Transcript day8
Understanding Statistics Note: Bring exam review questions next week. Please do not provide answers. Descriptive vs. Inferential • Descriptive statistics – Summarize/organize a group of numbers from a research study • Inferential statistics – Draw conclusions/make inferences that go beyond the numbers from a research study – Determine if a causal relationship exists between the IV and DV Descriptive statistics • A set of tools to help us exam data – Descriptive statistics help us see patterns. • 49, 10, 8, 26, 16, 18, 47, 41, 45, 36, 12, 42, 46, 6, 4, 23, 2, 43, 35, 32 – Can you see a pattern in the above data? • Imagine if the data set was larger. – 100 cases – 1000 cases • What could we do? What are Inferential Statistics? • Refer to certain procedures that allow researchers to make inferences about a population based on data obtained from a sample. • Obtaining a random sample is desirable since it ensures that this sample is representative of a larger population. • The better a sample represents a population, the more researchers will be able to make inferences. • Making inferences about populations is what Inferential Statistics are all about. Statistics vs. Parameters • A parameter is a characteristic of a population. – It is a numerical or graphic way to summarize data obtained from the population • A statistic is a characteristic of a sample. – It is a numerical or graphic way to summarize data obtained from a sample Sampling Error • It is reasonable to assume that each sample will give you a fairly accurate picture of its population. • However, samples are not likely to be identical to their parent populations. • This difference between a sample and its population is known as Sampling Error. • Furthermore, no two samples will be identical in all their characteristics. Hypothesis Testing • Hypothesis testing is a way of determining the probability that an obtained sample statistic will occur, given a hypothetical population parameter. • The Research Hypothesis specifies the predicted outcome of a study. • The Null Hypothesis typically specifies that there is no relationship in the population. Practical vs. Statistical Significance • The terms “significance level” or “level of significance” refers to the probability of a sample statistic occurring as a result of sampling error. • Significance levels most commonly used in educational research are the .05 and .01 levels. • Statistical significance and practical significance are not necessarily the same since a result of statistical significance does not mean that it is practically significant in an educational sense. Correlational Research The Nature of Correlational Research • Correlational Research is also known as Associational Research. • Relationships among two or more variables are studied without any attempt to influence them. • Investigates the possibility of relationships between two variables. • There is no manipulation of variables in Correlational Research. Purpose of Correlational Research • Correlational studies are carried out to explain important human behavior or to predict likely outcomes (identify relationships among variables). • If a relationship of sufficient magnitude exists between two variables, it becomes possible to predict a score on either variable if a score on the other variable is known (Prediction Studies). • The variable that is used to make the prediction is called the predictor variable (independent). Purpose of Correlational Research (cont.) • The variable about which the prediction is made is called the criterion variable (dependent). • Both scatterplots and regression lines are used in correlational studies to predict a score on a criterion variable • A predicted score is never exact. Through a prediction equation, researchers use a predicted score and an index of prediction error (standard error of estimate) to conclude if the score is likely to be incorrect. Correlation Coefficients • Pearson product-moment correlation – The relationship between two variables of degree. • Positive: As one variable increases (or decreases) so does the other. • Negative: As one variable increases the other decreases. – Magnitude or strength of relationship • -1.00 to +1.00 – Correlation does not equate to causation Positive Correlation Negative Correlation No Correlation Prediction Using a Scatterplot More Complex Correlational Techniques • Multiple Regression • Technique that enables researchers to determine a correlation between a criterion variable and the best combination of two or more predictor variables • Discriminant Function Analysis • Rather than using multiple regression, this technique is used when the criterion value is categorical • Factor Analysis • Allows the researcher to determine whether many variables can be described by a few factors • Path Analysis • Used to test the likelihood of a causal connection among three or more variables • Structural Modeling • Sophisticated method for exploring and possibly confirming causation among several variables Path Analysis Diagram What Do Correlational Coefficients Tell Us? • The meaning of a given correlation coefficient depends on how it is applied. • Correlation coefficients below .35 show only a slight relationship between variables. • Correlations between .40 and .60 may have theoretical and/or practical value depending on the context. • Only when a correlation of .65 or higher is obtained, can one reasonably assume an accurate prediction. • Correlations over .85 indicate a very strong relationship between the variables correlated. Magnitude of effect • Coefficient of determination – Also known as • Shared variance • The proportion of variance accounted for • Percentage of variance accounted for • Coefficient of nondetermination – Proportion of variance not accounted for r 2 1 r 2 Threats to Internal Validity in Correlational Research • Subject characteristics • Mortality • Instrument decay • Testing • History • Data collector characteristics • Data collector bias Causal-Comparative Research Similarities and Differences Between Causal-Comparative and Correlational Research • Similarities – Associative research – Attempt to explain phenomena of interest – Seek to identify variables that are worthy of later exploration through experimental research – Neither permits the manipulation of variables – Attempt to explore causation • Differences – Causal studies compare two or more groups of subjects – Causal studies involve at least one categorical variable – Causal studies often compare averages or use crossbreak tables instead of scatterplots and correlations coefficients The Basic Causal-Comparative Designs Independent variable Dependent variable I C (Group possesses characteristic) O (Measurement) II –C (Group does not possess characteristic) O (Measurement) I C1 (Group possesses characteristic 1) O (Measurement) II C2 (Group possesses characteristic 2) O (Measurement) Group (a) (b) Examples of the Basic CausalComparative Design Threats to Internal Validity in Causal-Comparative Research • Subject Characteristics • The possibility exists that the groups are not equivalent on one or more important variables • One way to control for an extraneous variable is to match subjects from the comparison groups on that variable • Creating or finding homogeneous subgroups would be another way to control for an extraneous variable • The third way to control for an extraneous variable is to use the technique of statistical matching Other Threats • • • • Loss of subjects Instrumentation History Maturation • Data collector bias • Regression Evaluating Threats to Internal Validity in Causal-Comparative Studies • Involves three sets of steps as shown below: – Step 1: What specific factors are known to affect the variable on which groups are being compared or may be logically be expected to affect this variable? – Step 2: What is the likelihood of the comparison groups differing on each of these factors? – Step 3: Evaluate the threats on the basis of how likely they are to have an effect and plan to control for them.