Establishing Causality (finishing up chapter 1)establishing causality means to demonstrate the outcomes effect by the treatment Vocabulary Treatment group-individuals that receive treatment  Control group-comparative individuals that offset the results of the treatment group who do not receive the treatment Anecdotal Evidence-the story an individual tells about own experienceo This information should not be used to make general statements about a group of individuals, the information if only pertinent to the individual himself/herself  Observational study- the deliberate placement of participants in to 1 of 2 groups, where there is a treatment administered and the differences between the groups are recorded o An observational study has preexisting group(groups are determined by treatment of interest records, or by characteristics that pertain to the study)o In an observational study If an outcome occurs more often in one group that another weknow that the treatment and the outcome are associatedAssociation does not equal Causation Association is less concrete than causation, unless the individuals in the study are identical we cant conclude that the treatment CAUSED the outcome.  Sometimes there is something other than the treatment that influences the outcomes of the study. This is called the confounding variable. Confounding variable: characteristic other than the treatment that causes both outcomes, in other words it is a 3rd variableControlled Experiment  In a controlled experiment each subject randomly assigned to control or treatment group The sample size must be large enough for account for variables Random assignment to group makes groups more comparable o Subjects do not need to be randomly selected from the population, just randomly assigned in to groups. Random Assignment and Bias Random assignment often involves the use of computer programs or other physical methods( such as rolling a pair of dice) to divide the population in to control and treatment groups Bias may occur when assignment is not random and the results are influenced in a particular directionPlacebo effect  Reacting after being told of receiving treatment even if thee was no actual treatment given  In other words, reacting to a preconceived notion of the effects of the treatment rather than the treatment itself  The placebo is not a biological or physical reaction it is a psychological reaction. Blind vs Double Blind Studies  A Blind study is a controlled experiment where subject groups do not know whether they are in the control or treatment group A Double blind study is when BOTH the administrators and the subjects don’t know who is in thecontrol or treatment groups These practices minimize human interference in a study and make the study more true and less susceptible to bias Scientific Abstract  A summary of the experiment o Includes the objectives of the study, the method used, the results of the experiments, and the conclusion of the study overall. CHAPTER TWO-Visualizing StatisticsA brief overview: The goal: to organize data using the method that best showcases the data visually Distribution: describes the values, frequencies and shape of the dataQuestions you should ask yourself when viewing a distribution? Are their data values that are far away from the rest of the data? (outliers) Is the data distribution symmetrical? What is its shape? Are there data values that reoccur or appear more frequently? What are the most common values?Dot Plots A dot plot is a chart that contains a dot for each data value A dot plot is best for small data sets and easily displays the data neatly and visually so outliers can be spotted easily Here is an example of a dot plot taken from Google Image:Frequency histograms  A frequency histogram is a type of bar grapho The horizontal axis represents numerical values o The vertical axis represents the frequency of data values  Frequency histograms group data in to bins, also called intervals or classeso The width of each bin dictates how much detail the viewer can see Wide bin width show less detail Narrow bin width show more detail- However too narrow a bid width can present to much detail and confusethe viewer In frequency histograms data is easy to visualize and the distribution is clear and easy to recognize.  Used to emphasize how many are in each range Here is an example of a frequency histogram from google image: Relative Frequency Histograms Relative Frequency histograms are the same as frequency histograms but instead the vertical y axis represents the relative frequencies or percents The relative frequency is calculated by dividing the frequency by the sample size Used to emphasize proportion or percent in each rangeVisual Characteristics of Distribution Shape(symmetry, how many bumps or modes) Center(which represents the typical value) Spread(data is either closer or spread out)Skewness Distributions can either be skewed right, which means most data values are low and it tails off tothe right  Or skewed left, meaning most data values are large and it tails off to the left  Symmetric distributions are chacacterized by their symmetry. If you folded a symmetric distribution in half at the center each half would be roughly a mirror image of the other halfModes Unimodal-1 mound  Bimodal-2 mounds  Multimodal-more than 2 moundsWhat is a normal distribution? Symetric Unimodal Bell shaped  A normal distribution is the ideal model, in real situations data is usually “normal” Outliers An outlier is a value that is either much higher or lower than the rest of the data o Outliers can sometimes be the result of data errorsMeasuring Center For symetric distributions the center is the typical valueo Typical value: a value that gives us an idea of what is typical of that data set  The center is not the typical value for bimodal or skewed distributions. Variability  Variability describes the spread of data values High variability:data values are spread throughout a wide range Low Variability: data values are more clustered in a smaller rangeVISUALIZING CATAGORICAL VALUES Bar Chart: comparable to a histograms but the horizontal x axis can represent categorical dataPareto chart: orders categories by frequency (works nicely for many categories CHAPTER TWO CONTINUED NEXT LECTURE*all images from Google