scientific inquiry and analysis unit 3 sampling techniques scientific data analysis1

SCIENTIFIC DATA ANALYSIS 1

SCIENTIFIC INQUIRY AND ANALYSIS

UNIT 3SAMPLING TECHNIQUES


SAMPLING TECHNIQUESOBJECTIVES:The student will be able to:• Distinguish between populations and samples. Understand

statistics as a process for making inferences about a population based on a random sample from the population. (CCCS.HSS.IC.A.1)

• Recognize the differences among sample surveys, observational studies, and experiments. (CCSS.HSS.IC.B.3)

• Explain the importance of random selection in surveys and observational studies to reduce bias. (CCSS.HSS.IC.B.3)

• Use data from a sample to estimate a population mean and standard deviation. (CCSS.HSS.IC.B.4)


SAMPLING TECHNIQUES

• Data– May be either quantitative or qualitative.

Quantitative refers to actual numerical data while qualitative is a non-numerical observation (i.e. the color of a person’s eyes)

• Population – refers to all measurements or observations of interest (i.e. the height of all 1 year old boys in America)


SAMPLING TECHNIQUES

• Sample – it is usually not feasible to collect data of a whole population so a sample is used instead. A sample is simply just a part of the population that represents the whole population.

• In order to represent a population a random sample is used


SAMPLING TECHNIQUES

• Methods for producing data:– Sampling an existing population– Experimenting which is controlling a variable to

observe its effects on another variable.– Simulation is a numerical facsimile of real world

phenomena (i.e. using a computer simulator to see the effects of wind shear on an airplane wing.)

– Census is a measurement of the whole population.– Survey is asking questions to gather data.


SAMPLING TECHNIQUES

• Problems with surveys:– Are the questions asked in a neutral way or is their

bias in the wording?– Are respondents answering truthfully?– Is the sample representative of the population?


SAMPLING TECHNIQUES

• Hidden Bias:– In collecting of data by any method it is always

important to scrutinize the way data was collected to minimize skewing the results.

– i.e. Asking a uniformed police officer to conduct a survey about the use of illegal drugs.

– Care must be given so that all subjects are dealt with in the same exact manner so that conscious or unconscious preferential treatment or selection does not occur.


SAMPLING TECHNIQUES

• Generalization– Avoid the urge to draw conclusions or

generalizations from a collection of data wider than the actual data setting.

– New discoveries must be based on repeated studies.

– i.e. Finding that a certain medicine works on lab rats does not mean that it will work on humans.


SAMPLING TECHNIQUES

• Classification of data– Data fall into four categories: nominal level, ordinal level,

interval level and ratio level– Nominal Level: the lowest level which consists of names

only with no measure of quality (i.e. The Toyota dealer has an inventory of red, white, black and silver Corollas)

– Ordinal Level: the next level of data where data is arranged in some order; however, the differences between the data cannot be determined. (i.e. ranking restaurants by a four star system – excellent, very good, good, bad. Is there any difference between two restaurants rated very good?)


SAMPLING TECHNIQUES

• Classification of data (countined)– Interval Level: like ordinal level of data (which

can be ordered), interval has the additional property that the difference between the data can be calculated; however, the data may not have an intrinsic zero or starting point. Therefore, for this data differences in data is important, but not ratios. (i.e. something measured in °F since 30° F is not two times hotter than 15 ° F although you could say it is that 30° F is 15 ° F warmer.)


SAMPLING TECHNIQUES

• Classification of data (countined)– Ratio Level: like interval level of data (which can

be ordered), ratio has an intrinsic zero or starting point; therefore, both a difference and a ratio of the data are meaningful. (i.e. two salmon are caught. One is 6” and the second is 18”, therefore the second one is 3 times larger than the first one.)


SAMPLING TECHNIQUES

• In order for a Sample to be used to represent a Population, the sample has to be random. If the sample is not random that it may not represent the population.

• Types of Sampling:– Simple Random Sampling– Simulation Sampling– Systematic Sampling– Cluster Sampling– Convenience Sampling


SAMPLING TECHNIQUES

• Simple Random Sample: a sample that is selected such that any sample of size (n) has an equal probability of being selected and that any member of the population has equal probability of being included in the sample.


SAMPLING TECHNIQUES

• Procedure for a Simple Random Sample1. Number your population sequentially.2. Using a random generator or a random number

chart, select a random number.3. Based on the random number, select the

corresponding sample from the population.4. Repeat steps 2 & 3 until your sample size is met.


SAMPLING TECHNIQUES• Simple Random Sample Example (Survey of Mr. Pantaleo’s

Physics I Students)• Let’s say I wanted to get an idea of what students thought of

Physics I and how I taught it. I might come up with a survey that rates the class, the teacher, the content, etc. 1 – 10. The population of Mr. Pantaleo’s 2013-14 class was 70 students.1. Number your students sequentially.2. Using a random generator or a random number chart, select a

random number.3. Based on the random number, select the corresponding student

from the population.4. Repeat steps 2 & 3 until your sample size is met.


SAMPLING TECHNIQUES

• Simulation: a process of providing arithmetic imitations of real phenomena. The arithmetic imitation consists of a collection of things that happen at random. The situation is repeated and its outcome is observed.


SAMPLING TECHNIQUES

• Steps for a Simulation1. Identify the situation to be repeated.2. Explain how the outcome will be modeled3. Simulate the trial4. State clearly the response variable or the expected

outcome.5. Run several trials.


SAMPLING TECHNIQUES• Example of a Simulation (Blood Donors)In the U.S. 44% of the population have type O blood. How many donors would you have to examine before you got 3 Type O donors?

1. Identify the situation to be repeated. (Type O donor)2. Explain how the outcome will be modeled (Split donors into two

groups – type O and all others. Use two digit random numbers 00 – 43 indicates Type O, 44 – 99 indicates other type)

3. Simulate the trial (See next page)4. State clearly the response variable or the expected outcome. (3

type O)5. Run several trials.


SAMPLING TECHNIQUES

• Example of a Simulation (Blood Donors)00 – 43 type O, 44 – 99 all other types

Trial Results from Random # Generator

Number of Donors Picked

1 O N N N O O 6

2 N O O O 4

3 N N O N O N N O 8

4 O N O N O 5

5 N O N N O O 6

6 N N N O N O O 7

Average 6


SAMPLING TECHNIQUES

• Example: The Baseball World Series ends when a team wins 4 out of 7 games. Suppose that the sports analysts consider one team a bit stronger, with a 55% chance to win any individual game. Estimate the likelihood that the underdog wins the series using simulation. Use 10 trials.


SAMPLING TECHNIQUES• Other Sampling Techniques:

– Stratified Sampling: splitting a sample into groups to ensure a representative amount (i.e. men and women; freshmen, sophomores, juniors and seniors)

– Systematic Sampling: elements of a population are somewhat ordered so a random starting point and then every nth object is chosen. The problem with this is that if the population is repetitive or cyclic, this will not work. (For example a paper machine that makes large rolls of paper. Suppose the machine (due to a defect) creates an imperfection every 12th foot, but your sampling only checked every 11th foot. It may not detect the error or do it too late.)


SAMPLING TECHNIQUES

• Other Sampling Techniques:– Cluster Sampling: splitting demographic sections and

then randomly selecting a section or cluster. Then, every member of the cluster is counted. (i.e. A survey about the preparation of teachers for the upcoming PARCC exam in Union County. Maybe split up Union County by districts and randomly select a district. Within the district spit it up by schools and randomly select a school. Then, within the school survey all of the teachers within that school.)


SAMPLING TECHNIQUES

• Other Sampling Techniques:– Convenience Sampling: sampling data is readily or

conveniently available. The problem with this sampling is that it can be highly biased.


SAMPLING TECHNIQUES

• Experiments– Observational Studies: a study based on data in

which no manipulation of factors has been employed. (i.e. a study of scholastic performance of music students to non-music students)

– If a correlation in an observational study is seen, could it indicate a cause?


SAMPLING TECHNIQUES• Experiments

– In order to tie an observational study to a cause an experiment has to be done.

– Statistical Experiment: manipulates factor levels (variables) to create treatments or outcomes. Randomly assigns subjects to these treatments or outcomes. It then compares the responses of the subject groups across treatment levels or outcomes.

– Example: to see whether music studies effects academic performance, take a group of 3rd graders and force one group to take music lessons and force another group not to take music lessons. Later in their academic careers see if this had an effect on their academic performance.


SAMPLING TECHNIQUES

• Four Principles of Experimental Design– Control: control sources of variation other than

the factors we are testing by making conditions as similar as possible for all treatment groups. For the group(s) in which the variable changes, they are referred to as the experimental group(s). For the group(s) in which the variable does not change, they are referred to as the control group(s).


SAMPLING TECHNIQUES

• Four Principles of Experimental Design– Randomize: allows us to equalize the effects of

unknown or uncontrollable sources of variations. It does not eliminate these sources, but helps us to spread those out among all of the groups.

– Replicate: allows others to perform the same experiment and get the same results.


SAMPLING TECHNIQUES

• Four Principles of Experimental Design– Block: subjects may be sectioned off into distinct

groups or blocks in order to get representative groups and then the selection within a group is randomized. (i.e. back to the experiment of music and grades. Assume there is a disproportionate number of boys to girls (3:1). The boys may be blocked into one group and the girls in another block and selection from each group randomized so that one group does not have all boys.)

scientific inquiry and analysis unit 3 sampling techniques scientific data analysis1

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