Stats Exam 3 pt 2
If the absolute value of your correlation coefficient is 1, your error in prediction will be:
0
If there is no difference between what is observed and what is expected, your chi-square value will be:
0
What is the difference between a one-sample and a two-sample chi-square test?
A one-sample chi-square test includes only one dimension, whereas a two-sample chi-square test involves two dimensions.
Give an example of a research situation where the one-sample chi-square test would be the most appropriate statistical technique to use.
A researcher wants to answer the question whether political affiliation (i.e., Democrat, Republican, and Independent) is equally distributed across freshman at Yourstate University. A one-sample chi-square test would be used in this situation.
What must be done to categorical variables in order to use them in a regression analysis?
Dummy coding
What is the distance between each data point and the regression line called?
Error of the estimate
Statistics that are not governed by the parameters of the population are referred to as ___________ statistics.
Nonparametric
How do nonparametric statistics differ from parametric statistics?
Nonparametric statistics do not follow the same assumptions or rules as parametric statistics.
Write an equation for a null hypothesis and research hypothesis for a one-sample chi-square test involving three groups.
Null hypothesis H0: P1 = P2 = P3 Research hypothesis H1 : P1 ≠ P2 ≠ P3
Write an equation for a null hypothesis and research hypothesis for a one-sample chi-square test involving four groups.
Null hypothesis H0: P1 = P2 = P3 = P4 Research hypothesis H1 : P1 ≠ P2 ≠ P3 ≠ P4
Which of the following determines the direction of the regression line?
Slope
What does the one-sample chi-square test determine?
The one-sample chi-square test determines if what is observed in a distribution of frequencies would be what is expected to occur by chance.
If the correlation between variable X and variable Y is perfect, what do you know about the prediction?
The prediction will be perfect as well
Which of the following is used to compare the medians from two samples?
The sign test
A two sample chi-square focuses on whether two or more variables are significantly related, or dependent. (T/F)
True
Chi-square is a nonparametric statistical test. (T/F)
True
If you were interested in finding out if there was an association between whether college students were involved in a club on campus or not and the grades they earned, but you only had a letter grade (i.e., A, B, C, D) to use for the analysis, the chi-square test of independence could be used to find out the answer. (T/F)
True
In the SPSS output of a chi-square goodness of fit test, the "Asymp. Sig." is the p value. (T/F)
True
Nonparametric statistics can be preferred when you have sample sizes that are very small (less than 30). (T/F)
True
Which of the following symbols is associated with the independent variable in the regression equation?
X
Which of the following is also known as a regression weight?
b
Based on the formula for a regression line, what does a represent?
y intercept
In calculating a one sample chi-square test, if you had 7 degrees of freedom, your variable would have this number of categories:
8
What can be used at the basis for prediction?
Correlation
Nonparametric statistics are known as _______________.
Distribution-free statistics
In the chi-square test for independence, expected values and observed values are used, just like in the chi-square goodness of fit test. The difference is that in the test of independence there are three dimensions involved instead of one. (T/F)
False
Parametric statistics are preferred when you are analyzing categorical variables. (T/F)
False
If the absolute value of your correlation is very close to 0, your error in prediction will be:
High
What is another name for a regression line?
Line of best fit
A regression equation can be visually represented on a ____________.
Scatter plot
Write a sample research question where the chi-square test of independence would be the most appropriate statistical technique to use.
Students could give any example; the guidelines would be that two variables need to be used, the variables need to be categorical in nature, and they need to be testing for independence (or in the opposite view—testing for association or relatedness).
In the chi-square test of independence, both dimensions need to have at least two levels/ categories to compare, but they could have more. (T/F)
True
Nonparametric statistics incorporate fewer assumptions. (T/F)
True
The chi-square statistic measures the difference between the observed data and what would be expected by chance alone. (T/F)
True
The one sample chi-square focuses on the distribution of a single variable.(T/F)
True
The one sample chi-square test is also called goodness of fit. (T/F)
True
Which of the following nonparametric tests is used to compare the magnitude and direction of differences between two groups?
Wilcoxon rank
How do you interpret X2 (3) = 18.9, p < .05?
X2 represents the test statistic (chi-square) 3 is the number of degrees of freedom 8.9 is the obtained value of chi-square < .05 indicates that the probability is less than 5% on any one test of the null hypothesis that the frequency of votes is equally distributed across all categories. Since we defined .05 as the criterion for the research hypothesis being more attractive than the null hypothesis, our conclusion is that there is a significant difference between the two sets of scores.
How is the symbol Y' interpreted?
Y prime
Which of the following symbols is associated with the y-intercept in the regression equation?
a
The general formula for a regression line is ________.
bX + a = Y'
The regression line is drawn so that it ______________ the distance between itself and each of the points on the predicted (Y) variable.
minimizes
If you are not satisfied with the percent of variability on your criterion variable accounted for by the variability in the predictor variable, and if you have an idea of other variables that could account for the variability in the criterion variable, you could run a __________________.
multiple regression
Which of the following is the correct formula for calculating the degrees of freedom for a one-sample chi-square?
r - 1
Which of the following is like a standard deviation for all error scores in regression?
standard error of the estimate
Why is the regression line called the line of best fit?
Because the regression line minimizes the distance between each individual point and the regression line.
Which of the following is the most commonly used nonparametric test?
Chi-Square
Which of the following is the point at which the regression line crosses the y-axis?
Intercept
If the correlation between X and Y is equal to -1.0, what do we know about the prediction of Y by X?
It's perfect
Which of the following nonparametric tests is used to compare two independent samples?
Mann-Whitney U
What must be used to examine an outcome that is predicted from two independent variables?
Multiple regression
When computing a predicted value, you first:
Multiply the slope by the value of the independent variable
When conducting a chi-squared test, the categories of your variable(s) must be:
Mutually exclusive
In a scatter plot, if all data points were aligned along a 45° angle, your correlation would be:
Perfect
A positive trend line is associated with what type of slope?
Positive slope
If you are trying to predict Y scores from X scores, X is referred to as the __________.
Predictor variable
Based on the formula for a regression line, what does b represent?
Slope of a line
A two-sample chi-square is also known as a ________.
Test of independence
When adding additional predictors to a regression analysis, you should try to find predictors that are related to _____________ but not ______________.
The dependent variable, the independent variables
How is the regression line related to the correlation coefficient?
The regression line is a direct reflection of the correlation between two variables. The correlation coefficient is represented as a value, while the regression line is a visual representation.
what is the standard error of estimate?
The standard error of estimate is the measurement for how well (or poorly) one variable predicts another variable. When these differences from a distribution of data points are averaged, the standard error of estimate reflects how good the prediction is.
A perfect correlation would translate into perfect prediction in the case of linear regression. (T/F)
True
Error in prediction (error of estimate) is calculated as the distance between each individual data point and the regression line. (T/F)
True
In linear regression, a regression equation is determined, which can be used to plot a regression line. (T/F)
True
In linear regression, the outcome variable is called the criterion or dependent variable. (T/F)
True
One of the values of regression is that you can use data from past events (such as the existing relationship between two variables) and then apply it later with different cases when you have knowledge of only one variable. (T/F)
True
The standard error of estimate tells you how much imprecision there is overall in regard to the predictive power of the linear regression analysis. (T/F)
True
What is the level of risk associated with rejecting a true null hypothesis called?
Type I error
Why do we use Y' and not Y in the regression equation?
We use Y' because it is the predicted value of Y, not the actual Y value.
Which of the following is the Greek symbol chi?
χ
Which of the following is the correct formula for the one-sample chi-square?
χ2 = Σ (E - O)2 / E
If you have 30 respondents identifying their political preference (i.e., Democrat, Republican, Independent), what would the expected frequency be for each category?
10
If there are three categories for which you are calculating a one-sample chi-square, what are the degrees of freedom?
2
Using the regression formula with a slope = .704 and intercept = .719, what would the predicted college GPA be for a student whose current high school GPA = 3.2?
2.97
If you have 100 respondents identifying their region of residence (i.e., north, south, mid-west, or west), what would the expected frequency be for each category?
25
In order to meet the sample assumption associated with parametric statistics, how many subjects do you need?
30
If you have 100 respondents identifying their political affiliation (i.e. Democrat, Republican, or Independent) what would the expected frequency be for each category?
33
If there are five categories for which you are calculating a one-sample chi-square, what are the degrees of freedom?
4
Using the regression formula with a slope = 1000 and intercept = 25000, what would the predicted income be for someone who has 20 years of education?
45000
Using the regression formula with a slope = 2000 and intercept = 15000, what would the predicted income be for someone who has 16 years of education?
47000
In calculating a one sample chi-square test, if you had 4 degrees of freedom, your variable would have this number of categories:
5
If you have 100 respondents identifying their gender, what would the expected frequency be for each category?
50
What does a unique contribution mean for a variable?
A unique contribution means the variable explains differences in the predicted variable that the other variables used did not.
In multiple regression, added variables must be related to the outcome variable but ______________ with/of each other.
A) Related B) Independent C) Uncorrelated *D) Both B and C
When determining the number of predictor variables to use to predict a criterion variable, you need to keep these guidelines in mind:
A) The resources you have B) The theoretical history of potential variables C) Added predictor and criterion variables should have a relationship *D) All of the above
When computing a predicted value, your second step is to:
Add the intercept, or a, to the value of step one
Which of the following nonparametric tests is used to determine if the number of occurrences across categories is random?
Chi-square
To predict one variable from another, you must first:
Compute the correlation
More accurate predictions are associated with
Correlations having higher absolute values
If you are trying to predict Y scores from X scores, Y is referred to as the ________.
Criterion variable
The obtained value must be compared against which of the following?
Critical value
In regression, the criterion variable is also known as the ____________.
Dependent variable
Prediction through regression is the computation of past outcomes based on knowledge of present ones. (T/F)
False
Simple linear regression consists of a type of regression in which more than one independent variable is included in the analysis. (T/F)
False
Standard error of estimate is computed as the variance of all values for error in prediction. (T/F)
False
The error of estimate and the error of prediction are not the same thing.
False
The higher the absolute value of the correlation coefficient, the less accurate the prediction is of one variable based on the other variable. (T/F)
False
The regression line reflects the best estimate of predicted scores for the independent variable based on levels of the dependent variable. (T/F)
False
Which of the following computes the exact probability of outcomes in a 2 x 2 table?
Fisher's exact test
Which of the following compares the overall difference between two or more independent samples on more than one dimension?
Friedman two-way ANOVA
A one-sample chi-square is also known as a ________.
Goodness of fit test
In a one-sample chi-square test, if your respondents are distributed very unequally across the levels of your variable, your chi-square value will be:
High
Write a sample research question where the McNemar test would be the most appropriate statistical technique to use.
How effective is a phone call to undecided candidates on their voting for a particular issue?
Write a sample research question where the Kolmogorov-Smirnov test would be the most appropriate statistical technique to use.
How representative is a set of judgments—made about specific children—of the entire elementary school to which they go?
Which of the following nonparametric tests is used to determine if scores from a sample came from a specified population?
Kolmogorov-Smirnov
Which of the following compares the overall difference between two or more independent samples?
Kruskal-Wallis one-way ANOVA
What statistical technique is used to make predictions of future outcomes based on present data?
Linear regression
What is linear regression?
Linear regression is a statistical procedure used to predict a Y score from an X score based on the correlation between a distribution of X scores and a distribution of Y scores.
How does linear regression differ from multiple regression?
Linear regression is a statistical technique using a regression equation to determine the "line of best fit" from which a Y score can be predicted from an X score. Multiple regression has the same goal as linear regression (determining the "line of best fit"), but uses two or more independent variables rather than one independent variable (which is what is used in linear regression).
Does the dependent variable need to be a continuous variable?
No, the dependent variable can be categorical. It will need to be dummy coded to be used in the regression equation.
Which of the following is used to illustrate the "best guess" as to the predicted Y variable score based on X?
Regression line
Which of the following nonparametric tests is used to examine the correlation between ranks?
Spearman rank
What does the regression line represent?
The regression line represents four things. First it is the "line of best fit" which minimizes that distance between the line and each of the points of the predicted variable on a scatterplot. Second, the line allows us to predict one score given the value of the independent variable. The regression line also represents the distance between each individual point and the regression line, called the error in prediction/error in estimate. Finally, the line allows us to see how far off each of the data points are from a perfect correlation. If the correlation were perfect, all the data points would be lined up along a 45° angle.
Linear regression uses correlations between variables as the basis for the prediction of the value of one variable based on the value of another. (T/F)
True
The one sample chi-square is used to determine whether the distribution of a single categorical variable is significantly different from that which would be expected by chance. (T/F)
True
In the multiple regression formula, what does X2 represent?
Value of the second independent variable
Write a sample research question where the Fisher's exact test would be the most appropriate statistical technique to use.
What is the exact likelihood of getting six heads on a toss of six coins?
What important guideline should you keep in mind when choosing independent variables for multiple regression?
When using a multiple regression model, the predictor variables should be independent and unrelated with one another, but related to the outcome variable.
How would you represent the predicted score of Y based on a known value of X?
Y'
Which of the following symbols is associated with the predicted score in the regression equation?
Y'
What is the equation for a regression line?
Y' = bX + a
Which of the following is the correct formula for linear regression?
Y' = bX + a
Which of the following symbols is associated with the slope in the regression equation?
b
When in SPSS dialog box setting up the regression line, you can also choose options to get __________________ that will give you the boundaries within you can see the probability as to how good the prediction is.
confidence intervals
When using two predictor variables, these variables should be ____________.
independent
Which of the following is the symbol for summation?
Σ
