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What Are We Going To Cover Today:1. Institutional Review Board (IRB);2. Population and Sample;3. Descriptive Statistics: Measures of Central Tendency: Mean, Median, Mode, Range, Correlation Coefficient, Standard Deviation, and Distribution;4. Inferential Statistics: t-test, z-test, Analysis of Variance (ANOVA), and multivariate methods like factor analysis, and meta-analysis.
What is an Institutional Review Board (IRB)? and What is its purpose? An IRB of a private of public research entity is a federally-regulated committee charged with assuring that research involving human subjects is ethical, equitable, and humane. To this end, an IRB conducts both an initial review of a proposed research protocol as well as ongoing review of approved research. During the initial review, an IRB will consider whether a proposed research protocol meets established criteria for minimizing risks to human subjects. Based on this consideration, an IRB may approve or deny the protocol, or may alternatively condition approval upon certain changes to the protocol.
If a Teacher was conducting Action Research in his or her classroom, who or what in the school district would be the default IRB? The Board of Education
Population and Sample • The best sampling is probability sampling, because it increases the likelihood of obtaining samples that are representative of the population. • Probability sampling (Representative samples) • Probability samples are selected in such a way as to be representative of the population. They provide the most valid or credible results because they reflect the characteristics of the population from which they are selected
There are two types of probability samples: random and stratified:Random SampleThe term random has a very precise meaning. Each individual in the population of interest has an equal likelihood of selection. This is a very strict meaning. The assumption of an equal chance of selection means that sources such as a telephone book or voter registration lists are not adequate for providing a random sample of a community. WHYYYYYYYY?????????? The key to random selection is that there is no bias involved in the selection of the sample. Any variation between the sample characteristics and the population characteristics is only a matter of chance.Stratified SampleA stratified sample is a mini-reproduction of the population. Before sampling, the population is divided into characteristics of importance for the research. For example, if 38% of the population is college-educated, then 38% of the sample is randomly selected from the college-educated population. Stratified samples are as good as or better than random samples, but they require a fairly detailed advance knowledge of the population characteristics, and therefore are more difficult to construct.
Figure It Out: • You want to draw a stratified sample of 50 children from a school containing 70% girls and 30% boys. 35 Girls and 15 Boys
Inferential and Descriptive Statistics • Use descriptive statistics to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data. With descriptive statistics you are simply describing what is, what the data shows. • Use inferential statistics to make inferences from our data to more general conditions; • With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone. • Use inferential statistics to try to infer from the sample data what the population might think. • Or, use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study. • Researchers link inferential analyses to specific research questions or hypotheses
Main Types of Descriptive Statistics • Distribution: summary of the frequency of individual values or ranges of values for a variable. For instance, a typical way to describe the distribution of college students is by year in college, listing the number or percent of students at each of the four years. Or, we describe gender by listing the number or percent of males and females. “Frequency Table = histogram or bar chart” • Mean = arithmetic average • Median = the score found at the exact middle of the set of values. One way to compute the median is to list all scores in numerical order, and then locate the score in the center of the sample. • Mode = most frequently occurring value in the set of scores. To determine the mode, you might again order the scores as shown above, and then count each one. • Dispersion: refers to the spread of the values around the central tendency. • Range = refers to the spread of the values around the central tendency. • Standard Deviation = a more accurate and detailed estimate of dispersion because an outlier can greatly exaggerate the range. The Standard Deviation shows the relation a set of scores has to the mean of the sample.
Descriptive Statistics (cont.) • Correlation: A correlation is a single number that describes the degree of relationship between two variables. • Correlation Coefficient = r • r will always be between -1.0 and +1.0. if the correlation is negative, we have a negative relationship; if it's positive, the relationship is positive. • Null Hypothesis: r = 0 • Alternative Hypothesis: r <> 0 • A one tailed hypothesis specifies a directional relationship between groups. Here we are saying that we expect children in Samoa to be further from their mothers than children in Belize. We not only state that there will be differences between the groups but we specify in which direction the differences will exist. Anytime we expect a relationship to be directional (i.e. to go one specific way) we are using a one-tailed hypothesis. This is the opposite of a two-tailed hypothesis. A two tailed hypothesis would predict that there was a difference between groups, but, would make no reference to the direction of the effect. one and two tailed tests • As in all hypothesis testing, you need to first determine the significance level. Using the common significance level of alpha = .05 means a test where the odds that the correlation is a chance occurrence is no more than 5 out of 100.
Descriptive Statistics (cont.) • The Effect of Skew on the Mean and Median • The distribution shown below has a positive skew. The mean is larger than the median. The distribution shown below has a negative skew. The mean is smaller than the median.
Inferential Statistics • T - test - The t-test is the most commonly used method to evaluate the differences in means between two groups. For example, the t-test can be used to test for a difference in test scores between a group of patients who were given a drug and a control group who received a placebo; use with n<30. • Z – test = Same as the t-test but used with n>30. • ANOVA (Analysis of Variance) (f-test)= one-way Analysis of Variance which extended the analysis of groups from two (t) to three or more (F). One-sample, two-sample, and one-way ANOVA designs all involve a single independent (controlled) variable and a single dependent (measured) variable. • Factorial ANOVA designs which extend the number of independent variables in a study. Factorial designs can involve two independent variables (two-way), or three independent variables (three-way) or more. • “interaction” refers to the synergistic impact between independent variables on the dependent variable in an experiment. • When we extend a one-way ANOVA to a Multivariate ANOVA (MANOVA), we add one or more dependent variables to a design. A one-factor MANOVA consists of one independent variable (treatment) and tests two or more dependent variables (measurements). • A multi-factor MANOVA tests two or more independent variables against two or more dependent variables (i.e., combines factorial and multivariate designs).
Meta- versus Factor Analysis • Meta Analysis refers to a research strategy where instead of conducting new research with participants, the researchers examine the results of several previous studies. This is done with the purpose of gaining greater confidence in the results because of the larger pool of participants, as long as steps are taken to avoid errors that may have existed in the original studies. • Factor Analysis is a type of statistical procedure that is conducted to identify clusters or groups of related items (called factors) on a test. For example, when you take a multiple choice Introductory Psychology test, a factor analysis can be done to see what types of questions you did best on and worst on (maybe they did best on factual types of questions but really poorly on conceptual types of questions).