Read more about The beast of bias - summary of chapter 6 of Statistics by A.The second bias is ‘violation of assumptions’.An assumption: a condition that ensures that what you’re attempting to do works.If any of the assumptions are not true then the test statistic and p-value will be inaccurate and could lead us to the wrong conclusion.The main assumptions that we’ll look at are:additivity and linearitynormality of something or otherhomoscedasticity/ homogeneity of varianceindependenceAdditivity and. StatisticsChapter 6The beast of bias Bias: the summary information is at odds with the objective truth.An unbiased estimator: one estimator that yields and expected value that is the same thing it is trying to estimate.We predict an outcome variable from a model described by one or ore predictor variables and parameters that tell us about the relationship between the predictor and the outcome variable.The model will not predict the outcome perfectly, so for each observation there is some amount of error.Statistical bias enters the statistical process in three ways:things that bias the parameter estimates (including effect sizes)things that bias standard errors and confidence intervalsthings that bias test statistics and p-values An outlier: a score very different from the rest of the data.Outliers have a dramatic effect on the sum of squared error.If the sum of squared errors is biased, the associated standard error, confidence interval and test statistic will be too. Read more about The spine of statistics - summary of chapter 2 of Statistics by A.Statistical models are made up of variables and parameters.Parameters are not measured an are (usually) constants. ![]() Scientists are usually interested in finding results that apply to an entire population of entities.Populations can be very general or very narrow.Usually, scientists strive to infer things abut general populations rather than narrow ones.We collect data from a smaller subset of the population known as a sample, and use these data to infer things about the population as a whole.The bigger the sample, the more likely it is to reflect the whole population. The models need to be as accurate as possible so that the prediction we make about the real world are accurate too.The degree to which a statistical model represents the data collected is known as the fit of the model.The data we observe can be predicted from the model we choose to fit plus some amount of error. StatisticsChapter 2The spine of statisticsWhat is the spine of statistics?The spine of statistics: (an acronym for)Standard errorParametersInterval estimates (confidence intervals)Null hypotheses significance testingEstimation Testing hypotheses involves building statistical models of the phenomenon of interest.Scientists build (statistical) models of real-world processes to predict how these processes operate under certain conditions. Read more about Why is my evil lecturer forcing me to learn statisics? - summary of chapter 1 of statistics by A. ![]() ![]() ![]() (independent)Outcome variable: a variable thought to change as a function of changes in. A prediction tells us something about the hypotheses from which it derived.Falsification: the act of disproving a hypotheses or theory.Collecting data: measurement Independent and dependent variable Variables: things that can changeIndependent variable: a variable thought to be the cause of some effect.Dependent variable: a variable thought to be affected by changes in an independent variable.Predictor variable: a variable thought to predict an outcome variable. StatisticsChapter 1Why is my evil lecturer forcing me to learn statistics? Initial observation: finding something that needs explainingTo see whether an observation is true, you need to define one or more variables to measure that quantify the thing you’re trying to measure.Generating and testing theories and hypotheses A theory: an explanation or set of principles that is well substantiated by repeated testing and explains a broad phenomenon.A hypotheses: a proposed explanation for a fairly narrow phenomenon or set of observations.An informed, theory-driven attempt to explain what has been observed.A theory explains a wide set of phenomena with a small set of well-established principles.A hypotheses typically seeks to explain a narrower phenomenon and is, as yet, untested.Both theories and hypotheses exist in the conceptual domain, and you cannot observe them directly.To test a hypotheses, we need to operationalize our hypotheses in a way that enables us to collect and analyse data that have a bearing on the hypotheses.Predictions emerge from a hypotheses.
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