Tutorial General Linear Model [PDF]

analysis of the General Linear Model (GLM) in SPSS 12.0. Statistical design of the experiment: ... Select General Linear

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Angela Nunn; 03.03.2005

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Tutorial for performing the univariate analysis and the repeated measures analysis of the General Linear Model (GLM) in SPSS 12.0 Statistical design of the experiment: Five trees were exposed to 1xO3 and another 5 trees were exposed to 2xO3 from the year 2000 on. The variables bud break (bud; in day of year), senescence (sen; in day of year) and the length of the growing season (vegper; days) were determined annually (vergper98 – vergper03). The ordinal variable “treat” defines to which treatment group (1xO3 = 1; 2xO3 = 2) the different trees belong.

Data: Data in example_GLM.sav 1.) Define variables name type: text (string) or numeric (Numerisch) labels (Wertelabels) here you can define labels for the ordinal numbers you can set in your variables e.g. “treat”: 1 = 1xO3; 2 = 2xO3 scaling (Meßniveau): nominal, ordinal or metric (Metrisch)

2.) Enter data tree: specific name/number of tree or sample treenr: specific number of tree (n=10) treat: treatment group 1xO3 = 1; 2xO3 = 2 year: year of measurement and data of the different investigated variables: sen (senescence (day of year)); bud (bud break (day of year)); vegper (length of growing season (days)) … and so on Univariate module: The data that you want to analyse have to be coded in one variable, e.g. vegper98 (length of growing season in 1998) to determine if there has been a significant difference in the two treatment groups before the start of the O3 treatment. And with the univariate module you can only analyse one variable at the same time. Repeated measures: If you have measured the same variable more than once, e.g. bud break and senescence once every year, you have to use the repeated measures module to assess if the treatment (ozone) has a significant influence over the whole period.

Angela Nunn; 03.03.2005

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Therefore every measurement date has to be coded in an own variable, e.g. vegper98 (length of growing season in 1998), vegper99 … and so on.

Statistical analysis: Output in example_GLM.spo

Univariate module: 1.) Select General Linear Model (Allgemeines Lineares Modell) - Univariat

2.) Put the variable to be analysed in the field “Abhängige Variable” and the treatment factors into the field “Feste Faktoren”

Angela Nunn; 03.03.2005

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3.) Under options (Optionen) select “Deskriptive Statistik” to get a view on the means and standard deviations of your data and “Homogenitätstests” to test the homogeneity of the variance in your variables, which is a prerequisite for using the General Linear Model. Here you can also change the level of significance (Just in case! ☺)

4.) All other settings in the window “Univariat”, e.g. “Modell, Kontraste “… should be used in the default mode of SPSS. 5.) Results for vegper98: The output sheet of SPSS shows: “Zwischensubjektfaktoren” which shows the valid measurements for the two treatment groups: 1xO3; n=5 and 2xO3; n = 5. “Deskriptive Statistik” which gives the means, standard deviations and n for the two treatment groups. “Levene-Test” which tests if the variances are equal in the two treatments groups. This test has to be non-significant to be able to interpret the results of the GLM analysis. “Test der Zwischensubjekteffekte” which gives us information on the influence of the treatment on the investigated variable:

Angela Nunn; 03.03.2005

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in the year 1998, before the 2xO3 treatment started, there was no significant difference in the length of the growing season between the 1xO3 and 2xO3 trees!

Should be nonsignificant!

6.) Results for vegper00 in the year 2000, the first year of the 2xO3 treatment, there was a significant difference in the length of the growing season between the 1xO3 and 2xO3 trees!

Angela Nunn; 03.03.2005

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Should be nonsignificant!

Repeated measures: Now the question arises if this effect of the 2xO3 treatment on the length of the growing season of the 2xO3 trees is consistent over time? Here we have to use the repeated measured module of the GLM. 1.) Select General Linear Model (Allgemeines Lineares Modell) – repeated measures (Meßwiederholung)

Angela Nunn; 03.03.2005

2.) Define a name for the “Innersubjektfaktor” (Name des Innersubjektfaktors), e.g. “time” and how many times you repeated the measurements (Anzahl der Stufen) Click add (Hinzufügen)

3.) Click define (Definieren)

4.) Now put the different measurement dates (vegper98 to vegper02) in the order into the from, using the arrow.

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Angela Nunn; 03.03.2005

5.) Put the treatment factor (treat) in to the field for “Zwischensubjektfaktoren” In this window (Diagramme) you can select a plot, which shows you the two treatments plotted against time.

6.) Select “time “ as horizontal axis (x-axis) and “treat” as separate graphs on the y-axis

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Angela Nunn; 03.03.2005

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7.) Click add (Hinzufügen)

8.) Under options (Optionen) select “Deskriptive Statistik” to get a view on the means and standard deviations of your data and “Homogenitätstests” to test the homogeneity of the variance in your variables, which is a prerequisite for using the General Linear Model. Here you can also change the level of significance (Just in case! ☺)

9.) All other settings in the window “Meßwiederholung”, e.g. “Modell, Kontraste “… should be used in the default mode of SPSS. 10.) Results: The output sheet of SPSS shows: “Zwischensubjektfaktoren” which shows the valid measurements for the two treatment groups: 1xO3; n=5 and 2xO3; n = 5. “Deskriptive Statistik” which gives the means, standard deviations and n for the two treatment groups and each date separately.

Angela Nunn; 03.03.2005

“Multivariate Tests” gives information on the significance of the time factor and on interactions (Wechselwirkungen) between the time factor and the treatment factor: the time has a highly significant influence in the data set and there is a significant interactions between the time factor and the treatment factor for explanation look at the plot!

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Angela Nunn; 03.03.2005

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Should be nonsignificant!

“Levene-Test” which tests if the variances are equal in the two treatments groups. This test has to be non-significant to be able to interpret the results of the GLM analysis. “Test der Zwischensubjekteffekte” which gives us information on the influence of the treatment on the investigated variable: Over the time period investigated, there was no significant difference (p = 0.085) in the length of the growing season between the 1xO3 and 2xO3 trees!

Angela Nunn; 03.03.2005

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The plot we requested helps a lot in interpreting the results: One can see that the influence of the O3 treatment changes between the years (significant influence of the time factor and significant interaction between time and treatment as tested above in “Multivariate Tests”): in the first two years before the start of the O3 treatment (time 1 and 2) there was hardly any difference in the length of the growing season between the two groups of trees (this should be the case anyway!) In the first year of the 2xO3 treatment (time 3) a big difference between the 1xO3 and 2xO3 treatment occurred. This seemed to get smaller over the next few years. Until in 2003 (time 6) there is hardly any difference left! Maybe this is already the natural difference between the groups that had existed in 1998 and 1999 also. There is a possibility to take the intrinsic difference between the two groups of trees into account:

Angela Nunn; 03.03.2005

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Repeated measures analysis with covariates: We can use the two data points before the start of the O3 treatment as covariates, which takes the natural variance between the two groups of trees into consideration. 1.) Define a new time factor with 4 repeated measurements.

2.) Put the dates (in the correct order!), which had been treated with 2xO3 into the field “Innersubjektvariablen” (time) Click treatment into the field “Zwischensubjektfaktoren” as before and click the two dates where no 2xO3 treatment had been applied into covariates (Kovariaten)

Now the GLM corrects for the initial variance that existed between the two groups of trees before the start of the O3 treatment. The two covariates have no significant influence on the data set. Over the time period from 2000 - 2003, there was also no significant difference (p = 0.094) in the length of the growing season between the 1xO3 and 2xO3 trees!

Angela Nunn; 03.03.2005

However, looking at the plot one can see that the biggest treatment effect occurred in 2000 (the first year of the 2xO3 treatment) and that the effect became smaller over time until it disappeared completely in 2003 (which was extremely dry!)

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