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Fundamentals of Biostatistics

The Five Basic Words. Population All the members of a group about which you want to draw a conclusionSample The part of the population selected for analysisParameter A numerical measure that describes a characteristic of a populationStatistic A numerical measure that describes a character

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Fundamentals of Biostatistics

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    1. Fundamentals of Biostatistics Luis Maldonado, MD, MPH

    2. The Five Basic Words Population – All the members of a group about which you want to draw a conclusion Sample – The part of the population selected for analysis Parameter – A numerical measure that describes a characteristic of a population Statistic – A numerical measure that describes a characteristic of a sample Variable – A characteristic of an item or an individual that will be analyzed using statistics

    3. The Branches of Biostatistics Descriptive statistics - focuses on collecting, summarizing, and presenting a set of data Inferential statistics – focuses on analyzing sample data to draw conclusions about the population

    4. Descriptive Statistics Measures of Central Tendency The Mean The Median The Mode

    5. The Mean Easily calculated by adding all the observed data values and dividing by the total sample size of the group If an individual observation = x And the total number of observations = n Mean = (x1+x2+…+xn) divided by n

    6. The Mean Also known as the ‘arithmetic average’ The one main weakness of the mean: individual extreme values (also known as ‘outliers’) can distort its ability to represent the typical value of a variable

    7. The Median The middle value in a set of data values for a variable when the data values have been ordered from lowest to highest When the number of values is even the median is calculated by taking the mean of the values closest to the middle

    8. The Median To calculate the median: add 1 to the number of data values and divide that by 2 Example: if there are 7 sample values, divide (7+1) by 2 to get 4: the median is the 4th ranked value when all values are ranked from lowest to highest If there is an even number of values; lets say 8, divide (8+1) by 2 to get 4.5; the median is the mean of the 4th and 5th ranked values when all values are ranked from lowest to highest

    9. The Median Extreme values do NOT affect the median, making the median a good alternative to the mean to measure central tendencies when such values occur

    10. The Mode The value (or values) in a set of data values for a variable that appears most frequently Similar to the median, extreme values do not affect the mode, however, the mode can vary much more from sample to sample than the median or mean

    11. Shape of Distributions

    12. Skews Skewness is a parameter that describes asymmetry in a distribution Symmetrical shape or no skew indicates a set of data values in which the mean, median, and mode are equal Left-skewed (also known as negative skew) indicates a set of data values in which the mean is less than the median Right-skewed (also known as positive skew) indicates a set of data values in which the mean is greater than the median

    13. Measure of Variation Variation is the amount of dispersion, or ‘spread’ in the data The Range The Variance The Standard Deviation

    14. The Range The range is the difference between the largest and smallest data values in a set of values for a variable Range = Largest value – Smallest value Represents the largest possible difference between any 2 values in a set of data values for a variable

    15. The Range Is not a stable estimate; as sample size increases, the range also tends to increase Is not amenable to statistical testing Since the range is derived from the most extreme values, a sample may have a large range even when the majority of observations are fairly close in value

    16. The Variance and the Standard Deviation Provide a summary of the spread or dispersion of individual observations around the mean The Standard Deviation is equal to the square root of the Variance

    17. Variance First, calculate the difference between each observation (x) and mean (?) Then, the differences are squared (x-?)2, so that negative and positive deviations will not cancel each other out The resultant quantities are added together (S[x-?]2) And the sum is divided by the total number of observations minus 1 (S[x-?]2)/(n-1)

    18. Standard Deviation For sets of data values that are approximately normal in distribution, 68% of the individual values will lie within one standard deviation of the mean, 95% will fall within two standard deviations, and 99% are within three standard deviations ± 1 standard deviations = 68% ± 2 standard deviations = 95% ± 3 standard deviations = 99%

    19. Standard Deviations

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