Stat 1 Ch 1

Under Sampling Techniques Define Population

A Population consists of all subjects (human or otherwise) that are being studied

Under Sampling Techniques Define Sample

A Sample is a group of subjects selected from a population.

Under Sampling Techniques Define Cluster Sample

A cluster sample is obtained by dividing the population into sections or clusters and then selecting one or more clusters and using all members in the clusters as members of the sample.

Under Sampling Techniques Define Stratified Sampling

A stratified sample is obtained by dividing the population into subgroups or strata according to some characteristic relevant to the study. Then subjects are selected from each subgroup.

Under Sampling Techniques Define systematic sample

A systematic sample is a sample obtained by selecting every k member of the population where k is a counting number. Where k is a counting number.

Under Sampling Techniques Define Inferential statistics

Inferential statistics consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions.

Under Experimental Design Advantages of Experimental Study The researcher can decide how to select subjects and assign them to groups such as control and treatment groups. The researcher can manipulate variables such as dosages in medical studies.

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Under Misuses of Data Ambiguous Averages There are four commonly used measures that are loosely called averages •Mean •Median •Mode Midrange

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Under Levels of Measurement Classify each of the following according to level of measurement 3.Birth city for a sample of students

Birth city is an example of Nominal Level of Measurement No ranking or order can be placed on the data: Walla Walla, Washington Saskatoon, Saskatchewan. Crapstone, England

Define Continuous variables

Continuous variables can assume an infinite number of values between any two specific values. They are obtained by measuring.

Under Misuses of Data Define Data

Data is used appropriately every day to attempt to describe populations, compare populations, determine relationships between variables, test hypotheses, and make estimates about population characteristics. However, data is also frequently misused to sell products that don't work properly, to attempt to prove something true that is not really true, or to get our attention by using statistics to evoke fear, shock, and outrage.

Under Sampling Techniques Define Descriptive statistics

Descriptive statistics consists of the collection, organization, summarization, and presentation of data.

Define Discrete variables

Discrete variables assume values that can be counted.

Under Experimental Design Example of Experimental Study When a pharmaceutical company tests the side effects for experimental medications they will administer a placebo to a control group and the actual medical therapy to the treatment group. They would then compare to see if a statistical significance exists between the incidents of a side effect between the two groups. (Slide 50)

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Under Sampling Techniques Example of Stratified Sampling Suppose the school president wants to know the opinions of his students in a two year college. The president wishes to see the opinions of his first year and second year students if they differ. So the president will randomly select students from each subgroup to use in the sample.

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Under Sampling Techniques Example of a Cluster Sample Suppose the governor of a state would like to find out what the citizens think about a certain budget item that will require extra taxation. He is also concerned with the opinions of those who live in the western part of the state, the central part, and the eastern part. The governor will randomly select citizens from each part of the state to see if there are differences of opinion between the regions.

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Under Levels of Measurement Classify each of the following according to level of measurement 1.Points scored by basketball players in a game

Points scored by basketball players in a game is an example of Ratio Level of Measurement. The data values can be ordered: 10 points is less than 20 points Interval differences exist between the data values: 20 points minus 10 points = 10 points True Ratios exist between data values: 20 points/10 points = 2 to 1 ratio There exists a significant zero: Zero points implies that a player did not score.

Define Qualitative Variables

Qualitative Variables are variables that have distinct categories according to some characteristic or attribute.

Define Quantitative variables

Quantitative variables are variables that can be counted or measured.

Under Levels of Measurement Classify each of the following according to level of measurement 2.Time of day

Time of day is an example of Interval Level of Measurement Data values can be ordered: 2:30 comes before 5:00 Interval differences exist between the data values: There is a measurable span of 2.5 hours between 2:30 and 5:00 True ratios do not exist between the data values: It cannot be stated that 5:00 is twice as late as 2:30 There does not exist a true zero: If some requested the time, the reply would never be "zero"

Classify each Variable as a discrete or continuous variable. a.The number of hours during a week students reported that they watched television b.The number of touchdowns a player scored each year in football c.The amount of money a person earns per week at their job d.The weights of the football players on the teams that play in the NFL this year

a. Continuous, Since the variable is time and is measured b. Discrete, since number of touchdowns is counted c. Discrete, since the smallest value that money can assume is in cents d. Continuous, since the variable is measured

Classify whether the following variables are Qualitative or Quantitative. a. Religious Affiliation b. Height c. Body Temperature d. Geographic Location

a. Qualitative b. Quantitative c. Quantitative d. Qualitative

Under Sampling Techniques Other Sampling Method Define Convenience sample

researchers use subjects who are convenient. For example: a researcher wants to study peoples shopping habits, and waits at the mall and selects people at random

Examples of continuous variables

•Distance a frog jumps in a contest •Temperature of a frog •Weight of a frog

Examples of qualitative variables

•Hair color •Soft drink brand •Gender •Jersey number Although the variable jersey number is numerical. It bears no associated countable or measurable quantity.

Examples of Quantitative variables

•Number of frogs •Distance a frog can jump •Temperature of a frog •Age of a frog

Under Levels of Measurement Classify each of the following according to level of measurement 4.Level of agreement on a survey

Level of agreement on a survey is an example of Ordinal Level of Measurement Data can be ranked in order: Strongly Disagree, Disagree, Neutral, Agree No interval difference can be measured between the data values

Under Levels of Measurement Define Interval Level

The interval level of measurement ranks data, and precise differences between units of measure do exist; however, there is no meaningful zero. IQ is an example of the interval level of measurement. There is a meaningful difference of 1 point between an IQ score of 109 and an IQ score of 110. But there is no meaningful zero to this scale as IQ tests do not measure people who have no intelligence. Temperature of a jumping frog is another example. There is a meaningful difference of 1˚F between a temperature of 98.6˚F and 99.6˚F. But 0˚F does not imply that the frog has no temperature.

Under Levels of Measurement Define Nominal Level

The nominal level of measurement classifies data into mutually exclusive (non-overlapping) categories in which no order or ranking can be imposed on the data. The cars in a parking lot can be classified according to their color. There might be red, blue, green, or silver cars in the lot. But no ranking or order can be imposed on the variable "color." Classifying residents according to zip codes is also an example of the nominal level of measurement. Even though numbers are assigned as zip codes, there is no meaningful order or ranking.

Under Levels of Measurement Define Ordinal Level

The ordinal level of measurement classifies data into categories that can be ranked; however, precise differences between the ranks do not exist. T-shirt size is an example of the ordinal level of measurement. Letter Grade (A,B,C,D,F)

Under Levels of Measurement Define Ratio Level

The ratio level of measurement possesses all the characteristics of interval measurement, and there exists a true zero. In addition, true ratios exist when the same variable is measured on two different members of the population. If one person has 200 Instagram followers and another person has 100 followers, then not only is there an interval difference of 100 followers, but we can also state the relationship between them as a ratio of 2 to 1. Stated another way, the first person has twice as many followers as the second person. There is also a meaningful zero. If the value of the variable is zero, it implies that a person has no Instagram followers.

Under Experimental Design Define Experimental Study

The researcher manipulates one of the variables and tries to determine how the manipulation influences other variables.

Under Experimental Design Define Observational Study

The researcher merely observes what is happening or what has happened in the past and tries to draw conclusions based on these observations.

Under Sampling Techniques Define Census

When data are collected from every subject in the population, it is called a Census.

Under Sampling Techniques Other Sampling Method Define Volunteer or self selected sample

here subjects decide to participate or not on their own time. For example: online poll, flyer or voting

Under Sampling Techniques Define Random Sample

A random sample is a sample in which each member of the population has an equal probability of being selected.

Under Experimental Design Advantages of Observational Study Observational studies are typically carried out in a natural setting. Observational studies can be carried out in situations where intervention by the researcher would be considered unethical or even dangerous such as in the case of crime statistics. Observational studies can be done using variables where manipulation is impossible such as studies involving height, age, and race.

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Under Misuses of Data Ambiguous Averages Example A reporter of statistics, in an attempt to convince his reader to see his point of view, may use the mean to describe a data set that contains a few extreme data values when the median might be a much better descriptor of the central tendencies of the population.

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Under Misuses of Data Ambiguous Averages Example Problem Consider the following closing prices for all 10 homes sold in a given month in a small town. A quick examination of the data, shows that homes in this area frequently sell in the mid $100,000 of dollars. However, we can see that there are more expensive properties that sell in this market as well. (Slide 59) Mean = $235,400 Median = $158,500

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Under Misuses of Data Detached Statistics A claim that uses a detached statistic is one in which no comparison is made. Consider the statement: People who use this diet lose an average of 10 more pounds per day. No comparison is provided so the question that should be asked is: 10 more pounds per day than what?

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Under Sampling Techniques Difference between Cluster and Strata Although both use the method of subgroups The members of the stratified method have similar characteristics while the cluster vary in characteristics similar to a larger population. Example: If a researcher wanted to use freshman from a university to sample, the researcher would choose a random freshmen class out of the freshmen classes for a cluster sample. However if the researcher is using Stratified sampling, then the researcher would have to split the freshmen's into major, gender, age etc..

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Under Experimental Design Disadvantages of Observational Study A definite cause and effect relationship cannot be shown since the researcher cannot manipulate other influencing variables. The research is subject to the inaccuracies of other data gatherers such as in the case of historical data like crime statistics from the 1800s or health statistics from another country.

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Under Sampling Techniques Eliminate Bias In order to achieve this close approximation established sampling techniques are employed. These sampling techniques are designed to eliminate bias. Information obtained from a statistical sample is said to be biased if the results from the sample are radically different from the results of a census of the population.

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Under Sampling Techniques Example of Bias For instance if a pre-election poll suggests that a particular candidate for public office will receive approximately 62% of the vote and then loses the election when his or her opposition receives more than 50% of the vote then the polling results contained bias.

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Under Experimental Design Example of Observational Study If a researcher looks at the number of registered vehicles in the US from the years 1990 through 2015. Then the researcher is merely looking at a historical data set. There is no intervention by the researcher in the process of gathering and reporting this data. (Slide 46)

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Under Misuses of Data Implied Connections A claim might attempt to imply connections between 2 variables where no connection actually exists. The advertising claim "Eating one bowl of our oatmeal cereal every morning may improve your child's ability to focus at school" does not specifically guarantee an increase in academic performance. But the benefit is certainly implied.

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Under Misuses of Data Misleading Graphs Graphs that are inappropriately drawn can lead a reader to draw false conclusions. Compare the two graphs on the next slide that are intended to represent the results from the same preference survey. (Slide 66-68)

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Under Sampling Techniques Random Sample Example A computer generated code to select numbers at random and choosing you sample

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Under Sampling Techniques Suppose an employee in a polling firm wishes to gage the public attitude towards a specific public policy. Each member of the population could potentially have an opinion about the policy. However, it would be impossible from a time and expense standpoint to poll each member of the population. In cases like this where it would be impossible for researchers to gather the data associated with an entire population a subset of the population would be used as a representative. This subset is called a sample. In order for this sample to be of optimal use to the researcher in making predictions about the population. The sample must be a good representative of the population. This simply means that measures associated with the sample would very likely closely approximate those of the population.

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Under Misuses of Data Suspect Samples It is important that sample sizes are large enough, and that the subjects in the sample were selected randomly. Consider the statement "3 out of 4 doctors recommend pain reliever A". If the sample contained only 4 doctors, then the data set is certainly not large enough to draw a significant conclusion. A sample size of 100 doctors might suggest more reliable results. A sample size of 100 doctors might suggest more reliable results. However, if the 100 doctors in the survey were selected conveniently at a conference sponsored by Pain Reliever A, then the results might suggest some bias that would render the results unreliable. It is important that sample sizes are large enough, and that the subjects in the sample were selected randomly. If new media outlets relied on samples taken at elementary schools for election polling, your favorite super hero could very well be mistakenly reported as the front runner for the presidential election.

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Under Sampling Techniques Systematic Sample Example Suppose a bottling company would like to test the machines that are filling the bottles by selecting a sample of filled bottles and measuring the amount of product that the machine is putting in the bottles. The company statistician goes to the end of the bottling line and selects every 20th bottle and removes it for testing. This "system" has thus generated a systematic sample.

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Examples of discrete variables

•Number of frogs in a jumping contest •Number of basketball goals scored during a game •Number of tomato plants in a garden This variable can only take on counting numbers like 5, 6, 10, or 1000. It could not take on a value like 5.5, 10.6, or 99.9.

Under Sampling Techniques Four Methods of Sampling In order to eliminate bias, statisticians use four basic methods of sampling that are designed to ensure that each member of a population has an equal probability of being selected for the sample. These four sampling techniques are called

•Random Sampling •Systematic Sampling •Stratified Sampling •Cluster Sampling