conversations.from: human
conversations.value: What could be a title for a book about University, Washington, Pittsburgh with the genre: Science & Math, Mathematics?
conversations.from: assistant
conversations.value: A title for this book could be 'Understanding Statistics in the Behavioral Sciences'
conversations.from: human
conversations.value: the first five paragraphs for this book
conversations.from: assistant
conversations.value: Understanding Statistics in the Behavioral Sciences
  A single-factor study, as the name implies, is concerned with the effect of a single research factor on the dependent variable. As such, single-factor studies are among the simplest researchers use. For example, if we confine our attention solely to parental status, then the button-pushing study could be an example of a single-factor study. Moreover, it would be the simplest single-factor between-subjects study possible, one involving only two groups or two levels of the factor. We have already discussed in chapters 8 and how to analyze data from single-factor between-subjects studies when only two groups are involved, but studies involving more than two groups are common. For example, a researcher might want to investigate the effect of three or four different kinds of treatment on patients' neuroticism or the effect of religious background on individual attitudes toward abortion.
  In general terms, the analysis of data from a single-factor study allows us to determine whether knowing the group to which a subject belongs (which could be a self-assigned natural group or an experimenter-assigned experimental group) allows us to make better predictions than otherwise as to how that individual will respond. In statistical terms, the question is whether the proportion of variance accounted for by the research factor is significantly different from zero. The null hypothesis, which claims no effect for the research factor, would predict an R2 of zero. A sample will almost always yield a value of R2 higher than that, but the key statistical question is whether the obtained value of R2 would occur less than 5% of the time just due to the luck of draw, if the population value for R2 really were zero. If the F ratio associated with R2 exceeds the appropriate critical value, we declare the null hypothesis untenable and label our obtained value statistically significant: In other words, we claim a statistically significant effect.
  In order to test the significance of a single research factor, we need some way to represent the group to which each subject belongs. If the single research factor were a quantitative variable, like maternal age, then one predictor variable would suffice and for each subject the value for this variable would be that subject's age. This variable could be entered into a multiple-regression equation, where it would account for one degree of freedom.
  Similarly, if the single research factor were a binary qualitative variable, like parental status (parent vs. nonparent), again one predictor variable would suffice. Parents would be assigned one value, nonparents a second value. As we saw in Exercise 9.4, the values selected to represent the two groups are not critical; the two values must be different and that is all. A binary research factor, then, is represented with one coded variable and hence accounts for one degree of freedom.
  Qualitative research factors comprising more than two groups or levels are handled somewhat differently. The general rule is, a factor with G groups or levels must be represented with G − 1 coded variables. There are several ways to do this, but we emphasize two here: dummy variable coding, because it is so simple, and contrast coding, because contrasts can be interpreted as planned comparisons.
conversations.from: human
conversations.value: Delete the last sentence.
conversations.from: assistant
conversations.value: Understanding Statistics in the Behavioral Sciences
  A single-factor study, as the name implies, is concerned with the effect of a single research factor on the dependent variable. As such, single-factor studies are among the simplest researchers use. For example, if we confine our attention solely to parental status, then the button-pushing study could be an example of a single-factor study. Moreover, it would be the simplest single-factor between-subjects study possible, one involving only two groups or two levels of the factor. We have already discussed in chapters 8 and how to analyze data from single-factor between-subjects studies when only two groups are involved, but studies involving more than two groups are common. For example, a researcher might want to investigate the effect of three or four different kinds of treatment on patients' neuroticism or the effect of religious background on individual attitudes toward abortion.
  In general terms, the analysis of data from a single-factor study allows us to determine whether knowing the group to which a subject belongs (which could be a self-assigned natural group or an experimenter-assigned experimental group) allows us to make better predictions than otherwise as to how that individual will respond. In statistical terms, the question is whether the proportion of variance accounted for by the research factor is significantly different from zero. The null hypothesis, which claims no effect for the research factor, would predict an R2 of zero. A sample will almost always yield a value of R2 higher than that, but the key statistical question is whether the obtained value of R2 would occur less than 5% of the time just due to the luck of draw, if the population value for R2 really were zero. If the F ratio associated with R2 exceeds the appropriate critical value, we declare the null hypothesis untenable and label our obtained value statistically significant: In other words, we claim a statistically significant effect.
  In order to test the significance of a single research factor, we need some way to represent the group to which each subject belongs. If the single research factor were a quantitative variable, like maternal age, then one predictor variable would suffice and for each subject the value for this variable would be that subject's age. This variable could be entered into a multiple-regression equation, where it would account for one degree of freedom.
  Similarly, if the single research factor were a binary qualitative variable, like parental status (parent vs. nonparent), again one predictor variable would suffice. Parents would be assigned one value, nonparents a second value. As we saw in Exercise 9.4, the values selected to represent the two groups are not critical; the two values must be different and that is all. A binary research factor, then, is represented with one coded variable and hence accounts for one degree of freedom.
  Qualitative research factors comprising more than two groups or levels are handled somewhat differently. The general rule is, a factor with G groups or levels must be represented with G − 1 coded variables.
conversations.from: human
conversations.value: another paragraph
conversations.from: assistant
conversations.value: It might seem economical to use only four predictor variables for subject, repeating the S1–S4 pattern for both drug and placebo subjects. Codes for variable A distinguish between drug and placebo groups, so this scheme would also assure a different pattern of predictor variable values for each of the 10 scores. But it would not reflect the reality of the situation. Variable S1, for example, would be coded 1 for both subjects one and six only if they were the same subject, and for the independent groups design they are not.
conversations.from: human
conversations.value: the last two paragraphs
conversations.from: assistant
conversations.value: The first number in each row, N, indicates the number of trials that are categorized either plus or minus. The remaining numbers represent unlikely values for the number of pluses. The column in which the value falls indicates the probability of that or a smaller number of pluses occurring (lower tail), or the probability of that or a larger number of pluses occurring (upper tail), assuming the null hypothesis value of P = 0.5. Probability values for the columns represent selected standard values.
  The first number in each row gives a Z score accurate to the first decimal digit. Subsequent columns provide the second decimal digit. The numbers in the table give the proportion of area under the normal curve to the left of the indicated Z score. For example, the proportion of area to the left of a Z score of −1.96 is.0250 and the proportion of area to the left of a Z score of +2.58 is.9951.
conversations.from: human
conversations.value: Delete the last sentence.
conversations.from: assistant
conversations.value: The first number in each row, N, indicates the number of trials that are categorized either plus or minus. The remaining numbers represent unlikely values for the number of pluses. The column in which the value falls indicates the probability of that or a smaller number of pluses occurring (lower tail), or the probability of that or a larger number of pluses occurring (upper tail), assuming the null hypothesis value of P = 0.5. Probability values for the columns represent selected standard values.
  The first number in each row gives a Z score accurate to the first decimal digit. Subsequent columns provide the second decimal digit. The numbers in the table give the proportion of area under the normal curve to the left of the indicated Z score. For example, the proportion of area to the left of a Z score of −1.96 is.0250 and the proportion of area to the left of a Z score of +2.58 is.