BIOSTATS - chapter 8

• Variable - a measure of a single characteristic that can vary
• Variation - is seen not only in the presence or absence of disease but also in the stages or extent of disease
• 2 MEASUREMENT OF ERROR

  • Systemic error - type of variation that can distort data systematically in one direction

  • Can introduce bias

  • Random error - type of variation that arerandom

  • Does not introduce bias
• Biological difference - difference in genes, nutrition, race, environmental exposures, sex, age
• STATISTICS AND VARIABLES

  • Quantitative data - characterized by using a defined continuous measurement of scale
  • Qualitative data - described by features, generally in words rather than numbers
• TYPES OF VARIABLES

  • nominal variable
  • dichotomous (binary) variable
  • ordinal (ranked) variable
  • continuous (dimensional) variable
  • ratio variable
• nominal variables - naming or categoric variables that are not based on measurement scales or rank order
• dichotomous (binary) variables - "cut into two" variables with only two levels
• ordinal ( ranked ) variables - data can be characterized in terms of three or more qualitative values that have a clearty implied direction from better to worse
• continuous (dimensional ) variables - data are measured on continuous measurement scales.
• • ratio variables - if a continuous scate has a true 0 point
• Dichotomous, nominal and ordinal variables are referred as Discrete Variables because the numbers of possible values they can take are countable
• Risk and Proportions - two important types of measurement in medicine, share some characteristics of a discrete variable and some characteristics of a continuous variable
• Unit of observation - is the person or thing from which the data originated.
• frequency distribution - shows the values of the variable along one axis and the frequency of the value along the other axis.
• Types of frequency distribution

  • Real frequency distribution
  • theoretical frequency distribution
• Real frequency distribution - types of frequency distribution that are those obtained from actual data or a sample
• Theoretical frequency distribution - type of frequency distribution that are calculated using assumptions about the population from which the sample was obtained.
• normal distribution - also called as "Gaussian Distribution"

  • described after Johann karl Gauss
  • looks something like a bell shape seen from the side
• Parameters of a Frequency Distribution

  • measures of central tendency
  • Measures of dispersion
• measures of central tendency

  • mode - most commonly observed value
  • median - the middle observation when data have been arranged in order from the lowest value to the highest value.
  • Mean - is the average value, or the sum (S) of all the observed values (xi) divided by the total number of observations (N)
• variance - the fundamental measure of dispersion
• Standard deviation - the square root of the variance
• Skewness - A horizontal stretching of a frequency distribution to one side or the other, so that one tail of observations is longer and has more observations than the other tail

  Kurtosis - is characterized by a vertical stretching or flattening of the frequency distribution
• Hypotheses testing of one mean

  • deals only with one sample or group
• Hypotheses testing of two mean

  • deals only with two sample or group
• T-test

  • used to compare the means of a continuous varuable in two research sample
• Two sample t-test

  • used if the two research sample come from two diffetent group
• Paired t-test

  • used if the two research sample come from the same diffetent group
• Central limit theorem

  • the entire data will approximate a normal distribution
  • the higher the sample the closer to a normal distribution
• Population variance is known

  • z test is used
  • sampling distribution of mean is normally distributed
• Population variance is unknown

  • t test is used
  • sampling distribution of mean is t-distributed
• Steps in hypothesis testing

  1. state the null and alternative hypothesis
  2. state the level of significance
  3. select test statistic
  4. determine critical region
  5. compute test statistic
  6. statisctical decision
  7. draw conclusion