Contents

- 1 Mẹo về What would you use to determine whether significant differences were observed between all level of your independent variable? Mới Nhất
- 2 Introduction
- 3 About the hsb data file
- 4 One sample t-test
- 5 One sample median test
- 6 Binomial test
- 7 Chi-square goodness of fit
- 8 Two independent samples t-test
- 9 Wilcoxon-Mann-Whitney test
- 10 Chi-square test
- 11 See also
- 12 Fisher’s exact test
- 13 One-way ANOVA
- 14 See also
- 15 Kruskal Wallis test
- 16 Paired t-test
- 17 Wilcoxon signed rank sum test
- 18 McNemar test
- 19 One-way repeated measures ANOVA
- 20 See also
- 21 Repeated measures logistic regression
- 22 Factorial ANOVA
- 23 See also
- 24 Friedman test
- 25 Ordered logistic regression
- 26 See also
- 27 Factorial logistic regression
- 28 See also
- 29 Correlation
- 30 See also
- 31 Simple linear regression
- 32 See also
- 33 Non-parametric correlation
- 34 Simple logistic regression
- 35 See also
- 36 Multiple regression
- 37 See also
- 38 Analysis of covariance
- 39 See also
- 40 Multiple logistic regression
- 41 See also
- 42 Discriminant analysis
- 43 See also
- 44 One-way MANOVA
- 45 See also
- 46 Multivariate multiple regression
- 47 Canonical correlation
- 48 Factor analysis
- 49 See also
- 49.1 How do you know if there is a significant difference in ANOVA?
- 49.2 What is an ANOVA test used for?
- 49.3 What statistical analysis should I use to compare two groups?
- 49.4 What does a one
- 49.5 Video What would you use to determine whether significant differences were observed between all level of your independent variable? ?
- 49.6 Share Link Down What would you use to determine whether significant differences were observed between all level of your independent variable? miễn phí

## Mẹo về What would you use to determine whether significant differences were observed between all level of your independent variable? Mới Nhất

Quý khách đang tìm kiếm từ khóa What would you use to determine whether significant differences were observed between all level of your independent variable? được Cập Nhật vào lúc : 2022-10-18 00:25:14 . Với phương châm chia sẻ Bí kíp về trong nội dung bài viết một cách Chi Tiết 2022. Nếu sau khi Read tài liệu vẫn ko hiểu thì hoàn toàn có thể lại Comments ở cuối bài để Ad lý giải và hướng dẫn lại nha.

## Introduction

This page shows how to perform a number of statistical tests using SPSS. Each section gives a brief description of the aim of the statistical test, when it is used, an example showing the SPSS commands and SPSS (often abbreviated) output with a brief

interpretation of the output. You can see the page Choosing the Correct Statistical Test for a table that shows an overview of when each test is appropriate to use. In deciding which test is appropriate to use, it is important to consider the type of variables that you have (i.e., whether your variables are categorical, ordinal or interval and whether they are normally distributed), see

What is the difference between categorical, ordinal and interval variables? for more information on this.

Nội dung chính

- IntroductionAbout the hsb data fileOne sample t-testOne sample median testBinomial testChi-square goodness of fitTwo independent samples t-testWilcoxon-Mann-Whitney testChi-square testFisher’s exact testOne-way ANOVAKruskal Wallis testPaired t-testWilcoxon signed

rank sum testMcNemar testOne-way repeated measures ANOVARepeated measures logistic regressionFactorial ANOVAFriedman testOrdered logistic regressionFactorial logistic regressionCorrelationSimple linear regressionNon-parametric correlationSimple logistic regressionMultiple regressionAnalysis of covarianceMultiple logistic regressionDiscriminant analysisOne-way MANOVAMultivariate multiple regressionCanonical correlationFactor analysisHow do you know if there is a significant difference in ANOVA?What is an ANOVA test used for?What statistical analysis should I use to compare two groups?What does a one

## About the hsb data file

Most of the examples in this page will use a data file called hsb2, high school and beyond. This data file contains 200 observations from a

sample of high school students with demographic information about the students, such as their gender (female), socio-economic status (ses) and ethnic background (race). It also contains a number of scores on standardized tests, including tests of reading (read), writing (write), mathematics (math) and social studies (socst). You can get the hsb data file by clicking on

hsb2.

## One sample t-test

A one sample t-test allows us to test whether a sample mean (of a normally distributed interval variable) significantly differs from a hypothesized value. For example, using the hsb2 data file, say we wish to test

whether the average writing score (write) differs significantly from 50. We can do this as shown below.

t-test

/testval = 50

/variable = write.

The mean of the variable write for this particular sample of students is 52.775, which is

statistically significantly different from the test value of 50. We would conclude that this group of students has a significantly higher mean on the writing test than 50.

## One sample median test

A one sample median test allows us to test whether a sample median differs significantly from a hypothesized value. We will use the same variable, write, as we did in the

one sample t-test example above, but we do not need to assume that it is interval and normally distributed (we only need to assume that **write** is an ordinal variable).

nptests

/onesample test (write) wilcoxon(testvalue = 50).

## Binomial test

A one sample binomial test allows us to test whether the proportion of successes on a two-level categorical dependent variable significantly differs from a hypothesized value. For example, using the

hsb2 data file, say we wish to test whether the proportion of females (female) differs significantly from 50%, i.e., from .5. We can do this as shown below.

npar tests

/binomial (.5) = female.

The results indicate that there is no statistically significant difference

(p. = .229). In other words, the proportion of females in this sample does not significantly differ from the hypothesized value of 50%.

## Chi-square goodness of fit

A chi-square goodness of fit test allows us to test whether the observed proportions for a categorical variable differ from hypothesized proportions. For example, let’s suppose that we believe that the general population consists of 10% Hispanic, 10% Asian, 10%

African American and 70% White folks. We want to test whether the observed proportions from our sample differ significantly from these hypothesized proportions.

npar test

/chisquare = race

/expected = 10 10 10 70.

These results show that racial

composition in our sample does not differ significantly from the hypothesized values that we supplied (chi-square with three degrees of freedom = 5.029, p. = .170).

## Two independent samples t-test

An independent samples t-test is used when you want to compare the means of a normally distributed interval dependent variable for two independent groups. For example, using the

hsb2 data file, say we wish to test whether the mean for write is the same for males and females.

t-test groups = female(0 1)

/variables = write.

Because the standard deviations for the two groups are similar (10.3 and 8.1), we will use the “equal variances assumed” test. The results indicate that there is a statistically significant difference between the mean writing score for males and females (t = -3.734, p. = .000). In other words, females have a statistically significantly higher mean

score on writing (54.99) than males (50.12).

See also

- SPSS Learning Module: An overview of statistical tests in SPSS

## Wilcoxon-Mann-Whitney test

The Wilcoxon-Mann-Whitney test is a non-parametric analog to the independent samples t-test and can be used when you do not assume that the dependent

variable is a normally distributed interval variable (you only assume that the variable is least ordinal). You will notice that the SPSS syntax for the Wilcoxon-Mann-Whitney test is almost identical to that of the independent samples t-test. We will use the same data file (the hsb2 data file) and the same variables in this example as we did in the

independent t-test example above and will not assume that write, our dependent variable, is normally distributed.

npar test

/m-w = write by female(0 1).

The results suggest that there is a statistically significant difference between the underlying distributions of the write scores of males and the write scores of females (z = -3.329, p. = 0.001).

See also

- FAQ: Why is the Mann-Whitney significant when the medians are equal?

## Chi-square test

A chi-square test is used when you want to see if there is a relationship between two categorical variables. In SPSS, the chisq option is used on the statistics subcommand of the

crosstabs command to obtain the test statistic and its associated p.-value. Using the hsb2 data file, let’s see if there is a relationship between the type of school attended (schtyp) and students’ gender (female). Remember that the chi-square test assumes that the expected value for each cell is five or higher. This assumption is easily met in the examples below.

However, if this assumption is not met in your data, please see the section on Fisher’s exact test below.

crosstabs

/tables = schtyp by female

/statistic = chisq.

These results indicate that there is no statistically significant relationship between the

type of school attended and gender (chi-square with one degree of freedom = 0.047, p. = 0.828).

Let’s look another example, this time looking the linear relationship between gender (female) and socio-economic status (ses). The point of this example is that one (or both) variables may have more than two levels, and that the variables do not have to have the same number of levels. In this example, female has two levels (male and female) and ses

has three levels (low, medium and high).

crosstabs

/tables = female by ses

/statistic = chisq.

Again we find that there is no statistically significant relationship between the variables (chi-square with two degrees of freedom = 4.577, p. =

0.101).

## See also

- SPSS Learning Module: An Overview of Statistical Tests in SPSS

## Fisher’s exact test

The Fisher’s exact test is used when you want to conduct a chi-square test but one or more of your cells has an expected frequency of five or less. Remember that the chi-square test assumes that

each cell has an expected frequency of five or more, but the Fisher’s exact test has no such assumption and can be used regardless of how small the expected frequency is. In SPSS unless you have the SPSS Exact Test Module, you can only perform a Fisher’s exact test on a 2×2 table, and these results are presented by default. Please see the results from the chi squared example above.

## One-way ANOVA

A one-way analysis of variance

(ANOVA) is used when you have a categorical independent variable (with two or more categories) and a normally distributed interval dependent variable and you wish to test for differences in the means of the dependent variable broken down by the levels of the independent variable. For example, using the hsb2 data file, say we wish to test whether the mean of write differs between the three

program types (prog). The command for this test would be:

oneway write by prog.

The mean of the dependent variable differs significantly among the levels of program type. However, we do not know if the difference is between only two of the levels or all three of the levels. (The F test for the Model is the same as the F test for

prog because prog was the only variable entered into the model. If other variables had also been entered, the F test for the Model would have been different from prog.) To see the mean of write for each level of program type,

means tables = write by prog.

From this we can see that the students in the academic program have

the highest mean writing score, while students in the vocational program have the lowest.

## See also

- SPSS Textbook Examples: Design and Analysis, Chapter 7SPSS Textbook Examples: Applied Regression Analysis, Chapter

8SPSS FAQ: How can I do ANOVA contrasts in SPSS?SPSS Library: Understanding and Interpreting Parameter Estimates in Regression and ANOVA

## Kruskal Wallis test

The Kruskal Wallis test is used when you have one independent variable with two or more levels and an ordinal dependent variable. In other words, it is the non-parametric version of ANOVA and a generalized form of the Mann-Whitney test method since it permits two or more groups. We will use the same data file as the one way ANOVA example above (the

hsb2 data file) and the same variables as in the example above, but we will not assume that write is a normally distributed interval variable.

npar tests

/k-w = write by prog (1,3).

If some of the scores receive tied ranks, then a correction factor is used, yielding a slightly different value of chi-squared. With or without ties, the results indicate that there is a statistically significant difference among the three type of programs.

## Paired t-test

A paired (samples)

t-test is used when you have two related observations (i.e., two observations per subject) and you want to see if the means on these two normally distributed interval variables differ from one another. For example, using the hsb2 data file we will test whether the mean of read is equal to the mean of write.

t-test pairs = read with write (paired).

These results indicate that the mean of read is not statistically significantly different from the mean of write (t = -0.867, p. = 0.387).

## Wilcoxon signed

rank sum test

The Wilcoxon signed rank sum test is the non-parametric version of a paired samples t-test. You use the Wilcoxon signed rank sum test when you do not wish to assume that the difference between the two variables is interval and normally distributed (but you do assume the difference is ordinal). We will use the same example as above, but we will not assume that the difference between read and write is interval and normally distributed.

npar test

/wilcoxon = write with read (paired).

The results suggest that there is not a statistically significant difference between read and write.

If you believe the differences between read and write were not

ordinal but could merely be classified as positive and negative, then you may want to consider a sign test in lieu of sign rank test. Again, we will use the same variables in this example and assume that this difference is not ordinal.

npar test

/sign = read with write (paired).

We conclude that no statistically significant difference was found (p.=.556).

## McNemar test

You would perform McNemar’s test if you were interested in the marginal frequencies of two binary outcomes. These binary outcomes may be the same outcome variable on matched pairs (like a case-control study)

or two outcome variables from a single group. Continuing with the hsb2 dataset used in several above examples, let us create two binary outcomes in our dataset: himath and hiread. These outcomes can be considered in a two-way contingency table. The null hypothesis is that the proportion of students in the himath group is the same as the proportion of students in

hiread group (i.e., that the contingency table is symmetric).

compute himath = (math>60).

compute hiread = (read>60).

execute.

crosstabs

/tables=himath BY hiread

/statistic=mcnemar

/cells=count.

McNemar’s chi-square statistic suggests that there is not a statistically significant difference in the proportion of

students in the himath group and the proportion of students in the hiread group.

## One-way repeated measures ANOVA

You would perform a one-way repeated measures analysis of variance if you had one categorical independent variable and a normally distributed interval dependent variable that was repeated least twice for each subject. This is the equivalent of the paired samples t-test, but allows for two or more

levels of the categorical variable. This tests whether the mean of the dependent variable differs by the categorical variable. We have an example data set called rb4wide, which is used in Kirk’s book Experimental Design. In this data set, y is the dependent variable, a is the repeated measure and s is the variable that indicates the subject number.

glm y1 y2 y3 y4

/wsfactor a(4).

You will notice that this output gives four different p.-values.

The output labeled “sphericity assumed” is the p.-value (0.000) that you would get if you assumed compound symmetry in the variance-covariance matrix. Because that assumption is often not valid, the three other p.-values offer various corrections (the Huynh-Feldt, H-F, Greenhouse-Geisser, G-G and Lower-bound). No matter which p.-value you use, our results indicate that we have a statistically significant effect of a the .05 level.

## See also

- SPSS Textbook Examples from Design and Analysis: Chapter 16SPSS Library: Advanced Issues in Using and Understanding SPSS MANOVASPSS Code

Fragment: Repeated Measures ANOVA

## Repeated measures logistic regression

If you have a binary outcome measured repeatedly for each subject and you wish to run a logistic regression that accounts for the effect of multiple measures from single subjects, you can perform a repeated measures logistic regression. In SPSS, this can be done using the GENLIN command and indicating binomial as the probability distribution

and logit as the link function to be used in the model. The exercise data file contains 3 pulse measurements from each of 30 people assigned to 2 different diet regiments and 3 different exercise regiments. If we define a “high” pulse as being over 100, we can then predict the probability of a high pulse using diet regiment.

GET FILE=’C:mydatahttps://stats.idre.ucla.edu/wp-content/uploads/2022/02/exercise.sav’.GENLIN highpulse (REFERENCE=LAST)

BY diet (order = DESCENDING)

/MODEL diet

DISTRIBUTION=BINOMIAL

LINK=LOGIT

/REPEATED SUBJECT=id CORRTYPE = EXCHANGEABLE.

These results indicate that diet is not statistically significant (Wald Chi-Square = 1.562, p. = 0.211).

## Factorial ANOVA

A factorial ANOVA has two or more categorical independent variables (either with or without the interactions) and a single normally distributed

interval dependent variable. For example, using the hsb2 data file we will look writing scores (write) as the dependent variable and gender (female) and socio-economic status (ses) as independent variables, and we will include an interaction of **female** by **ses**. Note that in SPSS, you do not need to have the interaction term(s) in your

data set. Rather, you can have SPSS create it/them temporarily by placing an asterisk between the variables that will make up the interaction term(s).

glm write by female ses.

These results indicate that the overall model is statistically significant (F = 5.666, p. = 0.00). The variables female and ses are also statistically significant (F = 16.595, p. = 0.000 and F = 6.611, p. = 0.002, respectively). However, that interaction between female and ses is not

statistically significant (F = 0.133, p. = 0.875).

## See also

- SPSS Textbook Examples from Design and Analysis: Chapter 10SPSS FAQ: How can I do tests of simple main effects in SPSS?SPSS FAQ: How do I plot ANOVA cell means in SPSS?SPSS Library: An Overview of SPSS GLM

## Friedman test

You perform a Friedman test when you have one within-subjects independent variable with two or more levels and a

dependent variable that is not interval and normally distributed (but least ordinal). We will use this test to determine if there is a difference in the reading, writing and math scores. The null hypothesis in this test is that the distribution of the ranks of each type of score (i.e., reading, writing and math) are the same. To conduct a Friedman test, the data need to be in a long format. SPSS handles this for you, but in other statistical packages you will have to

reshape the data before you can conduct this test.

npar tests

/friedman = read write math.

Friedman’s chi-square has a value of 0.645 and a p.-value of 0.724 and is not statistically significant. Hence, there is no evidence that

the distributions of the three types of scores are different.

## Ordered logistic regression

Ordered logistic regression is used when the dependent variable is ordered, but not continuous. For example, using the hsb2 data file we will create an ordered variable called write3. This variable will have the values 1, 2

and 3, indicating a low, medium or high writing score. We do not generally recommend categorizing a continuous variable in this way; we are simply creating a variable to use for this example. We will use gender (female), reading score (read) and social studies score (socst) as predictor variables in this model. We will use a logit link and on the print subcommand we have requested the parameter estimates, the (model) summary statistics and the test

of the parallel lines assumption.

if write ge 30 and write le 48 write3 = 1.

if write ge 49 and write le 57 write3 = 2.

if write ge 58 and write le 70 write3 = 3.

execute.

plum write3 with female read socst

/link = logit

/print = parameter summary tparallel.

The results indicate that the overall model is statistically significant (p. < .000), as are each of the predictor variables (p. < .000). There

are two thresholds for this model because there are three levels of the outcome variable. We also see that the test of the proportional odds assumption is non-significant (p. = .563). One of the assumptions underlying ordinal logistic (and ordinal probit) regression is that the relationship between each pair of outcome groups is the same. In other words, ordinal logistic regression assumes that the coefficients that describe the relationship between, say, the lowest versus all

higher categories of the response variable are the same as those that describe the relationship between the next lowest category and all higher categories, etc. This is called the proportional odds assumption or the parallel regression assumption. Because the relationship between all pairs of groups is the same, there is only one set of coefficients (only one model). If this was not the case, we would need different models (such as a generalized ordered logit model) to describe

the relationship between each pair of outcome groups.

## See also

- SPSS Data Analysis Examples: Ordered logistic regressionSPSS Annotated Output: Ordinal Logistic Regression

## Factorial logistic regression

A

factorial logistic regression is used when you have two or more categorical independent variables but a dichotomous dependent variable. For example, using the hsb2 data file we will use female as our dependent variable, because it is the only dichotomous variable in our data set; certainly not because it common practice to use gender as an outcome variable. We will use type of

program (prog) and school type (schtyp) as our predictor variables. Because prog is a categorical variable (it has three levels), we need to create dummy codes for it. SPSS will do this for you by making dummy codes for all variables listed after the keyword with. SPSS will also create the interaction term; simply list the two variables that will make up the interaction separated by the keyword by.

logistic regression female with prog schtyp prog by schtyp

/contrast(prog) = indicator(1).

The results indicate that the overall model is not statistically significant (LR chi2 = 3.147, p. = 0.677). Furthermore, none of the coefficients are statistically significant either. This shows that

the overall effect of **prog** is not significant.

## See also

- Annotated output for logistic regression

## Correlation

A correlation is useful when you want to see the relationship between two (or more) normally distributed interval variables. For example, using the

hsb2 data file we can run a correlation between two continuous variables, read and write.

correlations

/variables = read write.

In the second example, we will run a correlation between a dichotomous variable, female, and a continuous variable, write. Although it is assumed that the variables are interval and normally distributed, we can include dummy variables when performing correlations.

correlations

/variables = female write.

In the first example above, we see that the correlation between read and write is 0.597. By squaring the correlation and then multiplying by 100, you can determine what percentage of the variability is shared. Let’s round 0.597 to be 0.6, which when squared would be .36, multiplied by 100 would be 36%. Hence read shares about 36% of its variability with write. In the output for the second example, we can see the correlation

between write and female is 0.256. Squaring this number yields .065536, meaning that female shares approximately 6.5% of its variability with write.

## See also

- Annotated output for correlationSPSS Learning Module: An Overview of Statistical Tests

in SPSSSPSS FAQ: How can I analyze my data by categories?Missing Data in SPSS

## Simple linear regression

Simple linear regression allows us to look the linear relationship between one normally distributed interval

predictor and one normally distributed interval outcome variable. For example, using the hsb2 data file, say we wish to look the relationship between writing scores (write) and reading scores (read); in other words, predicting write from read.

regression variables = write read

/dependent = write

/method = enter.

We see that the relationship between write and

read is positive (.552) and based on the t-value (10.47) and p.-value (0.000), we would conclude this relationship is statistically significant. Hence, we would say there is a statistically significant positive linear relationship between reading and writing.

## See also

- Regression With SPSS: Chapter 1 – Simple and Multiple

RegressionAnnotated output for regressionSPSS Textbook Examples: Introduction to the Practice of Statistics, Chapter 10 SPSS Textbook Examples: Regression with Graphics, Chapter 2SPSS Textbook Examples: Applied Regression Analysis, Chapter 5

## Non-parametric correlation

A Spearman correlation is used when one or both of the variables are not assumed to be normally distributed and interval (but are assumed to be ordinal). The values of the variables are converted in ranks and then correlated. In our example, we will look for a relationship between read and write. We will not assume that both of these variables are normal and interval.

nonpar corr

/variables = read write

/print = spearman.

The results

suggest that the relationship between read and write (rho = 0.617, p. = 0.000) is statistically significant.

## Simple logistic regression

Logistic regression assumes that the outcome variable is binary (i.e., coded as 0 and 1). We have only one variable in the hsb2 data file that is coded 0 and 1, and that is

female. We understand that female is a silly outcome variable (it would make more sense to use it as a predictor variable), but we can use female as the outcome variable to illustrate how the code for this command is structured and how to interpret the output. The first variable listed after the logistic command is the outcome (or dependent) variable, and all of the rest of the variables are predictor (or independent) variables. In our example,

female will be the outcome variable, and read will be the predictor variable. As with OLS regression, the predictor variables must be either dichotomous or continuous; they cannot be categorical.

logistic regression female with read.

The results indicate that reading score (read) is not a

statistically significant predictor of gender (i.e., being female), Wald = .562, p. = 0.453. Likewise, the test of the overall model is not statistically significant, LR chi-squared – 0.56, p. = 0.453.

## See also

- Annotated output for logistic regressionSPSS Library: What kind of

contrasts are these?

## Multiple regression

Multiple regression is very similar to simple regression, except that in multiple regression you have more than one predictor variable in the equation. For example, using the hsb2 data file we will predict writing score from gender (female), reading, math, science and social

studies (socst) scores.

regression variable = write female read math science socst

/dependent = write

/method = enter.

The results

indicate that the overall model is statistically significant (F = 58.60, p. = 0.000). Furthermore, all of the predictor variables are statistically significant except for read.

## See also

- Regression with SPSS: Chapter 1 – Simple and Multiple RegressionAnnotated output for regressionSPSS Frequently Asked QuestionsSPSS Textbook Examples: Regression with Graphics, Chapter 3SPSS Textbook Examples: Applied Regression Analysis

## Analysis of covariance

Analysis of covariance is like ANOVA, except in addition to the categorical predictors you also have continuous predictors as well. For example, the one way ANOVA example used write as the

dependent variable and prog as the independent variable. Let’s add read as a continuous variable to this model, as shown below.

glm write with read by prog.

The results indicate that even after adjusting for reading score (read), writing scores still significantly differ by program type (prog), F = 5.867, p. = 0.003.

## See also

- SPSS Textbook Examples from Design and Analysis: Chapter 14SPSS Library: An Overview of SPSS GLMSPSS Library: How

do I handle interactions of continuous and categorical variables?

## Multiple logistic regression

Multiple logistic regression is like simple logistic regression, except that there are two or more predictors. The predictors can be interval variables or dummy variables, but cannot be categorical variables. If you have categorical predictors, they should be coded into one or more dummy variables. We have only one

variable in our data set that is coded 0 and 1, and that is female. We understand that female is a silly outcome variable (it would make more sense to use it as a predictor variable), but we can use female as the outcome variable to illustrate how the code for this command is structured and how to interpret the output. The first variable listed after the logistic regression command is the outcome (or dependent) variable, and all of the rest of the

variables are predictor (or independent) variables (listed after the keyword with). In our example, female will be the outcome variable, and read and **write** will be the predictor variables.

logistic regression female with read write.

These results show that both **read** and

**write** are significant predictors of **female**.

## See also

- Annotated output for logistic regressionSPSS Textbook Examples: Applied Logistic Regression, Chapter 2SPSS Code Fragments: Graphing Results in Logistic Regression

## Discriminant analysis

Discriminant analysis is used when you have one or more normally distributed interval independent variables and a categorical dependent variable. It is a multivariate technique that considers the latent dimensions in the independent

variables for predicting group membership in the categorical dependent variable. For example, using the hsb2 data file, say we wish to use read, write and math scores to predict the type of program a student belongs to (prog).

discriminate groups = prog(1, 3)

/variables = read write math.

Clearly, the SPSS output for this procedure is quite lengthy, and it is beyond the scope of this page to explain all of it. However, the main point is that two canonical variables are identified by the

analysis, the first of which seems to be more related to program type than the second.

## See also

- discriminant function analysisSPSS Library: A History of SPSS Statistical Features

## One-way MANOVA

MANOVA

(multivariate analysis of variance) is like ANOVA, except that there are two or more dependent variables. In a one-way MANOVA, there is one categorical independent variable and two or more dependent variables. For example, using the hsb2 data file, say we wish to examine the differences in read, write and math broken down by program type (prog).

glm read write math by prog.

The students in the different programs differ in their joint distribution of read, write and math.

## See also

- SPSS Library: Advanced Issues in Using and Understanding SPSS MANOVAGLM: MANOVA and MANCOVASPSS Library: MANOVA and GLM

## Multivariate multiple regression

Multivariate multiple regression is used when you have two or more dependent variables that are to be predicted from two or more independent variables. In our example using the hsb2 data file, we will predict write and read from female, math, science and social studies (socst) scores.

glm write read with female math science socst.

These results show that all of the variables in the model have a statistically significant relationship with the joint distribution of write and read.

## Canonical correlation

Canonical correlation is a multivariate technique used to examine the relationship between two groups of variables. For each set of variables, it creates latent variables and looks the relationships among the latent variables. It assumes that all variables in the model are interval and normally distributed. SPSS requires that each of the two groups of variables be separated by the keyword with. There need not

be an equal number of variables in the two groups (before and after the with).

manova read write with math science

/discrim.

* * * * * * A n a l y s i s o f V a r i a n c e — design 1 * * * * * *

EFFECT .. WITHIN CELLS Regression

Multivariate Tests of Significance (S = 2, M = -1/2, N = 97 )

Test Name Value Approx. F Hypoth. DF Error DF Sig. of F

Pillais .59783 41.99694 4.00 394.00 .000

Hotellings 1.48369 72.32964 4.00 390.00 .000

Wilks .40249 56.47060 4.00 392.00 .000

Roys .59728

Note.. F statistic for WILKS’ Lambda is exact.

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

EFFECT .. WITHIN CELLS Regression (Cont.)

Univariate F-tests with (2,197) D. F.

Variable Sq. Mul. R Adj. R-sq. Hypoth. MS Error MS F

READ .51356 .50862 5371.66966 51.65523 103.99081

WRITE .43565 .42992 3894.42594 51.21839 76.03569

Variable Sig. of F

READ .000

WRITE .000

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

Raw canonical coefficients for DEPENDENT variables

Function No.

Variable 1

READ .063

WRITE .049

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

Standardized canonical coefficients for DEPENDENT variables

Function No.

Variable 1

READ .649

WRITE .467

* * * * * * A n a l y s i s o f V a r i a n c e — design 1 * * * * * *

Correlations between DEPENDENT and canonical variables

Function No.

Variable 1

READ .927

WRITE .854

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

Variance in dependent variables explained by canonical variables

CAN. VAR. Pct Var DE Cum Pct DE Pct Var CO Cum Pct CO

1 79.441 79.441 47.449 47.449

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

Raw canonical coefficients for COVARIATES

Function No.

COVARIATE 1

MATH .067

SCIENCE .048

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

Standardized canonical coefficients for COVARIATES

CAN. VAR.

COVARIATE 1

MATH .628

SCIENCE .478

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

Correlations between COVARIATES and canonical variables

CAN. VAR.

Covariate 1

MATH .929

SCIENCE .873

* * * * * * A n a l y s i s o f V a r i a n c e — design 1 * * * * * *

Variance in covariates explained by canonical variables

CAN. VAR. Pct Var DE Cum Pct DE Pct Var CO Cum Pct CO

1 48.544 48.544 81.275 81.275

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

Regression analysis for WITHIN CELLS error term

— Individual Univariate .9500 confidence intervals

Dependent variable .. READ reading score

COVARIATE B Beta Std. Err. t-Value Sig. of t

MATH .48129 .43977 .070 6.868 .000

SCIENCE .36532 .35278 .066 5.509 .000

COVARIATE Lower -95% CL- Upper

MATH .343 .619

SCIENCE .235 .496

Dependent variable .. WRITE writing score

COVARIATE B Beta Std. Err. t-Value Sig. of t

MATH .43290 .42787 .070 6.203 .000

SCIENCE .28775 .30057 .066 4.358 .000

COVARIATE Lower -95% CL- Upper

MATH .295 .571

SCIENCE .158 .418

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

* * * * * * A n a l y s i s o f V a r i a n c e — design 1 * * * * * *

EFFECT .. CONSTANT

Multivariate Tests of Significance (S = 1, M = 0, N = 97 )

Test Name Value Exact F Hypoth. DF Error DF Sig. of F

Pillais .11544 12.78959 2.00 196.00 .000

Hotellings .13051 12.78959 2.00 196.00 .000

Wilks .88456 12.78959 2.00 196.00 .000

Roys .11544

Note.. F statistics are exact.

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

EFFECT .. CONSTANT (Cont.)

Univariate F-tests with (1,197) D. F.

Variable Hypoth. SS Error SS Hypoth. MS Error MS F Sig. of F

READ 336.96220 10176.0807 336.96220 51.65523 6.52329 .011

WRITE 1209.88188 10090.0231 1209.88188 51.21839 23.62202 .000

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

EFFECT .. CONSTANT (Cont.)

Raw discriminant function coefficients

Function No.

Variable 1

READ .041

WRITE .124

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

Standardized discriminant function coefficients

Function No.

Variable 1

READ .293

WRITE .889

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

Estimates of effects for canonical variables

Canonical Variable

Parameter 1

1 2.196

* * * * * * A n a l y s i s o f V a r i a n c e — design 1 * * * * * *

EFFECT .. CONSTANT (Cont.)

Correlations between DEPENDENT and canonical variables

Canonical Variable

Variable 1

READ .504

WRITE .959

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

The output above shows the linear combinations corresponding to the first canonical correlation. At the bottom of the output are the two canonical correlations. These results indicate that the first canonical correlation is .7728. The F-test in this output tests the hypothesis that the first canonical correlation is equal to zero. Clearly, F = 56.4706 is statistically

significant. However, the second canonical correlation of .0235 is not statistically significantly different from zero (F = 0.1087, p. = 0.7420).

## Factor analysis

Factor analysis is a form of exploratory multivariate analysis that is used to either reduce the number of variables in a model or to detect relationships among variables. All variables involved in the factor analysis need to be interval and are assumed to be

normally distributed. The goal of the analysis is to try to identify factors which underlie the variables. There may be fewer factors than variables, but there may not be more factors than variables. For our example using the hsb2 data file, let’s suppose that we think that there are some common factors underlying the various test scores. We will include subcommands for varimax

rotation and a plot of the eigenvalues. We will use a principal components extraction and will retain two factors. (Using these options will make our results compatible with those from SAS and Stata and are not necessarily the options that you will want to use.)

factor

/variables read write math science socst

/criteria factors(2)

/extraction pc

/rotation varimax

/plot eigen.

Communality (which is the opposite of uniqueness) is the proportion of variance of the variable (i.e., read) that is accounted for by all of the factors taken together, and a very low communality can

indicate that a variable may not belong with any of the factors. The scree plot may be useful in determining how many factors to retain. From the component matrix table, we can see that all five of the test scores load onto the first factor, while all five tend to load not so heavily on the second factor. The purpose of rotating the factors is to get the variables to load either very high or very low on each factor. In this example, because all of the variables loaded

onto factor 1 and not on factor 2, the rotation did not aid in the interpretation. Instead, it made the results even more difficult to interpret.

## See also

- SPSS FAQ: What does Cronbach’s alpha mean?

### How do you know if there is a significant difference in ANOVA?

If the F statistic is higher than the critical value (the value of F that corresponds with your alpha value, usually 0.05), then the difference among groups is deemed statistically significant.

### What is an ANOVA test used for?

ANOVA stands for Analysis of Variance. It’s a statistical test that was developed by Ronald Fisher in 1918 and has been in use ever since. Put simply, ANOVA tells you if there are any statistical differences between the means of three or more independent groups. One-way ANOVA is the most basic form.

### What statistical analysis should I use to compare two groups?

The two most widely used statistical techniques for comparing two groups, where the measurements of the groups are normally distributed, are the Independent Group t-test and the Paired t-test.

### What does a one

One-Way ANOVA (“analysis of variance”) compares the means of two or more independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different. One-Way ANOVA is a parametric test. This test is also known as: One-Factor ANOVA.

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