retort, "But half our citizens make less than \$10,000 per year." Both are right, but neither cites a statistic with impassive objectivity. The first invokes a mean, the second a median.

Mean Arithmetic mean the balance point sum all observations
divide the sum by the number of observations Means are higher than medians in such cases because one millionaire may outweigh hundreds of poor people in setting a mean; but he can balance only one mendicant in calculating a median

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

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

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.

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

Single Modal

Bimodal Example

Symmetrical: The relationship between the Mean, Median, & Mode

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

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

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

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

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

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.

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

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)

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% =

Variance and Std Deviation
Standard Deviation

Example Using data on the sexual activity of male and female subjects can be found in Chatterjee, Handcock, and Simonoff (1995) A casebook for a first course in statistics. New York: Wiley. They provide data on the reported number of sexual partners for 1682 females and 1850 males. The dependent variable is the number of reported partners.

Descriptive Statistics
Male Female (n=1850) (n=1685) Mean Median Mode

Using Excel When Syntax in Known
Write them right into the spreadsheet Be sure to start with an equal sign Use your mouse to highlight data to analyze

Using Excel When Syntax in Unknown
Use the wizard and follow in instructions. All wizards work about the same way. Select the fx button to select appropriate test Select category and then desired test

Follow the Wizard Either highlight the array or just write it in
These icons reduce/enlarge the Wizard box

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