Biostats I Midterm
CRME 240
Terms
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- Weighted Arithmetic Mean
- The arithmetic mean after assigning different weights to the measurements.
- Central Limit Theorem
- The theorem that states that the sum of a large number of independent and identically-distributed random variables will be approximately normally distributed (i.e., following a Gaussian distribution, or bell-shaped curve) if the random variables have a finite variance.
- Tukey Trimean (f)
- xbar T = (Lower Hinge + 2*Median + Upper Hinge)/4
- Standard Normal Deviate
- Synonym: z Score
- Extreme Outlier
- A number that is more than 3 times the H-spread above the upper hinge or below the lower hinge.
- Relative Standing
- Assessing the way in which numbers in a distribution are ordered, one to another (ie percentiles, quantiles, deciles).
- Arithmetic Mean (f)
- xbar = sigma x/N
- Residual
- The difference between a number and the value of the number that is predicted by some mathematical model. (Subtract the dataum from the expected value and plot the residuals, this may make a relationship pop out.)
- Interpolation
- The use of a formula to estimate an intermediate data value.
- Quadratic Mean/RMS (f)
- RMS = square root of ((sigma (x squared))/N)
- Stem-and-Leaf Diagram
- A visual summary of your data. This diagram provides a partial sorting of the data and allows you to detect the distributional pattern of the data.
- Revelation
- Your job as data analyst is to decipher the information carried by your data, not simply to use some method that others have used.
- One Sample t test
- A test that is used when we want to know whether our sample comes from a particular population. It is used when the standard deviation of the population is unknown or N < 30.
- Five-line Summary
- Five stems per interval (star, t, f, s, dot)
- Geometric mean
- xbar g = Nth root of (pi x)
- Pythagorean Means
- Arithmetic, Harmonic, and Geometric Means. For a given data set, the harmonic mean is always the least of the three, while the arithmetic mean is always the greatest of the three and the geometric mean is always in between.
- Standard Error
- The estimated standard deviation of the error in that method of estimation or estimation. It therefore estimates the standard deviation of the sample mean based on the population. Specifically, it estimates the standard deviation of the difference between the measured or estimated values and the true values. Note that while this definition makes no reference to a normal distribution, many uses of this quantity implicitly assume such a distribution.
- Percentile Rank
- The percentage of numbers that falls below a particular number (socre).
- Degrees of Freedom
- The number of numbers in a sample that have no restrictions for providing an unbiased estimate of a parameter.
- Ordinal Scale
- A measurement scale that assigns values to objects based on their ranking with respect to one another. (ie the pain scale)
- Heterogeneous Variance
- The assumption that the variance within each of the populations is not equal.
- Extreme Outlier (f)
- O = 4U-3L
- Satterthwaite Adjustment
- An adjustment to the calculation of the t score and degrees of freedom when variances are unequal.
- Geometric Mean
- Derived from averaging the sides of rectangles into squares, or boxes into cubes, ect. Will not work if there are negatives or zero's in the data.
- Arithmetic Mean
- The sum of all the members of the list divided by the number of items in the list.
- Tukey Trimean
- A mean based on the lower hinge, median, and upper hinge.
- Nominal Scale
- This scale is really a list of categories to which objects can be classified. No quantitative information is conveyed and no ordering of the items is implied. "Numbers = Names"
- Ratio Scale
- These scales are like interval scales except they have true zero points. (ie a ruler)
- Outlier (f)
- * = 2.5U-1.5U
- Z Score
- Tells you how far a number is above or below the mean in terms of standard deviations. It is dimentionless/unitless.
- T Score (f)
- T = Mean + DS(z), the mean and SD are from a reference distribution
- Distribution of t
- A probability distribution that arises in the problem of estimating the mean of a normally distributed population when the sample size is small.
- Range (f)
- R = Highest - Lowest
- Spread, variation
- How data are arranged around a central tendency. Examples include range, standard deviation, and percentiles.
- The 4 R's of EDA
- Resistance, Re-expression, Residuals, Revelation
- Student's t-Test for Related Samples
- Use this test to compare two small sets of quantitative data when samples are not collected independently of one another, or paired, so that each member of one sample has a unique relationship with a particular member of the other sample (e.g., the same people measured before and after an intervention, or IQ test scores of a husband and wife).
- Resistance
- A statistic is one that is not highly influenced by outlying data.
- Upper and Lower Hinges
- Median of the upper or lower half of the data set.
- T Score (Transformed Score)
- A score utilized in setting up norms for standardized tests; obtained by linearly transforming normalized standard scores.
- Location, Central tendency
- Measures of the location of the middle or the center of a distribution. Examples are mean, median, and mode.
- Median
- The middle number in a given sequence of numbers, taken as the average of the two middle numbers when the sequence has an even number of numbers: 4 is the median of 1, 3, 4, 8, 9.
- Standard Deviation
- A measure of the dispersion of a collection of values. It is defined as the root-mean-square deviation of the values from their mean, or as the square root of the variance. The reason the variance needs to be square is that if they were just summed the value would be zero idicating no variability.
- Pooled Variance
- An estimate of a population's variance obtained by combining or pooling data from two or more samples.
- Sampling Distribution for the Difference of two Sample Means
- The distribution that would result if we repeated the following three steps over and over again: (1) sample n1 scores from Population 1, and n2 scores from Population 2, (2) compute the means of the two samples (M1 and M2), (3) compute the difference between means M1 - M2. Standard Error for the Difference of Means - A statistical index of the probability that a difference between two sample means is greater than zero. Or a statistical index decribing the sampling distribution for the difference of two sample means.
- One-line Summary
- One stem per interval
- Alpha Level
- The P-value that we as researchers decide to accept before we will be confident enough to release a finding. This is our predetermined acceptance level.
- Depth of the Hinge (f)
- d(H) = (d(M)+1)/2
- Binary Variable
- A variable that categorizes data into two groups, such as bankrupt versus solvent or energy versus non-energy company.
- Coded Table
- A table produced by substituting symbols that denote if the data is in a particular spread (ie H-spread or outlier) to look for patterns.
- Maxim number of lines in a S&L Diagram (f)
- L = 10 * log10 (N)
- Exploratory Data Analysis
- An approach to analyzing data for the purpose of formulating hypotheses worth testing, complementing the tools of conventional statistics for testing hypotheses. It was so named by John Tukey., Using graphs and numerical summaries to describe variables in a data set and their relationship
- Next Power of Ten for S&L Diagram (f)
- I = R / L
- Outlier
- A number that is more than 1.5 times the H-spread above the upper hinge or below the lower hinge.
- Quadratic Mean (RMS)
- A statistical measure of the magnitude of a varying quantity. It is used to deal with outliers, but primarily when there are positive and negative numbers and zero is a reference point. e.g., sinusoids.
- Box Plot
- Depicts groups of numerical data through their five-number summaries (the smallest observation, lower quartile (Q1), median (Q2), upper quartile (Q3), and largest observation). It may also indicate which observations, if any, might be considered outliers. Invented by Tukey.
- Two-tail test
- A test where the portion of the distribution designated for rejection of the null hypothesis (the alpha level) is contained with in two tails of the distribution.
- One Sample z test
- A test that is used when we want to know whether our sample comes from a particular population. It is used when the standard deviation of the population is known and N > 30.
- Two-line Summary
- Two stems per interval (star, dot)
- Normal Distribution
- A theoretical frequency distribution for a set of variable data, usually represented by a bell-shaped curve symmetrical about the mean. Also called Gaussian distribution.
- Depth of a Number
- How far a number is from one of the two ends of the sorted data
- Depth of the Median (f)
- d(M) = (n+1)/2
- Percentile Point
- A number (score) below which a given percentage of other numbers falls. Depth of this point is simply p*N (p(N) = .2*40 to find the 20th percentile point of 40 numbers). If there are multiple scores on the point the point must be interpolated [x = LRL + ((pN-Sb)/Sw))] (Sb scores below, Sw scores within, LRL lower real limit of interval)
- Sampling Distribution
- The probability distribution, under repeated sampling of the population, of a given statistic (a numerical quantity calculated from the data values in a sample).
- Bin Width
- Ranges of data values used in a histogram.
- Harmonic Mean (f)
- xbar h = N/(singma (1/x))
- Interval Scale
- A scale where one unit on the scale represents the same magnitude on the trait or characteristic being measured across the whole range of the scale. There is no absolute zero. (ie a thermometer)
- Hinge Spread
- Describes the range of that half of the data which falls in the middle of the distribution.
- Homogeneous Variance
- The assumption that the variance within each of the populations is equal.
- Z Score (f)
- z = (x-xbar)/s [This conversion process is called standardizing or normalizing.]
- Trimmed Mean
- The arithmetic mean after eliminating a given percentage of high and low measurements.
- One-tail test
- A test where the portion of the distribution designated for rejection of the null hypothesis (the alpha level) is contained with in one tail of the distribution.
- Frequency Histogram & Polygon
- A representation of a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies.
- Glyph
- An image that communicates a message without the use of words.
- Non-Parametric (Rank Sum) Tests
- A test that does not assume a normal distribution (ie can use either normal or non-normal distributions) and is relatively insensitive to outliers.
- Confidence Interval
- It gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.
- Student's t-Test for Independent Samples
- Use this test to compare two small sets of quantitative data when samples are collected independently of one another. When one randomly takes replicate measurements from a population he/she is collecting an independent sample.
- Mann-Whitney U Test
- A non-parametric test for assessing whether two samples of observations come from the same distribution. The null hypothesis is that the two samples are drawn from a single population, and therefore that their probability distributions are equal. It requires the two samples to be independent, and the observations to be ordinal or continuous measurements, i.e. one can at least say, of any two observations, which is the greater.
- Side-by-side Stem-and-leaf Diagram
- Stem-and-leaf diagram used to compare two data sets.
- Letter Value Display
- A method of displaying simple statistical parameters including hinges, the statistical median, and upper and lower values.
- Harmonic Mean
- Is appropriate for situations when the average of rates is desired. It is taking the inverse of all of the numbers, computing the arithmetic mean, and then taking the inverse of the mean. Will not work if there are 0's in the data. Use only if outliers are on the high side.
- Hypothesis Testing
- A method of making statistical decisions using experimental data.
- Re-expression
- The application of any type of non linear transformation to look for relationships that may not be seen at first.
- Weighted Mean (f)
- xbar w - sigma wx/ sigma w
- Null Hypothesis (Ho)
- A hypothesis (scenario) set up to be nullified, refuted, or rejected ("disproved" statistically) in order to support an alternative hypothesis.