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- Basic Concepts
- Descriptive analysis
- Means Tests
- Testing for Relationship
- Construct Validation
- Quantitative Analysis for A Complete Paper

- Levels of measurement | Significance
- YouTube video reference
- Significance -- Confidence Level
- 95%, p < .05, t-value > 1.960 (df = infinity)
- 99%, p < .01, t-value > 2.576 (df = infinity)
- 99.9%, p < .001, t-value > 3.291 (df = infinity)

- Significance -- Confidence Interval
- Lower, Upper

- Defining variables in SPSS - - -
**Video**6min10sec - How to Import data from an excel file to SPSS
- How to calculate mean scores in SPSS
- How to transform and reverse scores (recode) in SPSS

Confidence Level

- 95%, p < .05, t-value > 1.960 (df = infinity)
- 99%, p < .01, t-value > 2.576 (df = infinity)
- 99.9%, p < .001, t-value > 3.291 (df = infinity)

Confidence Interval

- Lower, Upper

Variable view

Variable Name: Not more than 8 characters, not start with a number, no space or symbol

Label: Any number of character, can have space or symbol

Type: Numeric for analysis

Variable Type

- String: including text or some special character, need to clean up and change back to Numeric for calculation

Decimals: Change to zero if it is an integer

Value

Value Labels:

- 7-point, 5-point Likert's scale
- Add 1-7 with value labels

Missing

Missing Value:

- Can just leave it blank
- Just to make sure you have input the data
- Sometimes, you forget whether you have input or not
- By practice, type 99, 999 or 9999 (depending on whether there is the same number/value in the valuable

Measure: Scales of measurement

- Nominal: By category
- Ordinal: By ranking of order
- Scale: Interval and ratio, continuous variable, for calculation of means and standard deviations

Data view

Import data from an excel file to SPSS

- Steps: File >> Import Data >> Excel

Read variable names from first row of data

- variable names should not have more than 8 characters, no space, start with an alphabet, not with a number

Type: Numeric

- Imported data may wrongly be interpreted as "String"
- Change back to "Numeric" for calculation

Decimal: Change to "0" if decimal places are not needed

Value

Value Labels

- Name each score

For example, for a 7-point Likert Scale

- "1" - Strongly disagree
- "2" - Disagree
- "3" - Somewhat disagree
- "4" - Neutral
- "5" - Somewhat agree
- "6" - Agree
- "7" - Strongly agree

Value:

- Copy Value and paste to all

Missing

Missing Values:

- Type the missing value so that SPSS will not wrongly calculate the missing data, e.g., 9, 99 or 999 (Make sure not to overlap with the data)

Measure

Scales of Measurement

- Imported data may wrongly be interpreted as "Nominal" even they are continuous numbers
- Change "Measure" to "Scale

Steps: Transform >> Compute Variable

- Target Variable: Create a new variable and give a name
- Numeric Expression: Add all the indicators/items in the variable/construct, divided by the total number of items
- E.g., POAM = (POAM1 + POAM2 + POAM3 + POAM4 + POAM5) / 5

OR Select a formula for the calculation

- Function group: Select a category from the list, e.g., All
- Functions and special variables: Select a formula from the list, e.g., Mean

- E.g., PORC = (PORC3 + PORC4 + PORC5) / 3

- E.g., OKSB = (OKSB1 + OKSB2 + OKSB3 + OKSB4 + OKSB5) / 5

Descriptive Statistics:

- To report the descriptive statistics for the newly created variable (summed/average score of each variable)
- Steps: Analyze >> Descriptive Statistics >> Descriptives

- Select only the summed score variables
- E.g., POAM, PORC, OKSB

Results: Descriptive Statistics Table, including minimum, maximum, mean, standard deviation

Regression: To test the relationship between the variables

- Steps: Analyze >> Regression >> Linear

- Dependent variable: OKSB
- Independent variables: POAM, PORC

Regression Results

- Model Summary: R Square
- ANOVA: F-value and Significance
- Coefficients: Standardized coefficients beta, t-value, sig.

Steps: Transform >> Record into Different Variables

From the left-hand side, select the variable to record, click the middle arrow and move the variable to the right-hand side

- In the Output variable:
- Name: Give a new name
- Label: Give a new label
- Click "Change" to update the output variable

- Click "Old and New Values"

- Old Value: Click "Value" and input a value
- New Value: Click "Value" and input the changed value

For example,

- 1, 2, 3 are recoded to 1 (Range, lowest through value, input "3")
- 4 is recorded to 2 (Old Value, "4"; New Value, "2"
- 5, 6, 7 are recorded to 3 (Range, value through highest, input "5")

Reverse values for a negation item

- Steps: Transform >> Compute Variable
- Target Variable: Input a new variable name, e.g., OKSB1ve
- Numeric Expression: 8 - OKSB1 (reverse a 7-point Likert Scale)
- 8-"7" = "1"; 8-"6" = "2"; 8-"5" = "3"; 8-"4" = "4"; 8-"3" = "5"; 8-"2" = "6"; 8-"1" = "7"

- How to run frequency distribution in SPSS - - -
**Video**4min13sec - How to run descriptive analysis in SPSS

Step:

- Analyze >> Descriptive Statistics >> Frequencies

Select the variable on the left-hand side

Click the middle arrow to move the variable to the right-hand side, e.g., gender

Select "Charts" if you need to draw a chart

Select a chart type, e.g., "Bar charts"

Click "Continue" and then click "OK"

The results show the Frequency Table, with frequency, per cent, valid per cent and cumulative per cent

The results show the Bar Chart

Step: Analyze >> Descriptive Statistics >> Descriptives

Click to select a variable from the left hand side, e.g., score

Click the middle arrow to move it to the right hand side

Click "Options" for more

Confirm mean, standard deviation, minimum, maximum are selected

Click "Continue", then click "OK"

Results show the Descriptive Statistics Table, including the variable name, the number of the sample, minimum, maximum, mean and standard deviation

To compare the mean of the sample to the mean of the population.

The measurement of the variable should be continuous (scale), e.g., IQ score.

Step: Analyze >> Compare Means >> One-Sample T Test

Click to select the variable from the left-hand side

Click the middle arrow to move to the right-hand side

Type the mean of the population for comparison to the "Test Value", e.g., 105

Check "Option" for Confidence Interval Percentage, e.g., 95%

Results show the descriptive statistics table, including the sample size, mean, standard deviation and standard error mean

Results show the One-Sample Test, including the t-value, degree of freedom (df), significance (2-tailed)(p-value), mean difference, the lower and upper value of the 95% confidence interval of the difference

The data looks something like this.

- There are two conditions, 1 and 2.
- For example, A class is teaching face-to-face where B class is teaching online.
- For example, Group A is taking a placebo where Group B is taking a new medicine.

Steps: Analyze >> Compare Means >> Independent-Samples T Test

Test Variable(s)

- Click and select the left-hand side variable for comparing means, e.g., score
- Click the middle arrow to move to the "Test Variable(s)"

Grouping Variable

- Click and select the left hand Grouing Variable, e.g., condition
- Click the middle arrow to move to the "Grouping Variable"
- Click "Define Groups"

The value in the condition is 1 and 2, therefore, put 1 in Group 1 and 2 in Group 2

Click "Continue" and click "OK"

Results show the descriptive statistics, including the condition 1 and 2, sample sizes, means, standard deviations, standard error means

Results show the Independent Samples Test, including under the "Equal variance assumed," the t-value, df, sig., mean difference, standard error difference, the lower and the upper value of the 95% confidence interval of the difference (the mean difference can be any value within this range)

To compare the means, the variable should be continuous (Scale)

The data file should look like this:

- There are two measurements of the same subject
- For example, before the treatment (pre) and after the treatment (post)
- For example, first taught by face-to-face, then taught by online

Steps: Analyze >> Compare Means >> Paired-Samples T Test

Click and select the left hand side variables

Click the middle arrow to move to right hand side "Paired Variables" one by one, Variable 1 and Variable 2

Results show the descriptive statistics, including the two measurements, the means, the sample size (Must be the same), standard deviations, standard error means

Results show the paired samples correlations

As the same subject was measured two times, there existed correlation between the two measurements

Results show the Paired Samples Test, including the mean difference between the two measurements, the standard deviation, the standard error mean, the lower and the upper value of the 95% confidence interval difference, the t-value, df (n-1), sig.

If you would like the post value to minus the pre value, place the [post] variable to Variable 1, the [pre] value to Variable 2

Paired Samples Statistics are the same

Paired Samples Correlations are the same

The mean difference will be positive in the Paired Samples Test

One-way ANOVA compares means of 3 or more groups

- One variable is the grouping variable
- One variable is the measurement for comparison

The data file looks like this

- Grouping variable with values 1, 2, and 3 (3 conditions)
- Measurement for comparison should be a continuous variable (Scale)

Steps: Analyze >> Compare Means >> One-Way ANOVA

Select from the left-hand side variables and click the middle arrow to move to the right-hand side

- Dependent List: The measurement variable
- Factor: Grouping variable

Post Hoc analysis

- One-way ANOVA provides only significant or not significant for the means but will not provide more information
- Post Hoc analysis further compares the means between each pair of groups

Steps:

- Click "Post Hoc" analysis
- Select from the "Equal Variances Assumed" list, for "Tukey"

Results show the ANOVA table if the means are significantly different, e.g., Sig. (p-value) < .05

Post Hoc Tests

- Compares each pair of groups for the mean difference

For example,

- Group 1 and Group 2, mean difference is 6.70 (p < .001)
- Group 1 and Group 3, mean difference is 5.10 (p < .001)
- Group 2 and Group 3, mean difference is -1.60 ( p = .113, not significant)

Conclusion

- Group 2 and Group 3 are a homogeneous subset which has a significant mean difference with the Group 1 subset

Means

- ANOVA analysis does not provide the means
- Steps: Analysis >> Compare Means >> Means

From the left-hand side variables to select and to click the middle arrow to move to the right-hand side

- Dependent List: measurement variable
- Independent List: grouping variable

Results show the Means Report table for each group, including means, sample sizes, standard deviations

Correlation

- How to run correlation in SPSS - - -
**Video**2min10sec

Regression

- How to run simple regression in SPSS
- How to run multiple regression in SPSS - - - Simple & Multiple Linear Regression
**Video**9min30sec

Chi-square

- How to run chi-square test in SPSS - - -
**Video**3min57sec

Correlation analysis aims to find if variables are significantly related, either positively or negatively related (inverse relationship)

- Variables should be continuous (Scale) for calculation

The data looks like this

Steps: Analyze >> Correlate >> Bivariate

From the left hand side, select the variables and click the middle arrow to move them to the right hand side (Variables)

- Correlation Coefficients: Pearson
- Test of Significance: Two-tailed

Results show the Correlations Table

To report the results, the correlations table needs to be cleaned up

- To display only the lower triangle of a correlation matrix
- Right click to select "Export"

Save Document Type as, "Excel 97-2004 (*.xls)"

Select the location and give a file name

Open the excel file

Remove all the unnecessary columns and rows

- Leave only the variable and the correlation coefficients

Finally, present the Correlation Matrix as below

- To display only the lower triangle of a correlation matrix
- Adjust the decimal places to display consistently the correlation coefficients, e.g., 2 decimal places for all

Simple Regression:

- An independent variable is hypothesized to be significantly related (either positive or negative) to a dependent variable
- Both variables are continuous (Scale)

The data looks like this

Steps: Analyze >> Regression >> Linear

From the left-hand side, select the variable and click the middle arrow to move to the right-hand side:

- Dependent: Place the dependent variable
- Independent: Place the independent variable
- Method: Enter

Results: Variables Entered/Removed

- List the Variable Entered: Independent variable
- List the method use: Enter
- Note the dependent variable

Results: Model Summary

- R
- R-Square
- Adjusted R Square
- Standard Error of the Estimate

Results: ANOVA table

- Regression and Residual
- Sum of Squares, df, Mean Square, F-value, Sig.

Results: Coefficients

- Constant and Independent Variable
- Unstandardized Coefficients (B, Standard Error)
- Standardized Coefficients (Beta)
- t-value, Sig.

Multiple Regression:

- There are several independent variables which are hypothesized to be significantly related (either positive or negative) to a dependent variable (SPPS accepts only one dependent variable)
- All variables are continuous (Scale)

The data looks like this

Steps: Analyze >> Regression >> Linear

From the left-hand side, select the variable and click the middle arrow to move to the right-hand side:

- Dependent: Place the dependent variable
- Independent: Place all the independent variables

Method:

- Enter
- Stepwise
- Remove, Backward, Forward

Results: Variables Entered/Removed

- List the Variable Entered: All the independent variables
- List the method use: Enter
- Note the dependent variable

Results: Model Summary

- R, R-Square, Adjusted R Square, Standard Error of the Estimate

Results: ANOVA table

- Regression and Residual
- Sum of Squares, df, Mean Square, F-value, Sig.

Results: Coefficients

- Constant and Independent Variables
- Unstandardized Coefficients (B, Standard Error)
- Standardized Coefficients (Beta)
- t-values, Sig.

Chi-Square Test

- To find the relationship between two variables
- Measurement of the variables are categorical or discrete, not continuous

Data looks like this

Steps: Analyze >> Descriptive Statistics >> Crosstabs

By practice

- Row(s): for Independent variable
- Column(s): for Dependent variable

Option, "Cells":

- Accept the default value: Observed

Results: X*Y Crosstabulation

Option, "Cells":

- Checked more values:
- Counts: Observed, Expected
- Percentages: Row, Column, Total

Results: X*Y Crosstabulation

- Provide more details

(For construct having more than one item) --- A Complete Study** Video** 27min13sec

- Descriptive analysis for means and standard deviations of variable items
- Construct Validation
- Reliability or Internal Consistence (for each variable)
- Cronbach's alpha > .7

- Construct validity (Factor Reduction, Factor loadings, principal component analysis, varimax rotation, eigen values, % of variance explained)
- Exhibit Convergent validity (factor loadings > .7)
- Exhibit Discriminant validity (No crossloading or not serious below .3/.4)

- Reliability or Internal Consistence (for each variable)
- Compute summed average score for each variable
- Descriptive statistics for summed average score
- Multiple Linear Regression
- Model summary, R-square
- ANOVA, F-value, sig,/p-value
- Standardized coefficient beta, p-value

- Reliability / Internal consistency
- How to analyze internal consistency in SPSS

- Factor analysis (discriminant/convergent validity)
- How to run factor reduction in SPSS

Steps:

- Analyze >> Scale >> Reliability Analysis

Select all the items in ONE construct

- Click the middle arrow to move to right hand side "Items"
- Model: Alpha

Click "Statistics"

Descriptives for

- Check "Item"
- Check "Scale"
- Check "Scale if item deleted"

Results: Case Processing Summary

- Sample size

Reliability (Internal Consistency) Statistics:

- Cronbach's Alpha, literature recommended > 0.7
- e.g., 0.903 > 0.7 for all the 5 items of POAM
- POAM is internally consistent

Item Statistics

- mean, standard deviation, sample size

Item-Total Statistics

- Cronbach's Alpha if Item Deleted: Check if remove any one of the items, the Cronbach's Alpha value can be uplifted, then remove the item
- Especially, sometimes, an item deviates a lot from the other items. Remove it can increase the alpha value a lot
- Removal of any one item of POAM will get the alpha value between 0.869 and 0.897
- Not more than 0.903, all 5 items of POAM
- Therefore, no item will need to be removed from POAM

Scale Statistics

- man, variance, standard deviation, number of items

Repeat the steps for another construct

- PORC: 5 items

Results: Reliability (Internal Consistency) Statistics:

- Cronbach's Alpha, literature recommended > 0.7
- e.g., 0.908 > 0.7, for all the 5 items of PORC
- PORC is internally consistent

Results: Item-Total Statistics

- Removal of any one item of PORC will get the alpha value between 0.875 and 0.896
- Not more than 0.908, all 5 items of PORC
- Therefore, no item will need to be removed from PORC

Repeat the steps for another construct

- OKSB: 5 items

Results: Reliability (Internal Consistency) Statistics:

- OKSB Cronbach's Alpha = 0.923 > 0.7 for all the 5 items
- OKSB is internally consistent

Item-Total Statistics

- Removal of any one item of OKSB will get the alpha value between 0.896 and 0.916
- Not more than 0.923, all 5 items of OKSB
- Therefore, no item will need to be removed from OKSB

Steps:

- Analyze >> Descriptive Statistics >> Descriptives

Select all items from the left-hand side

- click the middle arrow to move all to the right-hand side, "Variable(s)"

Results: Descriptive Statistics Table

- List of each item, sample size, min, max, mean, standard deviation

Right click >> Copy As >> Excel Worksheet

Open the Descriptive Statistics excel file

- Add a column, "Cronbach's Alpha"
- Add the Cronbach's Alpha value for each construct
- POAM: 0.903; PORC: 0.908; OKSB: 0.923

Steps:

- Analyze >> Dimension Reduction >> Factor

Move all the items to the Variables

- click Extraction

Method: Principal components

- click Continue
- clcik Rotation

Method: Varimax

- Therefore, the items will be grouped to corresponding factors (components) accordingly
- click Continue

Scores

- click Continue
- click Options

Coefficient Display Format

- check, Suppress small coefficients
- Absolute value below: 0.4
- If all the factor scores are displayed, it is not easy to read
- If factor scores below 0.4 are not shown, it is easier to identify the serious cross-loadings
- Items with cross-loadings (loaded to more than one factor/component) should be removed, they cannot exhibit discriminant validity

Results: Communalities

- The list of extraction values for each item

Results: Total Variance Explained

- Read for components where Eigenvalues > 1
- Check the total variance explained (% of variance, cumulative %)

Results: Principal Component Matrix

- Not so useful as the components are not distinct

Results: Rotated Component Matrix

- This table is for report
- Each item is loaded clearly to the corresponding component
- Convergent validity: The factor loadings are strong: (1) They are acceptable if the value is > 0.5; (2) They are significant if the value is > 0.7
- Discriminant validity: The factors are distinct, i.e., there is no cross-loading where an item will not belong to more than one factor/component

Results: Component Transformation Matrix

Results: Component Score Coefficient Matrix

To report Rotated Component Matrix

- Right click to Copy As >> Excel Worksheet

Open in Excel

- Read from Total Variance Explained table
- Eigenvalues: input for each component
- % of variance: input for each component

Oh, something wrong

- PORC1 and PORC2 have cross-loaded to both component 1 and component 3
- it does not exhibit discriminant validity, they need to be removed

Repeat the steps but remove PORC1 and PORC2 for the factor analysis

Results: Rotated Component Matrix

- Discriminant validity: no cross-loadings
- Convergent validity: all factor loadings > 0.7, they are all significant

Results: Total Variance Explained

- The total % of variance explained increased, 75.942%

Reliability needs to be done again

- Repeat reliability analysis
- PORC: 3 items, PORC3, PORC4, PORC5

Results: Reliability Statistics

- Cronbach's Alpha: 0.864 > 0.7, exhibit internal consistency

The constructs are reliable and valid

- Report the Descriptive and Reliability Analysis
- Report the Factor Analysis

- Last Updated: May 10, 2024 12:18 PM
- URL: https://libguides.vtc.edu.hk/theilc
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