Welcome to MM207 Statistics Seminar with Ms. Hannahs 1  There are lots of topics each week, we can’t cover them all in Seminar, but I cover as much as I can. If I don’t cover it, you will have to do on your own or attend another seminar or watch the replays.  Remember Active On-Topic Participation for the entire Hour is an important part of your Seminar Grade! Answer questions from me or your classmates, ask relevant questions, give further clarification!  WARNING: Off-topic chatting during Seminar is distracting to me and to other students. Please keep it to a minimum, otherwise we may not get through many topics during our ‘hour’.

2 During Unit 1 check out EACH of these, especially StatCrunch. You need to learn this on your own by using the videos. There is a StatCrunch workshop on January 15 at 7pm ET. See Math newsletter or my announcements.

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Kaplan University Math Center Reference Library has lots of materials for MM207. USE THEM!! 5

Typing Math Use: * for multiplication (shift 8), x is for variables / for division (next to right shift key) ^ for exponents (shift 6), may need ( & ) to clarify also only one equals per line (on DB) only one step of a problem per line (on DB) Symbols are on DB under Ω 6

Statistics Statistics is the art and science of gathering, analyzing, and making inferences (predictions) from numerical information, data, obtained in an experiment. Statistics is divided into two main braches. – Descriptive statistics is concerned with the collection, organization, and analysis of data. – Inferential statistics is concerned with making generalizations or predictions from the data collected.

Statisticians A statistician’s interest lies in drawing conclusions about possible outcomes through observations of only a few particular events. – The population consists of all items or people of interest. – The sample includes some of the items in the population. When a statistician draws a conclusion from a sample, there is always the possibility that the conclusion is incorrect. Does the “Census” come from a sample or a population?

Basic Steps in a Statistical Study Step 1: State the goal of your study precisely; that is, determine the population you want to study and exactly what you’d like to learn about it. Step 2: Choose a sample from the population. Step 3: Collect raw data from the sample and summarize these data by finding sample statistics of interest. Step 4: Use the sample statistics to make inference about the population. Step 5: Draw conclusions; determine what you learned and whether you achieved your goal. Page 7 9

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Definitions A representative sample is a sample in which the relevant characteristics of the sample members are generally the same as the characteristics of the population. A statistical study suffers from bias if its design or conduct tends to favor certain results. 11

Summary of Sampling Methods Keep in mind the following three key ideas: A study can be successful only if the sample is representative of the population. A biased sample is unlikely to be a representative sample. Even a well-chosen sample may still turn out to be unrepresentative just because of bad luck in the actual drawing of the sample. 12

Types of Sampling A random sampling occurs if a sample is drawn in such a way that each time an item is selected, each item has an equal chance of being drawn. When a sample is obtained by drawing every nth item on a list or production line, the sample is a systematic sample. A cluster sample is sometimes referred to as an area sample because it is frequently applied on a geographical basis.

Types of Sampling continued Stratified sampling involves dividing the population by characteristics called stratifying factors such as gender, race, religion, or income. Convenience sampling uses data that are easily or readily obtained, and can be extremely biased.

Example: Identifying Sampling Techniques A raffle ticket is drawn by a blindfolded person at a festival to win a grand prize. Random ? Systematic ? Cluster ? Stratified ? Convenience ?

Example: Identifying Sampling Techniques A raffle ticket is drawn by a blindfolded person at a festival to win a grand prize. Random

Example: Identifying Sampling Techniques Students at an elementary school are classified according to their present grade level. Then, a random sample of three students from each grade are chosen to represent their class. Random ? Systematic ? Cluster ? Stratified ? Convenience ?

Example: Identifying Sampling Techniques Students at an elementary school are classified according to their present grade level. Then, a random sample of three students from each grade are chosen to represent their class. Stratified

Example: Identifying Sampling Techniques Every sixth car on highway is stopped for a vehicle inspection. Random ? Systematic ? Cluster ? Stratified ? Convenience ?

Example: Identifying Sampling Techniques Every sixth car on highway is stopped for a vehicle inspection. Systematic

Example: Identifying Sampling Techniques Voters are classified based on their polling location. A random sample of four polling locations are selected. All the voters from the precinct are included in the sample. Random ? Systematic ? Cluster ? Stratified ? Convenience ?

Example: Identifying Sampling Techniques Voters are classified based on their polling location. A random sample of four polling locations are selected. All the voters from the precinct are included in the sample. Cluster

Example: Identifying Sampling Techniques The first 20 people entering a water park are asked if they are wearing sunscreen. Random ? Systematic ? Cluster ? Stratified ? Convenience ?

Example: Identifying Sampling Techniques The first 20 people entering a water park are asked if they are wearing sunscreen. Convenience

Basic Types of Statistical Studies 1.In an observational study, researchers observe or measure characteristics of the subjects but do not attempt to influence or modify these characteristics. 2.In an experiment, researchers apply some treatment and observe its effects on the subjects of the experiment. 25

Definitions The subjects of a study are the people, animals (or other living things), or objects chosen for the sample; if the subjects are people, they may also be called the participants in the study. 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. 26

The treatment group in an experiment is the group of subjects who receive the treatment being tested. The control group in an experiment is the group of subjects who do not receive the treatment being tested. In most cases, it is important to choose the members of the two groups by random selection from the available pool of subjects. A study suffers from confounding if the effects of different variables are mixed so we cannot determine the specific effects of the variables of interest. The variables that lead to the confusion are called confounding variables. 27 Page 24 Treatment and Control Groups

More Definitions A placebo lacks the active ingredients of a treatment being tested in a study, but looks or feels like the treatment so that participants cannot distinguish whether they are receiving the placebo or the real treatment. The placebo effect refers to the situation in which patients improve simply because they believe they are receiving a useful treatment. An experimenter effect occurs when a researcher or experimenter somehow influences subjects through such factors as facial expression, tone of voice, or attitude. In a meta-analysis, researchers review many past studies. The meta-analysis considers these studies as a combined group, with the aim of finding trends that were not evident in the individual studies. 28

Guideline 1: Identify the Goal, Population and Type of Study Based on what you hear or read about a study, try to answer these basic questions: What was the study designed to determine? What was the population under study? Was the population clearly and appropriately defined? Was the study an observational study, an experiment, or a meta-analysis? 29

Guideline 2: Consider the Source Statistical studies are supposed to be objective, but the people who carry them out and fund them may be biased. It is therefore important to consider the source of a study and evaluate the potential for biases that might invalidate the study’s conclusions. Guideline 3: Examine the Sampling Method A statistical study cannot be valid unless the sample is representative of the population under study. 30

Guideline 4: Look for Problems in Defining or Measuring the Variable of Interest Results of a statistical study may be difficult to interpret if the variables under study are difficult to define or measure. 31 Guideline 5: Watch Out for Confounding Variables Often, variables that are not intended to be part of the study can make it difficult to interpret results properly.

Guideline 6: Consider the Setting and Wording in Surveys Even when a survey is conducted with proper sampling and with clearly defined terms and questions, you should watch for problems in the setting or wording that might produce inaccurate or dishonest responses. Dishonest responses are particularly likely when the survey concerns sensitive subjects. 32

Guideline 7: Check That Results Are Fairly Represented in Graphics or Concluding Statements Even when a statistical survey is done well, it may be misrepresented in graphics or concluding statements. 33

Guideline 8: Stand Back and Consider the Conclusions Ask yourself questions such as these: Did the study achieve its goals? Do the conclusions make sense? Can you rule out alternative explanations for the results? If the conclusions make sense, do they have any practical significance? 34

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