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Confidence Interval for a
Correlation:
ZumaStat calculates the confidence interval and significance test for both
a Pearson correlation coefficient and a squared Pearson correlation
coefficient.
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Confidence Interval for a
Squared Multiple Correlation:
ZumaStat calculates the confidence interval and significance test for a
squared multiple correlation correlation.
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Confidence Interval for a
Partial Correlation:
ZumaStat calculates the confidence interval and significance test for both
a partial correlation and a squared partial correlation.
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Confidence Interval for a
Correlation Difference:
ZumaStat calculates a significance test and a confidence interval
for the difference between two correlations.
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Confidence Interval for a
Multiple Correlation Difference:
ZumaStat calculates a significance test and a confidence interval
for the difference between two multiple correlations calculated on
independent groups.
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Confidence Interval for a
Partial Correlation Difference:
ZumaStat calculates a significance test and a confidence interval
for the difference between two partial correlations calculated on
independent groups.
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Power Analysis:
ZumaStat offers power analysis for several
common statistical tests. Importantly, it permits you to conduct a power
analysis on a coefficient in a multiple regression model. Many researchers
conduct power analysis on the omnibus effects for an equation. But interest
usually is focused on what happens at the level of the coefficients within
the model. ZumaStat helps to ensure that you will have adequate statistical
power for such tests. You can also do power analysis on correlations,
difference between correlations, multiple correlations, hierarchical
regression and tests of group differences in regression coefficients. The
utilities allow you to either specify a desired level of power and an effect
size and determine the sample size you will need, or you can specify a
sample sizer and an effect size and obtain the statistical power associated
with it.
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Analysis of Precision:
Some researchers focus not on hypothesis testing but rather on magnitude
estimation. The focus in this approach is estimating the magnitude of an
effect rather than whether that effect is zero or not. When designing a
study, you want to make sure that your magnitude estimates will be
sufficiently precise and not subject to too much random error. ZumaStat
offers utilities for determining sample sizes you should use to minimize
sampling error. You provide a confidence interval width that you want to
achieve and ZumaStat suggests a sample size for you.
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Test of Within Equation Coefficients:
Researchers sometimes may desire to test the significance of the difference
between two regression coefficients from the same regression equation. This
could be done with the unstandardized coefficients (assuming common metrics)
or standardized coefficients. ZumaStat does all possible pairwise
comparisons of regression coefficients within a regression equation for both
the unstandardized and standardized case.
Many investigators often make statements about the relative importance of
predictors based on examination of their relative standardized regression
coefficients. However, rarely do they conduct formal significance tests of
the differences. This routine permits you to do so.
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Hierarchical Regression:
ZumaStat conducts a hierarchical F test or a test associated with a change
in R square when you add predictors to a regression equation. You
enter the squared Rs, the sample size and the number of predictors and
ZumaStat performs the relevant F test.
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All Possible Regressions:
ZumaStat provides a program for computing all possible regression equations
for up to 10 predictors, as an alternative to stepwise regression. It is
accomplished with a few simple clicks from SPSS.
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r to Z transforms:
Enter a correlation and get it's Fisher's Z transform. Enter a
Fisher's Z transform and get the correlation coefficient.
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Common Language Effect
Size:
The Common Language Effect Size (CLES) is a popular and intuitive index of
the strength of a relationship. It tells you the probability that an
individual who is above average on X will also be above average on Y.
It also reflects the probability that a randomly selected individual who has
a score higher than another individual on X will also have a score higher
than that individual on Y. ZumaStat converts a correlation coefficient
to a CLES.
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Interaction Analysis:
ZumaStat calculates standard errors and confidence intervals for slopes of
Y on X at different values of Z in interaction models involving continuous
variables.
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Point of Intersection:
Given two non-parallel regression lines, each representing the regression
of Y onto X, one often wants to know the exact value of X where the lines
intersect. This is important for the analysis of cross-over
interactions. You input the sloes and intercepts of the two lines and ZumaStat calculates
the point of intersection.
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Exploratory Interaction
Analysis:
If you use SPSS, ZumaStat offers a simple to use program for conducting
exploratory analyses for interactions. Suppose one wants to determine
if the slope of Y on X varies as a function of Z. ZumaStat will
segregate your data and calculate the slope of Y on X at each value of Z and
then report the various slopes to you as a function of Z in a table (along
with sample sizes). Trends in the slope changes can then be discerned.
This is a useful and simple to use exploratory method that relies on
principles of bandwidth regression.
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Polynomial Regression:
Enter a quadratic polynomial regression equation and ZumaStat calculates
the lowest point on the predicted curve, the highest point on the predicted
curve and the rate of change between any two points on the curve. It
also generates a plot of the curve in Excel. It also does this for cubic
regression.
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Equivalence Testing:
It is well known that in null hypothesis testing, one can never accept the
null hypothesis. This means that you can never state that two or more
groups are equivalent on some outcome. Yet investigators often desire to
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There is a large literature on statistical equivalence
testing that addresses this issue. The first step, and one of the more
controversial ones, is to specify the value of a difference that defines a
trivial effect. This is referred to as an "equivalence threshold.” Any
absolute difference in the population less than the absolute value of the equivalence
threshold is deemed trivial and not of interest. For example, it might be
argued that a meaningful correlation difference between two populations
is .10 or greater, hence .10 becomes the threshold value. If a population
correlation difference for two groups is between –.10 and +.10, then the two groups
can be said to be “functionally equivalent” because the difference in
correlations is trivial. On the other hand, if the absolute population
correlation
difference between the two groups is larger than .10, then the difference is
meaningful.
Equivalence testing uses confidence interval based approaches
to test if population differences are within the range specified by a
threshold value. ZumaStat allows you to enter simple summary statistics
(such as correlations and sample sizes) and conducts formal equivalence
tests to determine group equivalence. Equivalence tests are provided for
comparing two groups on correlations, partial correlations, multiple
correlations and they also are used to determine if correlations, partial
correlations and multiple correlations can be deemed to be trivial.
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Meta-Analysis:
ZumaStat provides for meta analyses of correlation coefficients. It applies both fixed effects and random effects models for
averaging these statistics. It also generates a Q test for
homogeneity of correlations.
In addition, it provides programs for conducting contrast analyses of
different study groupings to determine if the average effect size for one
group of studies differs from the average effect size for another group of
studies. ZumaStat also provides utilities for weighted least squares
regression models predicting effect sizes from study characteristics that
are continuous or categorical in nature.
Finally, ZumaStat offers an extensive set of programs for conducting power
analysis in meta-analysis (see the complete list of programs in the 'List
of Programs' section). These include power analysis for the test of
average correlations, power analysis for contrasts between groups of
studies on average correlations, power analysis of WLS regression analyses
of correlations and power analysis for the Q test of homogeneity for
correlations for a fixed effects model.
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Reliability Adjustments:
ZumaStat offers a utility to adjust a correlation for unreliability,
telling you what the correlation would be if the measures were completely
reliable. ZumaStat also offers a utility to calculate the
reliability of a difference score based on the reliability of its
constituent parts. |
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Excel
Graphs: ZumaStat
will create an Excel scatterplot template that you can then easily place
data within. The creation
of the scatterplot is quick and painless. All you need is Excel.
ZumaStat also offers an Excel graphics connection for plotting several
regression lines on a graph to illustrate different slopes for interaction
analyses. Plots for quadratic and cubic regression models are also
provided. |
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Excel
Graphs for Regression Equations: ZumaStat
also creates Excel graphs to illustrate regression lines. You can plot up
to five equations on a single graph. Construction of the graphs is
simple and this is a great tool for illustrating interaction effects.
ZumaStat also includes a plotting strategy for regression equations with
quadratic and cubic terms. |
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Mediation Analysis:
Analysis of mediation requires several test of significance, as described
in the classic paper by Baron and Kenny (1986). ZumaStat
systematically helps you evaluate mediation based on the newer analytical
methods described by MacKinnon and his colleagues. These tests have more
statistical power than the classic tests suggested by Baron and Kenny. |
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Predicted Values in
Regression:
Enter a regression equation once and then calculate predicted values for a wide range of predictor
profiles, up to 1,000 predictor variables. |
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Confidence Intervals for a Path Coefficient:
You provide ZumaStat with a path coefficient and its standard error and
ZumaStat calculates its confidence interval. |
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Calculations from Summary Statistics:
Sometimes summary statistics are reported in articles (means, standard
deviations and correlations) and you want to perform analyses other than
what the author performed. ZumaStat will perform a complete multiple
regression analysis from such summary statistics for up to 10 predictor
variables. ZumaStat also does partial correlation, semi-partial
correlation and simple bivariate regression from summary statistics.
These utilities also are useful as a learning or teaching device. For
example, to see how collinearity affects different statistics, run the
multiple regression program several times varying the correlations among
the predictors. |
