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data

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observations (such as measurements, genders, survey responses) that have been collected

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statistics

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a collection of methods for planning experiments, obtaining data, and then then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data.

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population

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the complete collection of all elements (scores, people, measurements, and so on) to be studied.

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census

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the collection of data from every member of the population

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sample

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a sub-collection of elements drawn from a population

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nominal

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level of measurement characterized by data that consist of names, labels, or categories only. The data cannot be arranged in an ordering scheme (such as low to high). ex. survey responses yes, no, undecided

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ordinal

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level of measurement involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaningless. ex. course grades A, B, C, D, F

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interval

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level of measurement like the ordinal level, with the additional property that the difference between any two data values is meaningful. However, there is no natural zero starting point. ex. years 1000, 2000, 1776, and 1492.

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ratio

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the interval level pf measurement modified to include the natural zero starting point (where zero indicates that none of the quantity is present). For values at this level, differences and ratios are meaningful. ex. prices of college textbooks ($0 represents no cost)

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nominal

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categories only

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ordinal

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categories with some order

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interval

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differences but no natural starting point

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ratio

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differences AND a natural stating point

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parameter

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a numerical measurement describing some characteristic of a population

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statistic

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a numerical measurement describing some characteristic of a sample.

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quantitative data

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numbers representing counts or measurements. ex. weights of supermodels

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qualitative

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aka categorical or attribute data. can be separated into different categories that are distinguished by some nonnumeric characteristics. ex: genders (male/female) of professional athletes.

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discrete

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type of quatitative data. data result when the number of possible values is either a finite number or a 'countable' number of possible values. 0, 1, 2, 3... ex. the number of eggs a hen lays

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continuous

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(numerical) data result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps. ex. The amount of milk that a cow produces; e.g. 2.343115 gallons per day.

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process of statistics

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1) Identify the research objective 2)Collect the information needed to answer the question 3)Describe the data 4)Draw conclusions from the data (make inferences)

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random sample

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members of the population are selected in such a way that each individual member has an equal chance of being selected.

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simple random sample

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subjects selected in such a way that every possible sample of the same size n has the same chance of being chosen

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how to do a simple random sample

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1) put item in order number items 1 through n 2) Randomly select five numbers using a random number generator. (sl. 64) 3)Match the generated random numbers to the corresponding items

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stratified sample

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obtained by separating the population into homogeneous, nonoverlapping groups called strata, and then obtaining a simple random sample from each stratum. The individuals within each stratum should be homogeneous (or similar) in some way. To obtain the stratified sample, conduct a simple random sample within each group.

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systematic sample

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obtained by selecting every kth individual from the population. The first individual selected is a random number between 1 and k.

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steps in a systematic sampling

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Step 1: Determine the population size, N. Step 2: Determine the sample size desired, n. Step 3: Compute N/n and round down to the nearest integer. This value is k. Step 4: Randomly select a number between 1 and k. Call this number p. Step 5: The sample will consist of the following individuals: p, p + k, p + 2k,..., p + (n - 1)k

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cluster sample

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obtained by selecting all individuals within a randomly selected collection or group of individuals

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experimental unit

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aka subject. a person, object or some other well-defined item upon which a treatment is applied.

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control group

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serves as a baseline treatment that can be used to compare to other treatments.

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placebo

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an innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication.

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step 1 of an experiment

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-Identify the problem to be solved. -Should be explicit -Should provide the experimenter direction -Should identify the response variable and the population to be studied. -Often referred to as the claim.

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step 2

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Determine the factors that affect the response variable. -Once the factors are identified, it must be determined which factors are to be fixed at some predetermined level (the control), which factors will be manipulated and which factors will be uncontrolled.

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step 3

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Determine the number of experimental units

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step 4

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Determine the number of predictor variables 1. Control: There are two ways to control the factors. (a) Fix their level at one predetermined value throughout the experiment. These are variables whose effect on the response variable is not of interest. (b) Set them at predetermined levels. These are the factors whose effect on the response variable interests us. The combinations of the levels of these factors represent the treatments in the experiment. 2. Randomize: Randomize the experimental units to various treatment groups so that the effects of variables whose level cannot be controlled is minimized. The idea is that randomization "averages out" the effect of uncontrolled predictor variables.

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step 5

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Conduct the experiment a) Replication occurs when each treatment is applied to more than one experimental unit. This helps to assure that the effect of a treatment is not due to some characteristic of a single experimental unit. It is recommended that each treatment group have the same number of experimental units. b) Collect and process the data by measuring the value of the response variable for each replication. Any difference in the value of the response variable is a result of differences in the level of the treatment.

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step 6

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Test the claim -This is the subject of inferential statistics. -Inferential statistics is a process in which generalizations about a population are made on the basis of results obtained from a sample. Provide a statement regarding the level of confidence in the generalization. Methods of inferential statistics are presented later in the text.

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completely randomized design

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design in which each experimental unit is randomly assigned to a treatment. sl. 105-107

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matched pairs design

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an experimental design in which the experimental units are paired up. The pairs are matched up so that they are somehow related (that is, the same person before and after a treatment, twins, husband and wife, same geographical location, and so on). There are only two levels of treatment in a matched-pairs design.

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randomized block design

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Grouping similar (homogeneous) experimental units together and then randomizing the experimental units within each group to a treatment is called blocking. Each group of homogeneous individuals is called a block. A randomized block design is used when the experimental units are divided into homogeneous groups called blocks. Within each block, the experimental units are randomly assigned to treatments.

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confounding

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occurs when the effects of two or more explanatory variables are not separated. Therefore, any relation that may exist between an explanatory variable and a response variable may be due to some other variable

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lurking variable

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an explanatory variable that was not considered in a study, but that affects the value of a response variable in a study. Typically related to explanatory variables in a study.

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cross sectional studies

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observational studies thar collect information about individuals at a specific point in time or over a very short period of time

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case control studies

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observational studies which are retrospective, require an individual to look back in time or require the researcher to look at existing records. Individuals that have a certain characteristic are matched with those who do not

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superior observational study

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no study is superior, both have advantages and disadvantages that depend on the situation.

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prospective study

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collects the data over time

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sampling without replacement

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once an individual is selected, the individual cannot be selected again

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frame

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a list of the individuals in the population being studied

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cohort study

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observed over a long period of time

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k

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N/n

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treatment

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Any combination of the values of the factors (explanatory variables

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