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# Ch 1 Data Collection Section 1 & 2 MA155-70

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This 8 page Class Notes was uploaded by Alyssa Notetaker on Sunday September 13, 2015. The Class Notes belongs to MA155-70 at Southeast Missouri State University taught by Yanping Xia in Summer 2015. Since its upload, it has received 42 views. For similar materials see Statistical Reasoning in Mathematics (M) at Southeast Missouri State University.

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Date Created: 09/13/15

Chapter 1 Data Collection Sectionl Introduction to the Practice of Statistics Objective 1 Define Statistics and Statistical Thinking Statistics is the science of collecting organizing summarizing and analyzing information to draw conclusions or answer questions In addition statistics is about providing a measure of confidence in any conclusions Objective 2 Explain the Process of Statistics 0 The entire group of individuals to be studied is called the population An individual is a person or object that is a member of the population being studied A sample is a subset of the population that is being studied 0 Descriptive statistics consist of organizing and summarizing data Descriptive statistics describe data through numerical summaries tables and graphs 0 A statistic is a numerical summary based on a sample EXAMPLE Parameter versus Statistic Descriptive statistics consist of organizing and summarizing data Descriptive statistics describe data through numerical summaries tables and graphs A statistic is a numerical summary based on a sample Example 1 A college dean is interested in learning about the average age of faculty Identify the basic terms in this situation 1 The population is all faculty members at the college The average age of all faculty members is the parameter 2 A sample is any subset of that population for example we might select 10 faculty members and determine their age The average age of selected 10 faculty members is a statistic The Precess ef Statistics 1 Meatt y the research ehjecttye h researcher l nust determine the questients he er she wants answeredThe questiens l nust be detailed se that it identi ties the pepulatien that is te be studied and the questiens that are te be answered Cehect the state heestemr te shatter the qeesttehs pesed it i Gaining access te an entire pepulatien is eften difficult and eapensiye When cenducting re search we typically leek at a sample The cellectienef data step is yital te the statistical precess because if the data are net celleeted cerrectly the cen clusiens drasyn are lneayrli rigless De net eyerleek the inrpertance ef appre priate datacellectien precesses We discuss this step in detail in Sectiens 12 threugl l 16 Describe the date Obtaining descriptiye statistics ll3W5 the researeher te ebtain an eyeryiety ef the data and can preyide insight as te the type at sta tistical nietheds the researcher sheuld use We discuss this step in detail in Chapters 2 threugh 4 Petfetht fet ehce Apply the apprepriate techniques te eatend the results ebtained train the sample te the pepulatien and repert a leyel ef reliability in the results We discuss techniques fer lneasuring reliability in Chapters 5 threugl l 8 and inferential techniques in Chapters 9 threugh 15 Objective 3 Distinguish between Qualitative and Quantitative Variables Subdividing Variables Further Key Point Variables vary Consider the variable height If all individuals had the same height then obtaining the height of one individual would be sufficient in knowing the heights of all individuals Of course this is not the case As researchers we wish to identify the factors that in uence variability Qualitative or Categorical variables allow for classification of individuals based on some attribute or characteristic Quantitative variables provide numerical measures of individuals Arithmetic operations such as addition and subtraction can be performed on the values of the quantitative variable and provide meaningful results Objective 4 Distinguish between Discrete and Continuous Variables A discrete variable is a quantitative variable that has either a finite number of possible values or a countable number of possible values The term countable means the values result from counting such as O 1 2 3 and so on A continuous variable is a quantitative variable that has an infinite number of possible values it can take on and can be measured to any desired level of accuracy K u all it at 39 Qua n l i l a tiw rilalhlus a rialilu n ti u n u 25 13a ria bl es va ri a h c The list of observations a variable assumes is called data While gender is a variable the observations male or female are data Qualitative data are observations corresponding to a qualitative variable Quantitative data are observations corresponding to a quantitative variable Discrete data are observations corresponding to a discrete variable Continuous data are observations corresponding to a continuous variable Objective 5 Determine the Level of Measurement of a Variable A variable is at the nominal level of measurement if the values of the variable name label or categorize In addition the naming scheme does not allow for the values of the variable to be arranged in a ranked or specific order A variable is at the ordinal level of measurement if it has the properties of the nominal level of measurement and the naming scheme allows for the values of the variable to be arranged in a ranked or specific order A variable is at the interval level of measurement if it has the properties of the ordinal level of measurement and the differences in the values of the variable have meaning A value of zero in the interval level of measurement does not mean the absence of the quantity Arithmetic operations such as addition and subtraction can be performed on values of the variable 0 A variable is at the ratio level of measurement if it has the properties of the interval level of measurement and the ratios of the values of the variable have meaning A value of zero in the ratio level of measurement means the absence of the quantity Arithmetic operations such as multiplication and division can be performed on the values of the variable Levels of Measurement Nominal categorical names Ordinal nominal plus can be ranked order Interval ordinal plus intervals are consistent Ratio interval plus ratios are consistent true zero 0 The ordinal level of measurement provides a ranking system but it does not allow us to determine precise differences between measurements 0 If intervals are meaningful but ratios are not we say that the data are at the interval level of measurement 0 When both intervals and ratios are meaningful we say that data are at the ratio level of measurement Section 12 Observational Studies VS Designed Experiments Objective 1 Distinguish between an Observational Study and an Experiment Observational Study Observes individuals and measures variables of interest but does not attempt to in uence the responses Describes some group or situation Observational studies are valuable for discovering trends and possible relationships However it is not possible for observational studies to demonstrate a causal relationship Well designed studies can provide supporting evidence for the researcher s beliefs Definitions A variable is any item or quantity that can vary or take on different values The variables of interest in a statistical study are the items or quantities that the study seeks to measure When cause and effect may be involved an explanatory variable is a variable that may explain or cause the effect while a response variable is a variable that responds to change in the explanatory variable Confounding in a study occurs when the effects of two or more explanatory variables are not separated Therefore any relation that may exist between an explanatory variable and the response variable may be due to some other variable or variables not accounted for in the study A lurking variable is an explanatory variable that was not considered in a study but that affect the value of the response variable in the study In addition lurking variables are typically related to any explanatory variables considered in the study Objective 2 Explain the Various Types of Observational Studies Cross sectional Studies Observational studies that collect information about individuals at a specific point in time or over a very short period of time Case control Studies These studies are retrospective meaning that they require individuals to look back in time or require the researcher to look at existing records In case control studies individuals who have certain characteristics are matched with those that do not Cohort Studies A cohort study first identifies a group of individuals to participate in the study the cohort The cohort is then observed over a long period of time Over this time period characteristics about the individuals are recorded Because the data is collected over time cohort studies are prospective Observational Study Sample Survey A sample survey selects a sample of people from a population and interviews them to collect data A sample survey is a type of observational study crossseetional study A census is a survey that attempts to count the number of people in the population and to measure certain characteristics about them

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