1. Chapter 1 Introduction to Statistics

2. Statistical Methods Were developed to serve a purpose Were developed to serve a purpose The purpose for each statistical procedure provides a background or context for the details of the formulas and calculations The purpose for each statistical procedure provides a background or context for the details of the formulas and calculations If you understand why the procedure is needed, you will find it easier to learn the procedure. If you understand why the procedure is needed, you will find it easier to learn the procedure.

3. Definition of Statistics Facts and figures Facts and figures Refers to a set of methods and rules for organizing, summarizing, and interpreting information Refers to a set of methods and rules for organizing, summarizing, and interpreting information

4. Statistics Statistical procedures help ensure that the information or observations are presented and interpreted in an accurate and informative way. Statistical procedures help ensure that the information or observations are presented and interpreted in an accurate and informative way. Statistics provide researchers with a set of standardized techniques that are recognized and understood throughout the scientific community. Statistics provide researchers with a set of standardized techniques that are recognized and understood throughout the scientific community.

5. Population The set of all individuals of interest for a particular study. The set of all individuals of interest for a particular study. Populations are usually large Populations are usually large Ex. The number of women on the planet Ex. The number of women on the planet Populations can be limited Populations can be limited The number of female registered voters in the U.S. The number of female registered voters in the U.S.

6. Population (cont.) The population can vary in size from large to small The population can vary in size from large to small The population should always be identified by the researcher The population should always be identified by the researcher Populations do not have to be people Populations do not have to be people

7. Population (cont.) It is impossible to examine every individual in a population It is impossible to examine every individual in a population Researchers typically select a smaller more manageable group – called a sample Researchers typically select a smaller more manageable group – called a sample

8. Sample A sample is intended to represent a population A sample is intended to represent a population A sample should always be identified in terms of the population from which it was selected A sample should always be identified in terms of the population from which it was selected Samples can vary in size Samples can vary in size

9. Sample of Scores The book will discuss a sample of scores The book will discuss a sample of scores Each sample of individuals produces a corresponding sample (or population) of scores Each sample of individuals produces a corresponding sample (or population) of scores Occasionally a set of scores is called a statistical population or a statistical sample to differentiate from a population or sample of individuals Occasionally a set of scores is called a statistical population or a statistical sample to differentiate from a population or sample of individuals

10. Parameters and Statistics Always distinguish if the data come from a population or a sample Always distinguish if the data come from a population or a sample A characteristic that describes a population is called a parameter A characteristic that describes a population is called a parameter Example: the population average Example: the population average A characteristic that describes a sample is called a statistic A characteristic that describes a sample is called a statistic Example: the average score Example: the average score

11. Parameters and Statistics Typically the research process begins with a question about a population parameter Typically the research process begins with a question about a population parameter The actual data come from a sample and are used to compute sample statistics The actual data come from a sample and are used to compute sample statistics

12. Parameter A parameter is a value, usually a numerical value, that describes a population A parameter is a value, usually a numerical value, that describes a population May be obtained from a single measurement May be obtained from a single measurement Or may be derived from a set of measurements from the population Or may be derived from a set of measurements from the population

13. Statistic A statistic is a value, usually a numerical value that describes a sample A statistic is a value, usually a numerical value that describes a sample May be obtained from a single measurement, or it may be derived from a set of measurments from the sample May be obtained from a single measurement, or it may be derived from a set of measurments from the sample

14. Descriptive and Inferential Statistical Methods After data are obtained, statistical methods are used to organize and interpret the data After data are obtained, statistical methods are used to organize and interpret the data Methods are categorized into two general methods descriptive and inferential Methods are categorized into two general methods descriptive and inferential

15. Descriptive Statistics Statistical procedures that are used to summarize, organize, and simplify data Statistical procedures that are used to summarize, organize, and simplify data

16. Inferential Statistics Consist of techniques that allow us to study samples and then make generalizations about the populations from which they were selected Consist of techniques that allow us to study samples and then make generalizations about the populations from which they were selected One problem with using samples – provide only limited information about the population One problem with using samples – provide only limited information about the population

17. Inferential Statistics (cont.) Samples should be representative of its population Samples should be representative of its population General characteristics should be consistent with the characteristics of the population General characteristics should be consistent with the characteristics of the population There is usually some discrepancy or sampling error that needs to be addressed when using inferential statistics There is usually some discrepancy or sampling error that needs to be addressed when using inferential statistics

18. Sampling Error The discrepancy, or amount of error, that exists between a sample statistic and the corresponding population parameter The discrepancy, or amount of error, that exists between a sample statistic and the corresponding population parameter The statistic obtained using a sample will not be the same if you measured the entire population The statistic obtained using a sample will not be the same if you measured the entire population Two or more samples within a population will also find different statistics Two or more samples within a population will also find different statistics

19. Margin of Error The margin of error is the sampling error The margin of error is the sampling error

21. Figure 1.1 The role of statistics in research Copyright © 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning Step 1: Data CollectionStep 2: Descriptive Statistics Step 3: Inferential Statistics: Interpret the results

22. The Scientific Method and the Design of Research Studies Variable Variable A characteristic or condition that changes or has different values for different individuals A characteristic or condition that changes or has different values for different individuals Example 1 – height, weight, gender, SES Example 1 – height, weight, gender, SES Example 2 – Environmental conditions – temperature, time of day, size of the room Example 2 – Environmental conditions – temperature, time of day, size of the room When variables are measured, the resulting values are often identified by letters (i.e. X,Y) When variables are measured, the resulting values are often identified by letters (i.e. X,Y)

23. Constant A value that does not change is called a constant A value that does not change is called a constant A constant is a characteristic or condition that does not vary but is the same for every individual A constant is a characteristic or condition that does not vary but is the same for every individual Science involves a search for relationships between variables Science involves a search for relationships between variables

24. Correlations The simplest way to look for relationships between variables is to make observations of the two variables as they exist naturally for a set of individuals The simplest way to look for relationships between variables is to make observations of the two variables as they exist naturally for a set of individuals This is called the correlational method This is called the correlational method

25. Correlational Method With the correlational method, two variables are observed to see whether there is a relationship With the correlational method, two variables are observed to see whether there is a relationship The correlational method involves measuring two different variables for each individual The correlational method involves measuring two different variables for each individual After measurements are obtained, the researcher examines the data to see whether there are any consistent trends or patterns After measurements are obtained, the researcher examines the data to see whether there are any consistent trends or patterns

26. Correlational Method (cont.) It is often tempting to conclude that one variable is causing changes in the other variable It is often tempting to conclude that one variable is causing changes in the other variable However, this conclusion is not justified However, this conclusion is not justified A limitation of the correlational method is that it simply describes the relationship – it does not explain the cause and effect mechanism of the relationship A limitation of the correlational method is that it simply describes the relationship – it does not explain the cause and effect mechanism of the relationship

27. To establish a cause and effect relationship, it is necessary to exert a much greater level of control over the variables being studied. To establish a cause and effect relationship, it is necessary to exert a much greater level of control over the variables being studied. This is accomplished by the experimental method This is accomplished by the experimental method Highly structured Highly structured Systematic approach to the study of the relationships between variables Systematic approach to the study of the relationships between variables

28. The Experimental Method Goal is to establish a cause-and-effect relationship between two variables Goal is to establish a cause-and-effect relationship between two variables Method is intended to show that changes in one variable are caused by changes in the other variable Method is intended to show that changes in one variable are caused by changes in the other variable

29. The Experimental Method (cont.) Two Distinguishing Characteristics Two Distinguishing Characteristics The researcher manipulates on of the variables and observes the second variable to determine whether or not the manipulation causes changes to occur The researcher manipulates on of the variables and observes the second variable to determine whether or not the manipulation causes changes to occur The researcher must exercise some control over the research situation to ensure that other, extraneous variables do not influence the relationship being examined The researcher must exercise some control over the research situation to ensure that other, extraneous variables do not influence the relationship being examined

31. Figure 1.2 An example of the experimental method Copyright © 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning

32. The Experimental Method (cont.) The researcher must rule out any other possible explanations for the difference to say that temperature affects memory performance The researcher must rule out any other possible explanations for the difference to say that temperature affects memory performance Random assignment of individuals Random assignment of individuals Helps assure that subjects are not very different from the other group Helps assure that subjects are not very different from the other group Treatment conditions must be identical Treatment conditions must be identical Hold all other variables constant Hold all other variables constant

33. Independent Variable The variable that is manipulated by the researcher. In behavioral research, the independent variable usually consists of the two (or more) treatment conditions to which subjects are exposed. The variable that is manipulated by the researcher. In behavioral research, the independent variable usually consists of the two (or more) treatment conditions to which subjects are exposed.

34. Dependent Variable The one that is observed for changes in order to assess the effect of the treatment The one that is observed for changes in order to assess the effect of the treatment In psychological research, the dependent variable is typically a measurement or score obtained for each subject. In psychological research, the dependent variable is typically a measurement or score obtained for each subject.

35. Experiment and Correlational In an experimental study, one variable is actually measured In an experimental study, one variable is actually measured In a correlational study, where both variables are measured, the data consist of two separate scores for each individual In a correlational study, where both variables are measured, the data consist of two separate scores for each individual

36. Control and Experimental Condition Individuals in a control condition do not receive the experimental treatment. They receive either no treatment, or a control or placebo treatment Individuals in a control condition do not receive the experimental treatment. They receive either no treatment, or a control or placebo treatment In an experimental condition, individuals receive the experimental treatment In an experimental condition, individuals receive the experimental treatment

37. Quasi-Experimental Method Instead of using an independent variable to create treatment conditions, a quasi- experimental research study uses a non- manipulated variable to define the conditions that are being compared. Instead of using an independent variable to create treatment conditions, a quasi- experimental research study uses a non- manipulated variable to define the conditions that are being compared. The non-manipulated variable is usually a subject variable (male vs. female) or a time variable (before vs. after treatment). The non-manipulated variable is usually a subject variable (male vs. female) or a time variable (before vs. after treatment).

38. Figure 1.3 Examples of the quasi-experimental method Copyright © 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning

39. Scales of Measurement The distinctions among the scales are important because they underscore the limitation of certain types of measurements and because certain statistical procedures are appropriate for data collected on some scales but not on others. The distinctions among the scales are important because they underscore the limitation of certain types of measurements and because certain statistical procedures are appropriate for data collected on some scales but not on others.

40. Nominal Scale A nominal scale consists of a set of categories that have different names. A nominal scale consists of a set of categories that have different names. Measurements on a nominal scale label and categorize observations but do not make any quantitative distinctions between observations. Measurements on a nominal scale label and categorize observations but do not make any quantitative distinctions between observations. A nominal scale consists of qualitative differences. It does not provide information about quantitative differences between individuals. A nominal scale consists of qualitative differences. It does not provide information about quantitative differences between individuals.

41. Ordinal Scale An ordinal scale consists of a set of categories that are organized in an ordered sequence. An ordinal scale consists of a set of categories that are organized in an ordered sequence. Measurements on an ordinal scale rank observations in terms of size or magnitude. Measurements on an ordinal scale rank observations in terms of size or magnitude. However, the data do not reveal how much better. However, the data do not reveal how much better.

42. Interval Scales An interval scale of measurement consists of an ordered set of categories (like an ordinal scale), with the additional requirement that the categories form a series of intervals that are all exactly the same size. An interval scale of measurement consists of an ordered set of categories (like an ordinal scale), with the additional requirement that the categories form a series of intervals that are all exactly the same size. Allows you to measure how much difference there is between two individual scores. Allows you to measure how much difference there is between two individual scores.

43. Ratio Scales A ration scale is an interval scale with the additional feature of an absolute zero point. A ration scale is an interval scale with the additional feature of an absolute zero point. In a ratio scale, ratios of numbers reflect ratios of magnitude. In a ratio scale, ratios of numbers reflect ratios of magnitude.

44. Discrete Variables A discrete variable consists of separate, indivible categories. A discrete variable consists of separate, indivible categories. No values can exist between two neighboring categories. No values can exist between two neighboring categories. Ex. Numbers of students in a class Ex. Numbers of students in a class 18 or 19 students, not 18.25 students 18 or 19 students, not 18.25 students

45. Continuous Variables A continuous variable is divisible into an infinite number of fractional parts. A continuous variable is divisible into an infinite number of fractional parts. There are an infinite number of possible values that fall between any two observed values. There are an infinite number of possible values that fall between any two observed values. Ex. Amount of time to complete a task. Ex. Amount of time to complete a task.

46. Figure 1.4 Representing time on a continuous number line Copyright © 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning

47. Real Limits Real limits are the boundaries of intervals for scores that are represented on a continuous number line. Real limits are the boundaries of intervals for scores that are represented on a continuous number line. The real limit separating two adjacent scores is located exactly halfway between the scores. The real limit separating two adjacent scores is located exactly halfway between the scores. Each score has two real limits – The upper real limit and the lower real limit. Each score has two real limits – The upper real limit and the lower real limit. Ex. Used for constructing graphs and for various calculations with continuous scales. Ex. Used for constructing graphs and for various calculations with continuous scales.

48. Figure 1.5 An illustration of real limits Copyright © 2002 Wadsworth Group. Wadsworth is an imprint of the Wadsworth Group, a division of Thomson Learning

49. Summation Notation The Greek letter sigma, or E, is used to stand for summation. The Greek letter sigma, or E, is used to stand for summation. The expression E X means to add all the scores for variable X. The expression E X means to add all the scores for variable X. Read as “the sum of.” Read as “the sum of.”