HS 2801 Notes (Week 10) - Descriptive & Comparative Statistics PDF

Week 10 Descriptive and Comparative statistics - Biostatistics: is the science of analyzing data and interpreting the results so that they can be applied to solving problems related to biology, health, or related fields - Univariate analysis: describes one variable in a data set...

Week 10 Descriptive and Comparative statistics - Biostatistics: is the science of analyzing data and interpreting the results so that they can be applied to solving problems related to biology, health, or related fields - Univariate analysis: describes one variable in a data set using simple statistics like counts (frequencies), proportions, and averages - Bivariable analysis: uses rate ratios, odds ratios, and other comparative statistical tests to examine the associations between two variables (mostly exposure and outcome) - Multivariable analysis: encompasses statistical tests such as multiple regression models that examine the relationships among three or more variables What is a variable - Any quantity that varies from one entity to another (sometime within an entity over time) - Any attribute, phenomenon, or event that can have different values - To describes characteristic of a person, place, thing, or idea - We measure variables when an experiment is carried out or an observation is made Types of variables - Nominal - No intrinsic or logical order or value - University programs - Countries - Types of fruits, can assign them different numbers but they do not have any other numeric properties - Ordinal - Intrinsic value but with no clear or equal differences between levels - a set of ordered categories - Primary vs. secondary vs. university education - Mild vs. moderate vs. severe pain - Rating scales (assigning numbers) - Legitimate to say: 1 ≠ 2; 5 > 4 > 3 > 2 > 1 - Can not say 4 is not 2 times larger than 2 - (4-3)=(3-2)=(2-1) - Displaying nominal (categorical) or ordinal (ranked) data - Can use pie chart or bar chart - Quantitative - Any positive real number, depends on the nature of the variable can be expressed in decimals  - Meaningful numeric scales - Age, blood pressure, # of friends, temperature - Assigned numbers have total mathematical meaning - Continuous - Can take any value - Can be plotted as line - Blood pressure or temperature - Discrete - Can take finite or limited number of values - Can be plotted as lines - Age, number of drinks - Interval vs ratio - Ratio variable - Ratio is meaningful - Zero means absence of characteristic - 0m = no height - Blood pressure, age, income, weight - Interval variable - Difference is meaningful - No natural zero - A value of 0 does not indicate total absence of the characteristic Mean: A sample mean is calculated by adding up all the values for a particular variable and dividing that sum by the total number of individuals with a value for the variable=arithmetic average Median: list number in ascending or descending order, gives data into 2 parts, find the number that's in the middle. If the middle has 2 numbers, you add them and divide by 2. Mode: most frequently occurring value for particular variable in data set Measure of variability (spread, dispersion) - The range for variable between minimum (lowest) and the maximum (highest) - Quartiles mark the three value that divide a data set into 4 equal part - Interquartile range (IQR) = capturs the middle 50% of values for numeric variable - from Q3-Q1 - Q2 is median - Minimum value = Q1 - IQR(1.5) - Maximum value = Q3 + IQR(1.5) Variance - extent of deviation from the average value of that variable in the data set - Calculated by adding together the squares of the differences between each observation and the sample mean (µ) and then dividing by the total number of observation - Standard deviation: square root of variance - Standard error: standard deviation/square root of n Confidence intervals (CI) - Provide information about the expected value of a measure in a source population based on the measured value in a study population - Larger sample will yield a narrower confidence interval - A 95% confidence interval is usually reported for statistical estimates, which means that 5% of the time the confidence interval is expected to miss capturing the true value of a measure in the source population - mean systolic blood pressure of a sample is 120 mmHg; 95%CI: 110-130 - We are 95% confident that the real average (in the source population) is between 110-130; 5% chance that the true value of mean is either larger than 130 or smaller than 110 Comparative statistics - Comparing main factors between exposed and unexposed in cohort studies - Average age of exposed=Average age of unexposed  - % male in exposed=% male in unexposed - Testing if randomization was effective in experimental studies - Comparing the outcome status - We can NOT just look at the calculated values (these are estimates from samples, subject to random sampling error) Inferential Statistics - Techniques that use statistics from a random sample of a population to make evidence based assumptions (inference) about the values of parameters in the population as a whole - Decision about parameters via information obtained from a sample is via hypothesis testing Hypothesis testing - To test an explicit statement or a ‘hypothesis’ about a population parameter - The null hypothesis (H0 ): there is no difference between the two or more values being compared - The alternative hypothesis (Ha ): there is a difference between the two or more populations being compared, there is association between exposure and outcome 1. Take a random sample from the population of interest 2. Set up two competing hypotheses (based on research question) - Null hypothesis; no effect, no difference between sample and original population - Alternate hypothesis: there is an effect, difference in the two populations 3. Use sample statistics (mean, frequency) to decide whether to support or reject the null a. By calculation of a test statistics 4. Determine if null hypothesis is really, trye, what the observed sample statistics will be Idea of probability p.value - Introduced by Fisher to determine whether the observed sample supports the null - Between 0.1 and 0.9: no reason to suspect null is false, no association -