What is Statistics WE RESEARCHERS WE RESEARCHERS USE STATISTICS THE USE STATISTICS THE WAY A DRUNKARD WAY A DRUNKARD USES A LAMP POST, USES A LAMP POST, MORE FOR SUPPORT MORE FOR SUPPORT THAN THAN ILLUMINATION. ILLUMINATION. Statistics The branch of mathematics that deals with the collection, collection, organization, organization, analysis, analysis, and interpretation of numerical data. Statistics is especially useful in drawing general conclusions about a set of data from a sample of the data. DATA -----DATUM. SINGULAR -----DATUM. --------DATA. PLURAL --------DATA. WE MAY DEFINE DATA AS NUMBERS AND THERE IS TWO KINDS OF NUMBERS THAT WE USE IN STATISTICS THE RESULTS OF : COUNTING AND MEASUREMENTS. MEASUREMENTS. variable ANY ASPECT OF AN INDIVIDUAL THAT IS MEASURED, LIKE BLOOD PRESURE, AGE, SEX etc. Variables divide into different types QUALITATIVE (CATEGORICAL) QUANTITATIVE (NUMERICAL) Read not to contradict and confute, not to believe and take for granted, not to find talk and discourse, but to weigh and consider. Sir Francis Bacon WHAT MAKE STATISTICS UNIQUE? ITS ABILITY TO QUANTIFY UNCERTAINTY, UNCERTAINTY, TO MAKE IT PRECISE. PRECISE. Good thinking! I’m 95 % confident that this afternoon I will score has probability between 73 % and 77 % of being best player A more positive example in statistics is the SALK POLIO VACCINE in 1954 vaccine trials were performed on some 400,000 children, with strict controls to eliminate biased results. Good statistical analysis of the results firmly established the vaccine’s effectiveness, and to day POLIO is almost unknown. To accomplish their feats of mathematical LEGERDEMAIN (STATISTICIANS) RELY ON THREE RELATED DISCIPLINE: Data analysis The gathering, display, and summary of data Probability The law of chance Statistical Inference The science of drawing statistical conclusions from specific data, using a knowledge of probability. Objectives of this course At the end of the course the students will be able to 1. organize data 2. summarize data 3. reach decision about a large body of data by examining only small part of the data. Objective number 1 and 2 we will discuss in DESCRIPTIVE STATISTICS. Objective number 3 we will discuss INFERENCIAL STATISTICS What is biostatistics Biostatistics is in effect, two words and two fields of study combined. The bio part involves biology, the study of living things. The statistics part involves ollection, Collection, Organization, Analysis, Organization, nalysis, and interpretation of numerical data Biostatistics is the application of statistics to a wide range of topics in biology. It has particular biology. applications to medicine and agriculture. to agriculture. Statistics calculations are an important part of data analysis, but interpreting data also requires a great deal of judgment Understanding the statistical calculations is only a small part of 1. evaluating clinical 2. pharmaceutical 3. biological research. Why is it hard to learn statistics? The terminology is deceptive You have to understand : 1. Significant 2. Error 3. Hypothesis 4. Null hypothesis 5. Confidence interval Level of significant p value Population Sample Paired and unpaired samples Remember The phrase statistically significant is seductive and is often misinterpreted. Statistics is at the interface of mathematics and science However You can learn to use statistical test and interpret the results even if you don’t fully understand how they work. Inductive reasoning often described as "going from the specific to the general." AND It is based on observing specific instances of a certain quality in individual members of a group of 1. people 2. animals or 3. events noting the individual members in which a certain quality occurs belong to a certain group generalizing to the conclusion that other members of that group have the same quality. For example if you were to go to a cat show, you would see many breeds of cats with tails. After walking up and down, you might begin to notice a pattern, and your reasoning might go something like this: –Siamese cats have tails. –Persian cats have tails. –Himalayan cats have tails. –Russian Blues have tails. –American Tabbies have tails. After a while, you would probably come to the conclusion - All cats have tails The problem with this conclusion is that it isn't true. The manx is one breed of cat that has no tail. So the conclusion of an inductive argument can be shown to be wrong if only one instance does not fit the general pattern. The Manx is a breed of cats with a naturally spine. occurring mutation of the spine. For this reason the result of an inductive argument is never considered to be TRUE or FALSE instead we refer to the conclusions reached through inductive reasoning as MORE OR LESS RELIABLE. Before proceeding, think about this question: What would make the conclusion from an inductive argument MORE reliable? In inductive reasoning, the more specific instances you observe, the more reliable your conclusion. Because the conclusion from an inductive argument cannot be considered true or false the conclusion must be qualified. The conclusion from your observations about cats and their tails might be qualified in one of the following ways: –Many cats have tails. –Some cats have tails. –Most cats have tails. Cats, general, –in general, have tails. –Cats tend to have tails. A conclusion that is more or less reliable The more specific instances observed the more reliable the conclusion. Deductive reasoning Inductive Reasoning allows you to learn something new about the world. Deductive Reasoning allows you to apply what you have learned. The classic example of a deductive argument All men are mortal. man. Abdullah is a man. Therefore Abdullah is mortal. mortal. The first premise ("All men are mortal.") is the result of inductive reasoning. The second premise identifies a specific member of that group (Abdullah). While Inductive Reasoning results in conclusions that are more or less reliable, Deductive Reasoning results in conclusions false: that are true or false: In order for the conclusion of a deductive reasoning process to be true, all of its premises must be true. . Most people would agree that the first premise given is true. Most people would also agree that the second premise given is true IF both of the premises are true, then the conclusion must also be true if and only if it follows necessarily from the information given in the premises. Suppose we return to our observations about cats and their tails and the conclusion we arrived at by using inductive reasoning: Most cats have Remember that this tails. conclusion had to be qualified. Ra is a cat. I could show you pictures. Ra has a tail. Therefore, this conclusion follow necessarily? A trick question: When it rains, the streets get wet. The streets are wet. Therefore, it has been raining. Is the conclusion valid? Why or why not? The conclusion to that trick question is NOT valid: – When it rains, the streets get wet. – The streets are wet. – Therefore, it has been raining. The conclusion of a deductive argument must follow necessarily from the argument's premises; however, the first premise in this argument is a conditional statement. (It gives a condition under which something becomes true.) The statement can be restated like this: IF it rains, THEN the streets get wet. The problem with the conclusion from the above argument is that there are other conditions which may cause the streets to get wet: snow, sleet or other forms of precipitation besides rain fire hydrants being opened people washing their cars in the streets flooding IF- When a premise using IF-THEN (or in our example WHEN) is given, the second premise must give the specific condition stated in the first premise: the IF part of the statement: When it rains, the streets get wet. It has been raining. Therefore, the streets are wet. Giving the second part of a conditional statement (the THEN part), results in an invalid argument. Another way of looking at this problem is to think in terms of our first argument (about Abdullah): Step in Process Socrates Rain Argument Argument Identify a shared All men are All rainy days quality of the set: mortal cause the streets to get wet. Identify a member Abdullah is a man It is raining today. of the set: Valid conclusion: Abdullah is The streets are mortal. wet. All men are mortal. Abdullah is mortal. Therefore, Abdullah is a man. •This conclusion does not follow necessarily from the premises because Abdullah could be a cat, a mule, a dog, or any other living thing.