Spirit Week Survey Results 1) What grade are you in? 6 9thgraders, 610thgraders, 13 11thgraders, 15 12th graders 2) On a scale of 1-5,1 being the lowest, how much did you enjoy taking part in spirit week? 3 said 1, 6 said 2, 11 said 3, 11 said 4, and 9 said 5 3) How do you feel that spirit week affected your school spirit? 9unchanged10slight increase15average increase 6 great increase 4) If you were to choose one, what was your favorite event? 18 said Lip-synching 8 Color Day 5 Powderpuff 1Homecoming 8 Decade Day 0 Penny Wars
Spirit Week Survey Results 5) If you were to choose one, what was your least favorite event? 3 said Lip-synching 1 Color Day 1 Powder puff 1Homecoming 9Decade Day 25 Penny Wars 6) On a scale from 1-5,one being the lowest, how much did you like the idea of each grade having a homecoming nominee? 23 said 1, 4 said 2, 6 said 3, 3 said 4, 4 said 5 7) How much did you participate in spirit week? 4 said Very Little 20 said Somewhat 6 said A Lot 8) Did spirit week take away from your class time? 18 said Yes 22 Said No 9) IF you answered yes to question 8, were your teachers__________? 6 said Not Understanding 8 said Somewhat Understanding 4 said Very Understanding
What was your least favorite event of Spirit Week?
Our Survey The population was the whole school, approximately 650 people. The size of our sample was 40 people. Our sample was collected by going into classrooms and having the first 40 people we saw fill out our survey. Our design was convenience sampling with a voluntary response.
Controlled Experiments Block Design An experiment is a study in which the investigator imposes a change or treatments on one or more groups. When the study involves two or more groups, we say that it is a comparative experiment. The purpose of an experiment is to determine the effect of the independent explanatory variables on a dependent response variable. Experiments are performed on units. Human units are called subjects. A control group generally consists of the units who are not to receive the treatment that is the focus of the experiment. The other group is called the treatment group since units in the treatment group receive the treatment. A major challenge in the experimentation is to design the experiment so that the explanatory variables are not confounded. Technically, two variables are confounded if the investigator cannot separately identify their effects on the response variable. One potential source of confounding is the effect of lurking variables. A lurking variable is a variable that has an effect on the response variable but is not measured as part of the study of interest. The determination of a relationship between the response variable and the explanatory variables, sometimes called factors, is the focus of the experimental process. A treatment is a combination of specific values of each of the factors; these values are often called levels.
Block Design When an investigator expects that one specific characteristic of the experimental units will likely affect the results of the experiment, a block design is appropriate. A block design is similar to the procedure of selecting a stratified sample that we considered in the sample survey section. In both cases, either strata or blocks are created to control for the effects of one or more lurking variables. Then, assignment into groups within the strata or blocks is accomplished randomly using probability. The goal of these techniques is to make the groups being compared as similar as possible apart from the treatment. A useful blocking strategy is the matched pairs design. In this design, data from two variables are paired in order to control for lurking variables.
Chapter 4 Planning a Study Four major types of collection strategies: -Census -Sample Survey -Controlled Experiment -Observational Study
Chapter 4 Sec 1 Basic Terminology and Census Population-The entire collection of objects you are interested in. Parameters-Statistical measures that are computed regarding the characteristics of a population. Sample-A subset of the populations. Statistics- Statistical measures calculated about a sample. Census- A method of data collection in which all members of a population are included in the survey.
Chapter 4 Sec 2 Sampling Statistical Inference: The process of drawing conclusions about the nature of the entire population based on the data from a sample. Sample design: Refers to the technique employed to select a subset of a participants from the population and gather the data from the population. Here are the 4 types of sample designs: Voluntary Response: A general appeal is made for responses to one or more questions. Convenience Sampling: Members of the population are chosen based on the convenience of including them. Quote Sampling: Interviewers are assigned to interview a fixed quota of members of the population. Sampled Random Sampling (SRS):Involves selecting individuals at random from the population without replacement. A sample of size n is to be chosen from the population, where every chance in equal.
4.2 Continued However, the first 3 types of sampling techniques above are flawed because they may be biased. Bias is a systematic error that favors a particular segment of the population or tends to encourage only certain outcomes in the data. Simple Random Samples are usually expensive to conduct and inconvenient, especially with large populations. 3 other acceptable methods of sampling which uses probability in its selection process is: Stratified Random Sample: Divide the population into groups of individuals that are similar in some way. Multi Stage Cluster Sample: Method in which the population is divided into a number of groups from which samples are drawn; these are then divided into groups from which samples are drawn once again and etc. Systematic Sample: Every nth item is included in the sample. Like every 4th or 7th. Bias can arise in several ways. Sampling Frame: The lost of possible subjects who could be selected in a sample. If the sampling frame is not equal to the population, the sample will be biased in the way the sampling frame is biased. Sampling errors can be summarized in three categories: Random Sampling Error: Error that occurs because of chance variation. Sampling Method Error: Error that occurs because of the choice of sampling method. Non-Sampling Method Error: Error that occurs in the responses by members in he sample.
Chapter 4 Sec 3Controlled Experiments Experiment – A study in which the investigator imposes a change or treatment on one or more groups. Comparative Experiment- When the study involves 2 or more groups. The purpose of an experiment is to determine the effect of the independent explanatory variables on a dependent response variable. Experiments are performed on units. Human units are called subjects. A control group generally consists of the units who are not to receive the treatment that is the focus of the experiment. The other group is called the treatment groups since units in the treatment group receive the treatment. The determination of a relationship between the response variable and the explanatory variables, sometimes called factors, is the focus of the experimental process. A treatment is a combination of specific values of each of the factors: the values are often called levels. The three major requirements for controlled experiment: -comparison -randomization -replication
4.3 Continued Comparison: Control group is used. In a drug trial, one unit is place under a variable drug and the other under a placebo, a treatment that should have no physical effect on the unit. Randomization: Assigning units to control and treatment groups using probability. Replication: Experimental results are attempted to be replicated or just repeated testing is done with larger numbers to see if chance variance can be reduced. The principles of experimental design are: Control: Using a control helps us find the variables in the experiment and find differences in the response variable. Randomization: Assign units into a control group like placebo and treatment groups to make sure they are similar as possible before the treatment begins. Replication: Repeat the experiment and attempt to replicate the results on many units to reduce chance variance.
Chapter 4 Sec 4Observational Studies In an observational study, a researcher collects information about a population by measuring a variable of interest.An important difference between observational studies and experiments is the nature of any conclusion. If an experiment is correctly designed and conducted, causation between the explanatory and response variables can be concluded. A correctly designed and conducted observational study only provides evidence of an association between explanatory and response variables. In order to control for sources that are confusing, most studies strive to identify treatment and control groups that are the same. The difference between a sample survey and observational study is that in a sample survey the subject is asked for an opinion and in an observational study the investigator observes and collects data about the behavior.
Chapter 4 Test 1) Which of the following is true? I A simple random sample is any sampling technique where each element of the population has the same chance of being selected. II A simple random sample is a sample where every set of n elements in the population has the same chance of being selected. III From a population of N=30, there are 60 equally likely possible samples of size 3 if we are sampling with replacement. A. I only B. II only C. III only D. I and II only E. None of the above
2) Creating a sample of children by starting with the third name in the directory and selecting every 8th name best describes: A. Random sampling B. Systematic sampling C. Convenience sampling D. Stratified sampling E. Multi stage cluster sampling 3) Which of the following are true statements? I A census aims to contain only a portion of the entire population. II Statistics is a statistical measure that is computed regarding the characteristics of a population. III The sample size is too large relative to the population size to conduct the sample. A. I only B. II only C. I and II only D. II and II only E. None of the above
Chapter 4 Test 4) Which of the following are true statements? I A census aims to contain only a portion of the entire population. II Statistics is a statistical measure that is computed regarding the characteristics of a population. III The sample size is too large relative to the population size to conduct the sample. A. I only B. II only C. I and II only D. II and II only E. None of the above
5) A measurable characteristic about an entire population is A. A census B A population C A parameter D A statistic E A sample
6) Which of the following is not a source of bias in sample surveys? A. non-response B. Wording of questions C. Voluntary response D. Use of a telephone survey E. All are sources of bias
Chapter 4 Test 7) A randomized block design is similar to which of the following sampling designs? Simple Random Sample (SRS) Convenience Sample Systematic Sample Stratified Sample Cluster Sample 8) The 3 principles of experimental design include: control, replication, homogeneity randomization, control, homogeneity Simple Random Sample, replication, homogeneity Control, Randomization, Replication 9) Which of the following can be used to show a cause and effect relationship between two variables? A parameter An observational study A sample survey A controlled experiment A cluster sample 10) A newspaper in Montana conducted a poll of its readers on their opinions about if Tiger Woods will continue with golf. 70 % of their readers took part in this survey. This is an example of A sample survey An experiment An observational study A systematic random sample A cluster sample
Chapter 4 Test 11) To conduct a survey of local businesses, a researcher opens the yellow pages to a random page, closes his eyes, puts his finger down on the page, and then reads off the next 50 businesses. Which of the following are true statements? I. The survey incorporates chance. II. The procedure results in a simple random sample. III. The procedure could easily result in selection bias. (A) I and II (B) I and III (C) II (D) I,II, and III (E) None of the above. Open Ended: 1) What is the difference between observational study and sample survey? 2) Describe the advantages and disadvantages of a Simple Random Sample.
Bohan Questions 1. C 2. A 3. C 4. We think an observational study is possible. First, you can take the three brands and make a bad of popcorn, but make sure that each bag contains a specific amount of kernels. Therefore, you can control the amount of popcorn being popped and then count the kernels that didn’t pop. With those numbers you can determine the percentage of popcorn that didn’t pop, and thus determine the best brand.
1. C 6. B E 11. E A 2. C 7. D 12. E 3. A B 8. E 13. D 4. E 9. E 14. A E 5. C 10. E 15. D C or B 1) a. To chose the same number of freshmen, sophomores, juniors, and seniors, you could do a convenient sample of ten students in each grade. b. Use convenient sampling again, but use five girls and five boys out of the ten in each grade. c. If there are no restrictions, conduct a convenient simple random sample of 40 students.
Controlled Experiment Example of a control. A group of 40 people of the same body fat percentage and life styles are taken into a cholesterol level reducing drug trial for a drug VYTORIN to see the effects of the drug on cholesterol levels of the individuals. A sample of 10 is taken and given the same meal plan and exercise routine for one week and then cholesterol levels are read as the following, in mg/dL: 115 117 127 103 119 110 105 107 99 121 The sample group is then placed on VYTORIN, the first 5 subjects on a placebo and the remaining 5 on the treatment, a cholesterol level reducing drug, levels are once again taken: 113 115 119 105 118 110 100 105 97 119 Verify that: x1 ≈ 112, s1= 9 , x2 ≈ 110 , s2= 8
Blocking in Controlled Experiment Example of block design. The group of 40 is divided in 3 age groups, 18-25, 26-35, 36-45. Five are taken from each group and levels are taken once again. Three of the subjects are placed on the treatment and two on the placebo from each group and levels are taken. The results of the three groups are compared to each other and a result is drawn if the drug affects aged group differently.
What we learned… We learned a great amount from this project because it involved so many different parts. The first part was a process that including making a survey, distributing it, and then calculating the results. We learned that surveys are a great way to gather information about a myriad of things. Surveys help other people determine a populations opinions and thoughts, or gather other types of information about a particular subject. By conducting surveys, people can take steps to make effective changes. In addition, we also learned about how effective the Block Design can be. Block design is similar to selecting a stratified sample. Blocks and strata are both created to control the effects of lurking variables. We learned that block design can be very effective when dealing with one characteristic of the experimental units. By using blocks, results are more precise.
Feedback We really enjoyed doing this project together as a group. It made us realize all the effort and hard work it takes to conduct a survey. We suggest that you continue to give this project to your statistic students in the future. There was no part of the project we disliked, even though we are not that bright at answering the Bohan questions. However, he will make us use our noggin more and become smarter Statisticians.