C1, L1, S1 Chapter 1 What is Statistics ?

C1, L1, S2 Chapter 1 - What is Statistics? A couple of definitions: Statistics is the science of data. Statistics is the science and art of collecting, presenting, describing and drawing conclusions from data.

C1, L1, S3 Chapter 1 - What is Statistics? “The subject matter of statistics is the process of finding out more about the real world by collecting and making sense out of data” This course –is not just about doing statistical calculations –it is also about non-mathematical ideas –(about 50% of the course)

C1, L1, S4 Chapter 1 - What is Statistics? Non-mathematical ideas are at least as important as technical skills for –successful completion of statistical studies in real life –success in this course

C1, L1, S5 It is trying to give us some idea of: What is Chapter 1 trying to do? what statistics is all about collecting and making sense of data to answer questions about the real world the basic type of studies used to answer such questions, namely surveys, experiments, & observational studies practical considerations that must be kept in mind when conducting such studies the role of randomization in such studies

C1, L1, S6 Real problems Curiosity Pose the question Design method of data collection Interpret the results What do they mean? Collect Data Summary and analysis of data The Cycle Of Statistical Investigation Answer to original question

C1, L1, S7 Design Method of Data Collection Surveys and Polls Experimentation Observational Studies

C1, L1, S8 Polls and Surveys A poll or a survey is the process of collecting data from a sample, or subset, of the population in order to determine information about the whole population.

C1, L1, S9 Why Sample? Polls and Surveys “You don’t have to eat the whole ox to know that the meat is tough” –Samuel Johnson

C1, L1, S10 Why Sample? Polls and Surveys Cheaper Faster Practicality – access to the population may be difficult or impossible Accuracy – control of interviewers – collating information

C1, L1, S11 Our goal would be to have a sample that reflects the variation that the whole population exhibits, especially in terms of characteristics that may have an effect on whatever we wish to measure. We call such a sample “representative”. Why Sample? Polls and Surveys

C1, L1, S12 Circle Exercise - Sampling Consider the circles drawn on your handout. Our aim is to estimate the mean (average) diameter of these 60 circles.

C1, L1, S13 There are 6 different sizes: 0.5, 1.0, 1.5, 2.0, 2.5 and 3.5 units Circle Exercise - Sampling

C1, L1, S14 Circle Exercise - Sampling Carefully choose a sample of 5 from the population of 60 circles. On your sheet write down the number and diameter of each of the 5 circles. Calculate the mean (average) diameter of your sample of 5 circles. This is your estimate of the mean diameter of the 60 circles.

C1, L1, S15 Circle Exercise - Sampling A carefully selected sample: Mean diameter of sample:

C1, L1, S16 Circle Exercise - Sampling

C1, L1, S17 Pick another sample of size 5 from the population of 60 circles, using the table of random numbers at the bottom of the handout. Example: Start at a random place on the table Circle Exercise - Sampling

C1, L1, S18 Random Numbers Circle Exercise - Sampling

C1, L1, S19 Pick another sample of size 5 from the population of 60 circles, using the table of random numbers at the bottom of the handout. Example: Start at a random place on the table … Circle Exercise - Sampling in consecutive pairs: 47, 22, 17, 35, 98, 72, 08, 51, to give the circles numbered: 47, 22, 17, 35, 8

C1, L1, S20 Circle Number Diameter A random sample: Random numbers selected: Mean diameter of sample: Circle Exercise - Sampling = 0.7 units

C1, L1, S21 Circle Exercise - Sampling

C1, L1, S22 The mean diameter of the 60 circles is 1 unit. Conclusion: It is difficult to ‘carefully select’ a representative sample. Random samples generally gave mean diameters closer to the true mean diameter. Circle Exercise - Sampling

C1, L1, S23 Randomization In Surveys Surveys should use some form of random sampling to obtain a representative sample. Random sampling: ensures each person / item has an equal chance of being chosen in a given draw avoids subjective and other biases allows for calculation of likely size of sampling errors Note: The larger the sample, the more effective the randomization in producing a representative sample.

C1, L1, S24 Low bias, low precision High bias, high precision High bias, low precision Low bias, high precision (our aim!) Bias and Precision

C1, L1, S25 Low bias, low precision High bias, high precision High bias, low precision Low bias, high precision (our aim!) Bias and Precision Where: Bias is consistent repeated departure of the sample results in the same direction and Lack of precision is when in repeated sampling the values are spread out or scattered.

C1, L1, S26 Random Sampling Simple Random Sample (SRS) –Label each population member 1 to N and sample without replacement. –i.e., disregard repetitions and numbers bigger than N. Stratified Sampling page 9 Cluster Sampling page 9 Systematic Sampling –e.g., sample every 10th person on a list.