Chapter 10.docx

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David Nussbaum

Chapter 10 Bar chart 1. Type of graph used to depict frequency distributions 2. Contains solid bars separated by spaces 3. Good for displaying the distribution of variables measured at the nominal level because there is a gap between each category Between groups variance 1. The greater the differences in the means of the different groups, the larger the estimate of variability between groups 2. It is based on how much the individual group means differ from the overall mean for all scores in the experiment a. This overall mean is referred to as the grand mean b. As the differences between each group mean and the grand mean increases, so too will the between group variance 3. Between group variance represents systematic variance due to the manipulation of the independent variable a. Good experimental design seeks to maximize systematic variance by using powerful and effective independent variables that will distinguish the groups Bimodal 1. Has two categories with an equal number of cases that can be considered the model compared to the other categories Central tendency 2. One of three features that define the shape of a distribution 3. Usually summarized with one of three statistics a. Mean b. Median c. Mode 4. To pick which measure of central tendency to use, must look at a. Level of measurement b. Skewness of distribution c. Purpose for which statistic is used Chi square test of independence 1. Chi square a. An inferential statistic used to test hypotheses about relationships between variables in a contingency table 2. Chi square test of independent is also known as a two variable chi square Contingency table 3. Shows how responses to one question (the dependent variable) are distributed within the responses to another question (the independent variable) 4. Constructed to determine whether values of cases on the dependent variable are contingent on the value of those cases on the independent variable Correlation Critical t value 1. T-values for different levels of significance and different degrees of freedom that is taken from a full table Degrees of freedom 1. Determined on the basis of sample size 2. Equal the total number of participants minus the number of groups a. E.g. two groups of 10 = 20 – 2 i. Degrees of freedom = 18 3. Larger sample sizes provide greater degrees of freedom a. This adds to the statistical power of the study i. This is based on the idea that larger sample sizes provide better estimates (lower standard error of estimates) of population parameters than do smaller samples 1. With smaller samples, you will need a larger t-value in order to achieve statistical significance Descriptive statistics 1. Used to describe the variables in a study, both one at a time and in terms of their relations to each other 2. Examples of descriptive statistics a. Age b. Gender c. Socioeconomic status 3. Examples of studies a. Self esteem among college students b. Prevalence of mental illness in the general population 4. This is in comparison to inferential statistics Effect size F-test 1. AKA analysis of variance (ANOVA) Frequency distribution Histogram 1. Frequency distribution of a quantitative variable 2. Allow the researcher to display the distribution of cases across the categories or scores of a variable 3. Graphs have the advantage of providing a picture that is easier to comprehend Inferential statistics 1. Used to estimate characteristics of a population from those you find in a random sample of that population 2. Can also be used to test hypotheses about the relationship between variables a. How likely is it that the relationship found between the independent and dependent variables in the experiment was due to chance? b. How confident can we be that the effect observed was not simply due to chance 3. Inferential statistical tests to help answer these questions such as a. T test b. Chi square test Mean 1. Arithmetic average 2. Takes into account the value of each case in a distribution 3. It is a weighted average 4. Computed by adding up the values of all the cases and dividing by the total number of cases a. Taking into account the value of each case in a distribution 5. Calculation a. Sum of value of cases / number of all cases 6. Can only be used for quantities a. Must reflect an interval or ratio level of measurement Median 7. The position average or the point that divides the distribution in half 8. The 50 percentile 9. Inappropriate for variables measured at the nominal level a. Because their values cannot be put in order  there is no meaningful middle position 10. To determine the median a. Array the distribution of values in numerical order and find the value of the case that has an equal number above and below it b. If it falls between two cases, it is defined as the average of those two cases Mode 11. The most frequent value in a distribution 12. The probability average (it is the most probable value to obtain) 13. The mode is the only measure of central tendency for nominal scales of measurement a. It indicates the most frequently occurring value b. It does not use actual values of a scale, only the frequency of its appearance 14. Used less often than mean and median measures because it can easily give a misleading impression of a distributions central tendency a. E.g. i. Bimodal distributions have two modes 1. Technically speaking, the mode is the MOST frequent, so it would not account for the second most frequent value ii. The mode might fall far from the main clustering of cases in a distribution 1. With such a distribution it would be misleading to say that the variables central tendency was whatever the modal value was 15. Useful for answering questions asking for the most probable value a. E.g. which ethnic group is most common in a given school? Multifactor ANOVA 1. Experimenters often manipulate more than one factor or independent variable simultaneously a. When you have two or more independent variables within the same experiment b. Simplest multifactor ANOVA is the 2x2 ANOVA i. Used for an experiment that simultaneously varies two factors each with two levels 2. In comparison to the simple ANOVA, the mltifactor ANOVA is much more computationally complex given that there are both main and interaction effects that need to be tested 3. The ANOVA formulas will also differ depending on whether a between-subjects or within- subjects design is being used 4. Advantage a. The effects of all independent variables can be tested simultaneously b. Instead of statistically comparing each pair of conditions, levels or groups i. Tests all effects simultaneously, thereby reducing the likelihood of chance findings c. Provides a statistical significance test (F test) for each of the main effects of an experiment as well as their interactions i. Allows us to determine whether each of these effects are due to chance Normal distribution 1. A distribution that results from chance variation around a mean 2. It is symmetric and tapers off in a characteristic shape from its mean 3. If a variable is normally distributed a. 68% of its cases will be between +/- 1 standard deviation from its distribution’s mean b. 95% of its cases will lie between +/- 2 standard deviations from its distribution’s mean 4. This correspondence of the SD to the normal distribution enables us to infer how confident we can be that the mean of a population is within a certain range of the hypothetical population mean 5. 4 steps for computing the confidence limits around a mean a. Calculate standard error b. Decide on the degree of confidence c. Multiply the value of the SE by 1.96 d. Add and subtract the number in step C from the sample mean i. The resulting numbers are the upper and lower confidence limits Null hypothesis 1. In a test of the difference between two means, the null hypothesis states that the population means are equal a. Any differences observed in the study sample merely reflect random error b. Predicts that the independent variable will have no effect on the dependent variable – the intervention will not work c. Runs counter to the theory of the study i. It’s the reverse of what a researcher expects to demonstrate by
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