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  1. 1. An Introduction to Statistics and Research Design PPT 1
  2. 2. Statistics Defined Statistics is a branch of science that deals with collecting, sorting, editing, analyzing, interpreting, and storing data, information, knowledge, etc 2
  3. 3. Two Branches of Statistics Descriptive statistics ◦ Involves those methods involving the collection, presentation and characterization of a set of data in order to properly describe the various features of that set of data ◦ Organize, summarize, and communicate numerical information Inferential statistics ◦ Involves those methods that make possible the estimation of a characteristic of a population or the making of a decision concerning a population based only on sample results ◦ Use representative sample data to draw conclusions about a population ◦ The fundamental concepts of statistical inference consist of two major areas known as parameter estimation and hypothesis testing. 3
  4. 4. Branches of Statistics Descriptive: M = 80.2, SD = 4.5 ◦ Describes the average score on the first test Inferential: t(45) = 4.50, p = .02, d = .52 ◦ Infers that this score is higher than a normal statistics average 4
  5. 5. Samples and Populations A population is the whole set of measurements or counts about which we want to draw conclusion. ◦ Could be any size A sample is a set of observations drawn from a subset of the population of interest OR a sub set of a population, a set of some of the measurements or counts that comprises the population ◦ A portion of the population Sample results are used to estimate the population 5
  6. 6. Samples and Populations So, why would we use samples rather than test everyone? ◦ What would be more accurate? ◦ What would be more efficient? 6
  7. 7. Accuracy Vs Precision ◦Accuracy and precision are used synonymously in everyday speech, but in statistics they are defined more rigorously. ◦Precision is the closeness of repeated measurements Where as ◦Accuracy is the closeness of a measured or computed value to its true value 7
  8. 8. Statistics = Numbers Mostly, statistics is all about numbers. So … how can we make these observations into numbers? ◦ Think about all the different types of things you can measure… 8
  9. 9. Hypothesis Hypothesis is an assertion or conjecture concerning one or more populations. The truth or falseness of a statistical hypothesis is never known with absolute certainty unless the entire population is examined 9
  10. 10. Hypothesis ◦The structure of the hypothesis testing will be formulated with the use of the term null hypothesis. ◦This refers to any hypothesis to be tested and is denoted by H0. H0: 1 =  2 =  3 ◦ The rejection of H0 leads to the acceptance of an alternate hypothesis, denoted by H1 or HA. H1: Not all means are equal 10
  11. 11. Variables Variables ◦ Observations that can take on a range of values ◦ An example: Reaction time in the Stroop Task ◦ The time to say the colors compared to the time to say the word 11
  12. 12. Sources of Data Primary Vs. Secondary Data Sources ◦ There are many methods by which researchers can get the required data set. ◦ Firstly, they may seek data already published by governmental organizations (ministries, departments, agencies, etc.) or by non-governmental organization (international research and development organizations, regional networks, private companies, etc.). ◦ Such sources of data are categorized as secondary data sources. ◦ A second method of obtaining data is through designed experiments, dubbed as primary data sources. 12
  13. 13. Types of Variables Qualitative Variables ◦ Variables used when the characteristic under study concerns a traits/characters that can only be classified in categories and not numerically measured. ◦ The resulting data are called categorical data. ◦ Color, employment status and blood types are few examples. 13
  14. 14. Types of Variables Quantitative Variables ◦ If a characteristic is measured on a numerical scale, the resulting data consist of a set of numbers and are called measurement data. ◦ The term ‘quantitative variable’ is used to refer to a characteristic that is measured on numerical scale. ◦ A few examples of numerically valued variables are height, weight and yield. ◦ The variables that can only take integers are called discrete variables. ◦ The name discrete is drawn from the fact that the scale is made up of distinct numbers with gaps. ◦ On the other hand, variables that can take any value in an interval are called continuous variables. 14
  15. 15. Types of Variables Discrete ◦ Variables that can only take on specific values ◦ Number of students ◦ Tricky part … we can assign discrete values to things we’d normally consider words. ◦ Political party 15
  16. 16. Types of Variables Continuous ◦ Can take on a full range of values (usually decimals) ◦ How tall are you? 16
  17. 17. More Classification of Variables Discrete quantitative data are numerical responses, which arise from a counting process, while continuous quantitative data are numerical responses, which arise from a measuring process. Discrete Variables ◦ Nominal: is the simplest and most elementary type of measurement where numbers are assigned for the sole purpose of differentiating one object from another. When numbers are used in a nominal scale, it cannot be added them together, or it is not possible to calculate an average, because the scale does not have the necessary properties to do so ◦ Ordinal: implies the measurement that has the property of order. Here one object can be differentiated from the other and the direction of the difference can also be specified. Statements like ‘more than’ or ‘less than’ can be used because the measuring system has the property of order ◦ ranking of data 17
  18. 18. More Classification of Variables Continuous Variables ◦ Interval: used with numbers that are equally spaced ◦ Interval scale is known for its character to have equality of units. There are equal distances between observation points on the scale. This scale specifies not only the direction of the difference, as in the ordinal scale, but also indicates the amount of the difference as well. ◦ Ratio: has all the characteristics of interval scale plus an absolute zero. With an absolute zero point, statements can be made on ratios of two observations, such as ‘twice as long’ or ‘half as fast’. Most physical scales such as time, length and weight are ratio scales. 18
  19. 19. Examples of Variables Nominal: name of cookies Ordinal: ranking of favorite cookies Interval: temperature of cookies Ratio: How many cookies are left? 19
  20. 20. A distinction The previous information talks about the type of number you have with your variable. ◦ This type leads to the type of statistical test you should use 20
  21. 21. Variables Independent Variables (IVs) ◦ Variable you manipulate or categorize ◦ For a true experiment: must be manipulated – meaning you changed it ◦ Generally dichotomous variables (nominal) like experimental group versus control group ◦ For quasi experiment: used naturally occurring groups, like gender ◦ Still dichotomous, but you didn’t assign the group 21
  22. 22. Variables Independent Variables ◦ Special case: when IVs are categorical, the groups are called levels ◦ If political party is an IV, levels could be Democrat or Republican 22
  23. 23. Variables Dependent Variables (DVs) ◦ The outcome information, what you measured in the study to find differences/changes based on the IV ◦ Generally, these are interval/ratio variables (t-tests, ANOVA, regression), but you can use nominal ones too (chi-square) 23
  24. 24. Variables Confounding Variables ◦ Variables that systematically vary with the IV so that we cannot logically determine which variable is at work ◦ Try to control or randomize them away ◦ Confounds your other measures! 24
  25. 25. Reliability and Validity A reliable measure is consistent ◦ Measure your height today and then again tomorrow Standardized tests are supposed to be reliable 25
  26. 26. Reliability and Validity A valid measure is one that measures what it was intended to measure ◦ A measuring tape should accurately measure height A good variable is both reliable and valid ◦ How do we measure this? 26
  27. 27. Hypothesis Testing Process of drawing conclusions about whether a relationship between variables is supported or not supported by the evidence 27
  28. 28. Types of Research Designs Experiments: studies in which participants are randomly assigned to a condition or level of one or more independent variables 28
  29. 29. Experiments and Causality Experiments: able to make causal statements ◦ Control the confounding variables Importance of randomization 29
  30. 30. One Goal, Two Strategies Between-groups designs ◦ Different people complete the tasks, and comparisons are made between groups Within-groups designs ◦ The same participants do things more than once, and comparisons are made over time 30
  31. 31. Other Research Designs Not all research can be done through experimentation ◦ Unethical or impractical to randomly assign participants to conditions Correlational studies do not manipulate either variable ◦ Variables are assessed as they exist ◦ Cannot determine causality 31
  32. 32. Correlation Analysis Correlation analysis attempts to measure the strength of relationships between two variables by means of a single number called a correlation coefficient. It is important to understand the physical interpretation of this correlation coefficient and the distinction between correlation and regression. Correlation coefficients close to +1 or –1 indicate a close fit to a straight line (strong correlation) and values closer to zero indicate a very poor fit to a straight line or no correlation. There is no convention as to what values of correlation should be described as strong or weak. The negative correlation values tell that the values of one variable tend to get larger as the values of the variable get smaller and vice versa. 32
  33. 33. Regression Analysis Regression is similar to correlation in that testing for a linear relationship between two types of measurements is made on the same individuals. However, regression goes further in that we can also produce an equation describing the line of best fit through the points on the graph. Regression analysis concerns the study of the relationships between variables with the objective of identifying, estimating and validating the relationship. When using regression analysis, unlike in correlation, the two variables have different roles. Regression is used when the value of one of the variables is considered to be dependent on the other, or at least reliably predicted from the other. In correlation, we take measurement on individuals at random for both variables, but in regression we usually choose a set of fixed values for the independent variable (the one controlling the other). 33
  34. 34. Correlational Analysis Video game playing and aggression are related No evidence that playing video games causes aggression 34
  35. 35. Outlier Analysis Outlier: an extreme score - very high or very low compared to the rest of the scores Outlier analysis: study of the factors that influence the dependent variable 35