Is AMOS necessary to get a PhD?

Source: IBM SPSS. Click to enlarge image

This is a big question posted by most participants of OUM's 3rd colloquium held in KL from Aug 7 - 8, 2010.

So should you use AMOS? Ask yourself these questions:

First, do your models have multiple regressions that are embedded within each other? Second, do you have latent variables in your models? If you answered yes to both or either of these questions, you probably need to apply structural equation models. AMOS may be the best option for you.

Generally there are many statistical tools available to assist us in analyzing our data. Among the popular ones are SPSS, LISREL, MPlus and MStat. How about AMOS? Well actually AMOS is an add-on of SPSS, which most of us are familiar with. Before we dwell further, lets look at some of the writings about AMOS.

What Is AMOS?

AMOS (Analysis of Moment Structures) is an add-on module for SPSS. It is designed primarily for structural equation modeling, path analysis, and covariance structure modeling, though it may be used to perform linear regression analysis and ANOVA and ANCOVA. It features an intuitive graphical interface that allows the analyst to specify models by drawing them. It also has a built-in bootstrapping routine and superior handling of missing data. It reads data from a number of sources, including MS Excel spreadsheets and SPSS databases.

Source: http://www.utexas.edu/its/help/spss/526

Overview of AMOS:



Build structural equation models with more accuracy than standard multivariate statistics models using intuitive drag-and-drop functionality

IBM® SPSS® Amos (formerly Amos™) gives you the power to easily perform structural equation modeling (SEM). Using SEM, you can quickly create models to test hypotheses and confirm relationships among observed and latent variables – moving beyond regression to gain additional insight.
Structural equation modeling (SEM) can take your research to the next level

When you conduct research, you’re probably already using factor and regression analyses in your work. Structural equation modeling (sometimes called path analysis) can help you gain additional insight into causal models and explore the interaction effects and pathways between variables. SEM lets you more rigorously test whether your data supports your hypothesis. You create more precise models – setting your research apart and increasing your chances of getting published.

IBM SPSS Amos is the perfect modeling tool for a variety of purposes, including:

* Psychology – Develop models to understand how drug, clinical, and art therapies affect mood
* Medical and healthcare research – Confirm which of three variables –confidence, savings, or research – best predicts a doctor’s support for prescribing generic drugs
* Social sciences – Study how socioeconomic status, organizational membership, and other determinants influence differences in voting behavior and political engagement
* Educational research – Evaluate training program outcomes to determine impact on classroom effectiveness
* Market research – Model how customer behavior impacts new product sales or analyze customer satisfaction and brand loyalty
* Institutional research – Study how work-related issues affect job satisfaction
* Business planning – Create econometric and financial models and analyze factors affecting workplace job attainment
* Program evaluation – Evaluate program outcomes or behavioral models using SEM to replace traditional stepwise regression

Features and Benefits:

IBM SPSS Amos makes structural equation modeling (SEM) easy and accessible

IBM SPSS Amos builds models that more realistically reflect complex relationships because any numeric variable, whether observed (such as non-experimental data from a survey) or latent (such as satisfaction and loyalty) can be used to predict any other numeric variable.

Its rich, visual framework lets you to easily compare, confirm and refine models.

Quickly build graphical models using IBM SPSS Amos’ simple drag-and-drop drawing tools. Models that used to take days to create are just minutes away from completion. And once the model is finished, simply click your mouse and assess your model’s fit. Then make any modifications and print a presentation-quality graphic of your final model.

Its approach to multivariate analysis encompasses and extends standard methods – including regression, factor analysis, correlation and analysis of variance. New capabilities include bootstrapping of user-defined functions of the model parameter for increased model stability.

Obtain Bayesian estimates of model parameters and other quantities

Bayesian analysis enables you to apply your subject-area expertise or business insight to improve estimates by specifying an informative prior distribution. Markov chain Monte Carlo (MCMC) is the underlying computational method for Bayesian estimation. The MCMC algorithm is fast and the MCMC tuning parameter can be adjusted automatically.

Perform estimation with ordered categorical and censored data Create a model based on non-numerical data without having to assign numerical scores to the data. Or work with censored data without having to make assumptions other than the assumption of normality. You can also impute numerical values for ordered-categorical and censored data. The resulting dataset can be used as input to programs that require complete numerical data.

Impute missing values or latent variable scores

Choose from three data imputation methods: regression, stochastic regression, or Bayesian. Use regression imputation to create a single completed dataset. Use stochastic regression imputation or Bayesian imputation to create multiple imputed datasets. You can also impute missing values or latent variable scores.

See how easy it is to use IBM SPSS Amos:

1. Select a data file:

Click on picture to enlarge image

Input data from a variety of file formats (IBM® SPSS® Statistics, Micosoft® Excel, text files, or many others). Select grouping variables and group values. IBM SPSS Amos also accepts data in a matrix format if you’ve computed a correlation or covariance matrix.

2. Specify your model:

Click to enlarge image

Use drag-and-drop drawing tools to quickly specify your path diagram model. Click on objects in the path diagram to edit values, such as variable names and parameter values. Or simply drag variable names from the variable list to the object in the path diagram to specify variables in your model.

3. Select analysis properties:


Select the analysis properties you wish to examine, such as standardized estimates of parameters or squared multiple correlations. Constrain parameters for more precise models by directly specifying path coefficients

4. View output:

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IBM SPSS Amos output provides standardized or un-standardized estimates of covariances and regression weights as well as a variety of model fit measures. Hotlinks in the help system link to explanations of the analysis in plain English.

Click to enlarge image

IBM SPSS Amos output provides standardized or un-standardized estimates of covariances and regression weights as well as a variety of model fit measures. Hotlinks in the help system link to explanations of the analysis in plain English.

5. Assess your model’s fit:

Click to enlarge image

Make any modifications to your model and print publication-quality output.

System Requirements:

Operating system

* Microsoft® Windows® Vista® or Windows XP

Hardware

* Memory: 256 MB RAM minimum
* Minimum free drive space: 125 MB

Software

* Internet Explorer 6
* Microsoft .NET Framework 3.5 SP1 or higher


Source: http://www.spss.com/amos/


Example of an application of AMOS:

Antecedents and consequences of parasocial interaction with sport athletes and identification with sport teams.

RESULTS

Due to the limited sample size, the items of each construct were first summated to create single-item indicators. Structural equation modelling was then used to test the above hypotheses. The parsimony of this partially mediated structural model was appraised with the maximum likelihood method of parameter estimation via AMOS 4.0.

The overall model fit for the proposed model was not satisfactory ([chi square] =90.935, df= 20, p<.00 l; NFI =.984; RFI=.955; IFI=.987; TFI=.965; CFI=.987; RMSEA=. 134), since RMSEA is higher than .08 (Browne & Cudeck, 1993). Thus the original model was rejected and the modification indices were subsequently examined as a way of improving the model fit (Anderson & Gerbing, 1988). The modification indices showed that the model fit could be improved if the error (or unique) terms of parasocial interaction and team identification were allowed to correlate (the chi-square statistics would decrease by at least 53.456). Each error term represents much more than random fluctuations due to measurement error. It stands for anything else on which each variable may depend, but which are not measured in the model (Arbuckle & Wothke, 1999). Since parasocial interaction with favorite athletes and sport fan team identification both cover fans' sport involvement, it is reasonable to correlate their error terms. After the model modification, the goodness of fit statistics demonstrated that the modified model provided a much stronger fit ([chi square] =27.015, df= 19,p=. 104; NFI=.995; RFI=.986; IFI=.999; TFI=.996; CFI=.999; RMSEA=.046). Figure 2 shows the modified model and Table 2 reports the parameter estimates for causal paths.

Further reading: http://www.thefreelibrary.com/Antecedents+and+consequences+of+parasocial+interaction+with+sport...-a0227279262

Click here for the guide on AMOS 16:



http://www.amosdevelopment.com/download/Amos%2016.0%20User%27s%20Guide.pdf

Independent Samples T-Test and Levene's Test

What it does:

The Independent Samples T Test compares the mean scores of two groups on a given variable.

Where to find it:

Under the Analyze menu, choose Compare Means, the Independent Samples T Test. Move your dependent variable into the box marked "Test Variable." Move your independent variable into the box marked "Grouping Variable." Click on the box marked "Define Groups" and specify the value labels of the two groups you wish to compare.

Assumptions:

-The dependent variable is normally distributed. You can check for normal distribution with a Q-Q plot.
-The two groups have approximately equal variance on the dependent variable. You can check this by looking at the Levene's Test. See below.
-The two groups are independent of one another.

Hypotheses:

Null: The means of the two groups are not significantly different.
Alternate: The means of the two groups are significantly different.

SPSS Output

Following is a sample output of an independent samples T test. We compared the mean blood pressure of patients who received a new drug treatment vs. those who received a placebo (a sugar pill).



First, we see the descriptive statistics for the two groups. We see that the mean for the "New Drug" group is higher than that of the "Placebo" group. That is, people who received the new drug have, on average, higher blood pressure than those who took the placebo.



Next, we see the Levene's Test for Equality of Variances. This tells us if we have met our second assumption (the two groups have approximately equal variance on the dependent variable). If the Levene's Test is significant (the value under "Sig." is less than .05), the two variances are significantly different. If it is not significant (Sig. is greater than .05), the two variances are not significantly different; that is, the two variances are approximately equal. If the Levene's test is not significant, we have met our second assumption. Here, we see that the significance is .448, which is greater than .05. We can assume that the variances are approximately equal.

Finally, we see the results of the Independent Samples T Test. Read the TOP line if the variances are approximately equal. Read the BOTTOM line if the variances are not equal. Based on the results of our Levene's test, we know that we have approximately equal variance, so we will read the top line.



Our T value is 3.796.

We have 10 degrees of freedom.

There is a significant difference between the two groups (the significance is less than .05).

Therefore, we can say that there is a significant difference between the New Drug and Placebo groups. People who took the new drug had significantly higher blood pressure than those who took the placebo.

Source: http://www.wellesley.edu/Psychology/Psych205/indepttest.html

What statistical analysis should I use?

By Professor James D. Leeper, Ph.D

The following table shows general guidelines for choosing a statistical analysis. We emphasize that these are general guidelines and should not be construed as hard and fast rules. Usually your data could be analyzed in multiple ways, each of which could yield legitimate answers. The table below covers a number of common analyses and helps you choose among them based on the number of dependent variables (sometimes referred to as outcome variables), the nature of your independent variables (sometimes referred to as predictors). You also want to consider the nature of your dependent variable, namely whether it is an interval variable, ordinal or categorical variable, and whether it is normally distributed (see What is the difference between categorical, ordinal and interval variables? for more information on this). The table then shows one or more statistical tests commonly used given these types of variables (but not necessarily the only type of test that could be used) and links showing how to do such tests using SAS, Stata and SPSS.



Details at: http://www.ats.ucla.edu/stat/mult_pkg/whatstat/default.htm

One-Way ANOVA

By Susan Archambault (Psychology Department, Wellesley College)

What it does:

The One-Way ANOVA compares the mean of one or more groups based on one independent variable (or factor).

Where to find it:

Under the Analyze menu, choose Compare Means, then choose One-Way ANOVA. Move all dependent variables into the box labeled "Dependent List," and move the independent variable into the box labeled "Factor." Click on the button labeled "Options," and check off the boxes for Descriptives and Homogeneity of Variance. Click on the box marked "Post Hoc" and choose the appropriate post hoc comparison. Generally, for Psych 205 students, you can follow this rule: If there are equal numbers of cases in each group, choose Tukey. If there are not equal numbers of cases in each group, choose Bonferroni.

Assumptions:
-The dependent variable(s) is normally distributed. You can check for normal distribution with a Q-Q plot.
-The two groups have approximately equal variance on the dependent variable. You can check this by looking at the Levene's Test. See below.

Hypotheses:
Null: There are no significant differences between the groups' mean scores.
Alternate: There is a significant difference between the groups' mean scores.

SPSS Output

Following is a sample output of a One-Way ANOVA. We compared the mean level of prejudice of first-years, sophomores, juniors, and seniors. Mean level of prejudice is our dependent variable, and year in college is our independent variable.

First, we see the descriptive statistics for each of the 4 years in college.



It looks like first-years have the highest mean level of prejudice, and seniors have the lowest mean level of prejudice.

Next we see the results of the Levene's Test of Homogeneity of Variance.



This tells us if we have met our second assumption (the groups have approximately equal variance on the dependent variable). If the Levene's Test is significant (the value under "Sig." is less than .05), the two variances are significantly different. If it is not significant (Sig. is greater than .05), the two variances are not significantly different; that is, the two variances are approximately equal. If the Levene's test is not significant, we have met our second assumption. Here, we see that the significance is .435, which is greater than .05. We can assume that the variances are approximately equal. We have met our second assumption.

Finally, we see the results of our One-Way ANOVA:



Our F value is 3.110.

Our significance value is .027.

There is a significant difference between the two groups (the significance is less than .05).

Therefore, we can say that there is a significant difference between first-years, sophomores, juniors, and seniors on their level of prejudice.

We can look at the results of the Post-Hoc Comparisons to see exactly which pairs of groups are significantly different.

SPSS notes a significant difference with an asterisk (*). We can see that first-years and sophomores are significantly different than seniors.

Source: http://www.wellesley.edu/Psychology/Psych205/anova.html

How to convert from a two-tailed to a one-tailed test?

When you conduct a test of statistical significance, whether it is from a correlation, an ANOVA, regression or some other kind of test, you are given a p-value somewhere in the output. Unless you specify otherwise, this p-value (almost always) is for a two-tailed test. But what does this mean, really, and how can you convert this into a one-tailed test?

What is a two-tailed test?

First let's start with the meaning of a two-tailed test. If you are using a significance level of .05, a two-tailed test divides this value in half, meaning that .025 is in each tail of the distribution. While this makes it more difficult to achieve statistical significance, this means that you do not have make a prediction about the direction of the effect. In other words, the effect can be either positive or negative and still be statistically significant.

Converting a two-tailed to a one-tailed test

The easiest way to convert a two-tailed test into a one-tailed test is to divide in half the p-value provided in the output. In the output below, under the headings Ha: diff < 0 and Ha: diff > 0 are the results for the one-tailed tests, and the results in the middle, under the heading Ha: diff != 0 (which means that the difference is not equal to 0), is the two-tailed test. We can look at the output below and see that this is done to create the appropriate p-value for the predicted direction (see bolded portion). Notice, though, that there is no way to get a statistically significant result in the other direction. You need to make the directional prediction before you conduct the test, and if the result goes in the opposite direction, even if it would have been statistically significant with a two-tailed test, it is not statistically significant. To report the p-value in this direction, you would take the p-value from the one-tailed test and subtract that from 1. You can see this in the example below, 1 - .0001 = .9999.

Two-sample t test with equal variances

------------------------------------------------------------------------------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
male | 91 50.12088 1.080274 10.30516 47.97473 52.26703
female | 109 54.99083 .7790686 8.133715 53.44658 56.53507
---------+--------------------------------------------------------------------
combined | 200 52.775 .6702372 9.478586 51.45332 54.09668
---------+--------------------------------------------------------------------
diff | -4.869947 1.304191 -7.441835 -2.298059
------------------------------------------------------------------------------
Degrees of freedom: 198
Ho: mean(male) - mean(female) = diff = 0
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
t = -3.7341 t = -3.7341 t = -3.7341
P < t = 0.0001 P > |t| = 0.0002 P > t = 0.9999

Why would you use a one-tailed test?

Many researchers argue that it is very rarely appropriate to do a one-tailed test. However, if it is logically impossible for the result to go in one direction (for example, for the mean height of 5-year-olds to be smaller than the mean height of 15-year-olds) or if such a result is of no practical importance (for example, the experimental medicine is less effective than currently used medicine), then a one-tailed test is appropriate. Also note that a one-tailed test has more power than a two-tailed test. In other words, while the probability of a Type I error is the same (whatever alpha level is used), the probability of a Type II error is reduced. Hence, you are less likely to miss a statistically significant effect with a one-tailed test (assuming that you have accurately predicted the direction of the effect).

Another example

Now let's try an example using a regression analysis. Let's say that we have social studies, math and science test scores from high school students and that we predict that the science scores will positively predict the social studies scores. In other words, we want to conduct a one-tailed test, and we will be using the distribution immediately above. Below is the output.

Source | SS df MS Number of obs = 200
-------------+------------------------------ F( 2, 197) = 46.58
Model | 7363.62077 2 3681.81039 Prob > F = 0.0000
Residual | 15572.5742 197 79.0486001 R-squared = 0.3210
-------------+------------------------------ Adj R-squared = 0.3142
Total | 22936.195 199 115.257261 Root MSE = 8.8909
------------------------------------------------------------------------------
socst | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
science | .2191144 .0820323 2.67 0.008 .0573403 .3808885
math | .4778911 .0866945 5.51 0.000 .3069228 .6488594
_cons | 15.88534 3.850786 4.13 0.000 8.291287 23.47939
------------------------------------------------------------------------------

To get the p-value for the one-tailed test of the variable science (assuming that the effect is going in the predicted direction, which you can tell by the sign of the coefficient), you would divide the .008 by 2, yielding .004. If you had made your prediction in the opposite direction, the p-value would have been 1 - .004 = .996.

Source: http://www.businessanalysis.cn/x/html/62/t-2562.html

What are the differences between one-tailed and two-tailed tests?

When you conduct a test of statistical significance, whether it is from a correlation, an ANOVA, a regression or some other kind of test, you are given a p-value somewhere in the output. If your test statistic is symmetrically distributed, you can select one of three alternative hypotheses. Two of these correspond to one-tailed tests and one corresponds to a two-tailed test. However, the p-value presented is (almost always) for a two-tailed test. But how do you choose which test? Is the p-value appropriate for your test? And, if it is not, how can you calculate the correct p-value for your test given the p-value in your output?

What is a two-tailed test?

First let's start with the meaning of a two-tailed test. If you are using a significance level of 0.05, a two-tailed test allots half of your alpha to testing the statistical significance in one direction and half of your alpha to testing statistical significance in the other direction. This means that .025 is in each tail of the distribution of your test statistic. When using a two-tailed test, regardless of the direction of the relationship you hypothesize, you are testing for the possibility of the relationship in both directions. For example, we may wish to compare the mean of a sample to a given value x using a t-test. Our null hypothesis is that the mean is equal to x. A two-tailed test will test both if the mean is significantly greater than x and if the mean significantly less than x. The mean is considered significantly different from x if the test statistic is in the top 2.5% or bottom 2.5% of its probability distribution, resulting in a p-value less than 0.05.



What is a one-tailed test?

Next, let's discuss the meaning of a one-tailed test. If you are using a significance level of .05, a one-tailed test allots all of your alpha to testing the statistical significance in the one direction of interest. This means that .05 is in one tail of the distribution of your test statistic. When using a one-tailed test, you are testing for the possibility of the relationship in one direction and completely disregarding the possibility of a relationship in the other direction. Let's return to our example comparing the mean of a sample to a given value x using a t-test. Our null hypothesis is that the mean is equal to x. A one-tailed test will test either if the mean is significantly greater than x or if the mean is significantly less than x, but not both. Then, depending on the chosen tail, the mean is significantly greater than or less than x if the test statistic is in the top 5% of its probability distribution or bottom 5% of its probability distribution, resulting in a p-value less than 0.05. The one-tailed test provides more power to detect an effect in one direction by not testing the effect in the other direction. A discussion of when this is an appropriate option follows.

When is a one-tailed test appropriate?

Because the one-tailed test provides more power to detect an effect, you may be tempting to use a one-tailed test whenever you have a hypothesis about the direction of an effect. Before doing so, consider the consequences of missing an effect in the other direction. Imagine you have developed a new drug that you believe is an improvement over an existing drug. You wish to maximize your ability to detect the improvement, so you opt for a one-tailed test. In doing so, you fail to test for the possibility that the new drug is less effective than the existing drug. The consequences in this example are extreme, but they illustrate a danger of inappropriate use of a one-tailed test.

So when is a one-tailed test appropriate? If you consider the consequences of missing an effect in the untested direction and conclude that they are negligible and in no way irresponsible or unethical, then you can proceed with a one-tailed test. For example, imagine again that you have developed a new drug. It is cheaper than the existing drug and, you believe, no less effective. In testing this drug, you are only interested in testing if it less effective than the existing drug. You do not care if it is significantly more effective. You only wish to show that it is not less effective. In this scenario, a one-tailed test would be appropriate.





When is a one-tailed test NOT appropriate?

Choosing a one-tailed test for the sole purpose of attaining significance is not appropriate. Choosing a one-tailed test after running a two-tailed test that failed to reject the null hypothesis is not appropriate, no matter how "close" to significant the two-tailed test was. Using statistical tests inappropriately can lead to invalid results that are not replicable and highly questionable--a steep price to pay for a significance star in your results table!

Deriving a one-tailed test from two-tailed output

The default among statistical packages performing tests is to report two-tailed p-values. Because the most commonly used test statistic distributions (standard normal, Student's t) are symmetric about zero, most one-tailed p-values can be derived from the two-tailed p-values.

Below, we have the output from a two-sample t-test in Stata. The test is comparing the mean male score to the mean female score. The null hypothesis is that the difference in means is zero. The two-sided alternative is that the difference in means is not zero. There are two one-sided alternatives that one could opt to test instead: that the male score is higher than the female score (diff > 0) or that the female score is higher than the male score (diff < 0). In this instance, Stata presents results for all three alternatives. Under the headings Ha: diff < 0 and Ha: diff > 0 are the results for the one-tailed tests. In the middle, under the heading Ha: diff != 0 (which means that the difference is not equal to 0), are the results for the two-tailed test.



Note that the test statistic, -3.7341, is the same for all of these tests. The two-tailed p-value is P > |t|. This can be rewritten as P(>3.7341) + P(< -3.7341). Because the t-distribution is symmetric about zero, these two probabilities are equal: P > |t| = 2 * P(< -3.7341). Thus, we can see that the two-tailed p-value is twice the one-tailed p-value for the alternative hypothesis that (diff < 0). The other one-tailed alternative hypothesis has a p-value of P(>-3.7341) = 1-(P<-3.7341) = 1-0.0001 = 0.9999. So, depending on the direction of the one-tailed hypothesis, its p-value is either 0.5*(two-tailed p-value) or 1-0.5*(two-tailed p-value) if the test statistic symmetrically distributed about zero.

In this example, the two-tailed p-value suggests rejecting the null hypothesis of no difference. Had we opted for the one-tailed test of (diff > 0), we would fail to reject the null because of our choice of tails.

The output below is from a regression analysis in Stata. Unlike the example above, only the two-sided p-values are presented in this output.



For each regression coefficient, the tested null hypothesis is that the coefficient is equal to zero. Thus, the one-tailed alternatives are that the coefficient is greater than zero and that the coefficient is less than zero. To get the p-value for the one-tailed test of the variable science having a coefficient greater than zero, you would divide the .008 by 2, yielding .004 because the effect is going in the predicted direction. This is P(>2.67). If you had made your prediction in the other direction (the opposite direction of the model effect), the p-value would have been 1 - .004 = .996. This is P(<2.67). For all three p-values, the test statistic is 2.67.

Source: http://www.ats.ucla.edu/stat/mult_pkg/faq/general/tail_tests.htm