Math 1040, Chapter 1
Math 1040, Chapter 1 MATH 1040
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This 4 page Class Notes was uploaded by Linda Davila on Thursday January 21, 2016. The Class Notes belongs to MATH 1040 at Southern Utah University taught by Derek Hein in Winter 2016. Since its upload, it has received 18 views. For similar materials see Statistics in Mathematics (M) at Southern Utah University.
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If Linda isn't already a tutor, they should be. Haven't had any of this stuff explained to me as clearly as this was. I appreciate the help!
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Date Created: 01/21/16
Math 1014 Statistics Chapter One Branches of Statistics o Descriptive Gathers, sorts, summarizes, and displays the data o Inferential Involves using descriptive statistics to estimate population parameters Section 1.2 Data Classification o Types of Data Qualitative consist of labels or descriptions of traits. Quantitative consist of counts or measurements. Continuous quantitative data that can take on any value in a given interval and are usually measurements. Discrete quantitative data that can take on only particular values and are usually counts. o Ex. 1, 2, 3 not 1.5, 2.5, 3.5 (when using years people were born for example someone cannot be born year 1997.5 but can be born the year 1997) Neither data that is qualitative but is not numerical. o Levels or Measurement Nominal data at the nominal level of measurement are qualitative data consisting of labels or names. Ordinal data at this level or measurement are qualitative data that can be arranged in a meaningful order, but calculations do not make sense. Interval level data is quantitative that can be arranged in a meaningful order. Differences between data entries are meaningful. Calculations such as addition and subtraction make sense. Zero is a possibility and is just another number on the scale for instance. Ratio level measurements are quantitative data that can be ordered in a meaningful matter. Differences between data entries are meaningful. Calculations such as addition, subtraction, multiplication and division make sense. Zero is not possible, in this case zero is the absence or something. Counts tend to be at this level Ex. Finishing times of a race: Quantitative (because it is dealing with numbers), Continuous (because any value is possible), and Ratio (because all types of calculations are possible and make sense) Section 1.3 The Process of a Statistics Study o Conducting a Statistics Study Determine the design of the study A. State the questions B. Determine the population and variables C. Determine the sampling method Collect data Organize data Analyze the data to answer the question o Statistics study Observational study data that already exists. Conclusions can be obtained just by observing. Experimental study experiment generates data to help identify cause and effect relationships. o Observational Studies Representative sample A representative sample has the same relevant characteristics as the population and does not favor one group. A random sample is one where each member has an equal chance of being selected. o Sampling methods Simple random sampling each possible sample of the same size has the same chance of being selected. To calculate on a calculator: o randInt(#,#)= Stratified sample each stratum within your sample get sampled from. Needs a little from each chunk Cluster sampling needs to collects all data from a few chunks. Makes most sense when geographically convenient Systematic sample takes every (regularly chosen) subject. Must be determined with a random starting point. Ex. At a factory with random inspection on the lines, one way choose a random starting point to inspect the product; however, after that they much chose a certain number for every other time they will inspect and will check only that certain time, like the inspector will check the product every 15 time and will stick to that system. Convenient sampling not a reliable way of sampling and collecting data. We must never use this type of sampling! Always resorts in a biased sample! o Types of Observational Studies Cross sectional study data are collected at a single point in time. Think of it as a snap shot. Longitudinal study data are gathered by following a particular group over a period of time. Metaanalysis a study that compiles information from previous studies. Case study looks at multiple variables that affect a single event. o Experiments Treatment some condition that is applied to a group of subjects in an experiment. Subjects people or things being studied in an experiment. Participants people that are being studied. Response variable the variable in an experiment that responds to the treatment. Explanatory variable a variable in an experiment that causes the change in the response variable. Confounding variables these are factors other than the treatment that cause an effect on the subjects of an experiment. Control group a group of subjects to which no treatment is applied in an experiment. Or in most cases, this is the group that is given the placebo (see below). Treatment group subjects to which researchers apply treatment. Principles of experimental design Randomize the control and treatment group Control for outside effects on the response variable Replicate the experiment a significant number of times to see meaningful patterns Placebo Effect this is a response to the power of suggestion, rather than the treatment itself, by participants of an experiment. Placebo a substance that appears identical to the actual treatment but contains no intrinsic beneficial elements. Single Blind Experiment when subjects of an experiment aren’t aware which group they were placed in. Double Blind Experiment when neither the subjects nor the people interacting with them are aware of which group is which. Institutional Review Board Institutional Review Board is a group of people who review the design of a study. Informed consent involves completely disclosing to participants the goals. Section 1.4 How to Critique a Published Study o Consider the Setup Bias favoring of a certain outcome in a study. Sampling bias occurs when the sample chosen does not accurately represent the population being studied. Drop outs participants who begin the study but fail to complete. Processing errors errors that occur simply from the data being processed, such as typos when entering the data into a computer. No adherents participants who remain in the study until the end but stray from the directions they were given. Researcher bias occurs when a researcher influences the result of a study. Response bias occurs when a researcher’s behavior causes a participant to alter their response or give an inaccurate response. Participation bias when there is a problem with either the participant or lack thereof of those chosen for the study. Non Response bias when there is a lack of participation in a selfselected sample from certain segments of a population. Ex. When students are asked to fill out a teacher evaluation and some students don’t fill out the paper.
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