Intraclass Correlation Coefficient
Please check the following documents.
It can run on SPSS, but data cannot be interpreted about kappa, weighted kappa, ICC, consistency, and agreement.
- FIM_TOTAL1 and FIM_TOTAL1R
Correlations | |||
FIM_TOTAL1 | FIM_TOTAL1R | ||
FIM_TOTAL1 | Pearson Correlation | 1 | .912^{**} |
Sig. (2-tailed) | .000 | ||
N | 209 | 209 | |
FIM_TOTAL1R | Pearson Correlation | .912^{**} | 1 |
Sig. (2-tailed) | .000 | ||
N | 209 | 209 | |
**. Correlation is significant at the 0.01 level (2-tailed). |
There is a significant strong positive correlation between FIM_TOTAL1and FIM_TOTAL1R
- RAI_TOTAL1 and RAI_TOTAL1R
Correlations | |||
RAI_TOTAL1 | RAI_TOTAL1R | ||
RAI_TOTAL1 | Pearson Correlation | 1 | .935^{**} |
Sig. (2-tailed) | .000 | ||
N | 209 | 209 | |
RAI_TOTAL1R | Pearson Correlation | .935^{**} | 1 |
Sig. (2-tailed) | .000 | ||
N | 209 | 209 | |
**. Correlation is significant at the 0.01 level (2-tailed). |
There is a significant strong positive correlation between RAI_TOTAL1and RAI_TOTAL1R
SAMP WEEK 6
Calculate Intraclass Correlation Coefficient (ICC) and Kappa and Weighted Kappa:
Calculate the ICC for the following pairs of measures (In SPSS, use: Analyze > Scale > Reliability Analysis):
- FIM_TOTAL1 and FIM_TOTAL1R
- RAI_TOTAL1 and RAI_TOTAL1R
- SRH1 and SRH1R
- QoL1 and QoL1R
- In these calculations, consider whether you are interested in “consistency” or “agreement” as discussed in the course text (Streiner, Norman and Cairney, p. 167-169), and whether you are considering the times of the ratings (time 1 and time 2) as fixed or random factors.
- Compare the ICC values with the Pearson’s correlations obtained in Week 1; discuss how would you interpret the differences in the coefficients.
Calculate Kappa:
- In SPSS, for Kappa, use: Analyze > Crosstabs
- Take the admission and discharge scores for two individual items from the RAI or FIM scales (e.g., RAI_WALK1 and RAI_WALK2) and calculate kappa.
- Calculate kappa for SRH1 and SRH1R
- Use quadratic weights for weighted kappa. Briefly discuss differences in results between weighted and unweighted kappa.
Calculate Weighted Kappa:
- Calculate weighted kappa for the same items used above (RAI and/or FIM items, SRH)
- In SPSS, use: Analyze > Crosstabs, to create a table
- Using the values from the table, and using a quadratic weighting scheme, calculate weighted kappa using the utility in the VassarStats website.
Part 1 calculations
- FIM_TOTAL1 and FIM_TOTAL1R
Correlations | |||
FIM_TOTAL1 | FIM_TOTAL1R | ||
FIM_TOTAL1 | Pearson Correlation | 1 | .912^{**} |
Sig. (2-tailed) | .000 | ||
N | 209 | 209 | |
FIM_TOTAL1R | Pearson Correlation | .912^{**} | 1 |
Sig. (2-tailed) | .000 | ||
N | 209 | 209 | |
**. Correlation is significant at the 0.01 level (2-tailed). |
There is a significant strong positive correlation between FIM_TOTAL1and FIM_TOTAL1R
- RAI_TOTAL1 and RAI_TOTAL1R
Correlations | |||
RAI_TOTAL1 | RAI_TOTAL1R | ||
RAI_TOTAL1 | Pearson Correlation | 1 | .935^{**} |
Sig. (2-tailed) | .000 | ||
N | 209 | 209 | |
RAI_TOTAL1R | Pearson Correlation | .935^{**} | 1 |
Sig. (2-tailed) | .000 | ||
N | 209 | 209 | |
**. Correlation is significant at the 0.01 level (2-tailed). |
There is a significant strong positive correlation between RAI_TOTAL1and RAI_TOTAL1R
Solution
SAMP WEEK 6
Part 1 calculations
- FIM_TOTAL1 and FIM_TOTAL1R
Correlations | |||
FIM_TOTAL1 | FIM_TOTAL1R | ||
FIM_TOTAL1 | Pearson Correlation | 1 | .912^{**} |
Sig. (2-tailed) | .000 | ||
N | 209 | 209 | |
FIM_TOTAL1R | Pearson Correlation | .912^{**} | 1 |
Sig. (2-tailed) | .000 | ||
N | 209 | 209 | |
**. Correlation is significant at the 0.01 level (2-tailed). |
There is a significant strong positive correlation between FIM_TOTAL1and FIM_TOTAL1R
Intraclass Correlation Coefficient | |||||||
Intraclass Correlation^{b} | 95% Confidence Interval | F Test with True Value 0 | |||||
Lower Bound | Upper Bound | Value | df1 | df2 | Sig | ||
Single Measures | ,909^{a} | ,882 | ,930 | 21,145 | 208 | 208 | ,000 |
Average Measures | ,952^{c} | ,938 | ,964 | 21,145 | 208 | 208 | ,000 |
Two-way mixed effects model where people effects are random and measures effects are fixed. | |||||||
a. The estimator is the same, whether the interaction effect is present or not. | |||||||
b. Type A intraclass correlation coefficients using an absolute agreement definition. | |||||||
c. This estimate is computed assuming the interaction effect is absent, because it is not estimable otherwise. |
Two-way mixed model as observations are random, but raters are not.
Type is absolute agreement, as systematic differences are relevant.
The Pearson’s correlation coefficient is pretty close to single measure ICC, which is significant and excellent as its far above 0.75.
- RAI_TOTAL1 and RAI_TOTAL1R
Correlations | |||
RAI_TOTAL1 | RAI_TOTAL1R | ||
RAI_TOTAL1 | Pearson Correlation | 1 | .935^{**} |
Sig. (2-tailed) | .000 | ||
N | 209 | 209 | |
RAI_TOTAL1R | Pearson Correlation | .935^{**} | 1 |
Sig. (2-tailed) | .000 | ||
N | 209 | 209 | |
**. Correlation is significant at the 0.01 level (2-tailed). |
There is a significant strong positive correlation between RAI_TOTAL1and RAI_TOTAL1R
Intraclass Correlation Coefficient | |||||||
Intraclass Correlation^{b} | 95% Confidence Interval | F Test with True Value 0 | |||||
Lower Bound | Upper Bound | Value | df1 | df2 | Sig | ||
Single Measures | ,930^{a} | ,903 | ,949 | 29,764 | 208 | 208 | ,000 |
Average Measures | ,964^{c} | ,949 | ,974 | 29,764 | 208 | 208 | ,000 |
Two-way mixed effects model where people effects are random and measures effects are fixed. | |||||||
a. The estimator is the same, whether the interaction effect is present or not. | |||||||
b. Type A intraclass correlation coefficients using an absolute agreement definition. | |||||||
c. This estimate is computed assuming the interaction effect is absent, because it is not estimable otherwise. |
Two-way mixed model as observations are random, but raters are not.
Type is absolute agreement, as systematic differences are relevant.
The Pearson’s correlation coefficient is pretty close to single measure ICC, which is significant and excellent as its far above 0.75.
(single measure is for single rater, average measure is higher and is for reliability of different raters averaged together)
Correlations |
|||
SRH1 | SRH1R | ||
SRH1 | Pearson Correlation | 1 | ,837^{**} |
Sig. (2-tailed) | ,000 | ||
N | 209 | 209 | |
SRH1R | Pearson Correlation | ,837^{**} | 1 |
Sig. (2-tailed) | ,000 | ||
N | 209 | 209 | |
**. Correlation is significant at the 0.01 level (2-tailed). |
Intraclass Correlation Coefficient | |||||||
Intraclass Correlation^{b} | 95% Confidence Interval | F Test with True Value 0 | |||||
Lower Bound | Upper Bound | Value | df1 | df2 | Sig | ||
Single Measures | ,834^{a} | ,788 | ,871 | 11,147 | 208 | 208 | ,000 |
Average Measures | ,910^{c} | ,881 | ,931 | 11,147 | 208 | 208 | ,000 |
Two-way mixed effects model where people effects are random and measures effects are fixed. | |||||||
a. The estimator is the same, whether the interaction effect is present or not. | |||||||
b. Type A intraclass correlation coefficients using an absolute agreement definition. | |||||||
c. This estimate is computed assuming the interaction effect is absent, because it is not estimable otherwise. |
Two-way mixed model as observations are random, but raters are not.
Type is absolute agreement, as systematic differences are relevant.
The Pearson’s correlation coefficient is pretty close to single measure ICC, which is significant and excellent as its far above 0.75.
Correlations | |||
QoL1 | QoL1R | ||
QoL1 | Pearson Correlation | 1 | ,905^{**} |
Sig. (2-tailed) | ,000 | ||
N | 209 | 209 | |
QoL1R | Pearson Correlation | ,905^{**} | 1 |
Sig. (2-tailed) | ,000 | ||
N | 209 | 209 | |
**. Correlation is significant at the 0.01 level (2-tailed). |
Intraclass Correlation Coefficient | |||||||
Intraclass Correlation^{b} | 95% Confidence Interval | F Test with True Value 0 | |||||
Lower Bound | Upper Bound | Value | df1 | df2 | Sig | ||
Single Measures | ,890^{a} | ,847 | ,919 | 18,495 | 208 | 208 | ,000 |
Average Measures | ,942^{c} | ,917 | ,958 | 18,495 | 208 | 208 | ,000 |
Two-way mixed effects model where people effects are random and measures effects are fixed. | |||||||
a. The estimator is the same, whether the interaction effect is present or not. | |||||||
b. Type A intraclass correlation coefficients using an absolute agreement definition. | |||||||
c. This estimate is computed assuming the interaction effect is absent, because it is not estimable otherwise. |
Two-way mixed model as observations are random, but raters are not.
Type is absolute agreement, as systematic differences are relevant.
The Pearson’s correlation coefficient is pretty close to single measure ICC, which is significant and excellent as its far above 0.75.
RAI_WALK1 * RAI_WALK2 Crosstabulation | |||||||||
Count | |||||||||
RAI_WALK2 | Total | ||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | |||
RAI_WALK1 | 0 | 25 | 0 | 0 | 1 | 0 | 0 | 0 | 26 |
1 | 6 | 1 | 0 | 0 | 0 | 0 | 0 | 7 | |
2 | 67 | 9 | 7 | 0 | 1 | 0 | 1 | 85 | |
3 | 8 | 5 | 2 | 0 | 0 | 0 | 0 | 15 | |
4 | 23 | 4 | 4 | 0 | 1 | 0 | 1 | 33 | |
5 | 9 | 5 | 6 | 2 | 0 | 3 | 0 | 25 | |
6 | 7 | 2 | 4 | 1 | 2 | 0 | 2 | 18 | |
Total | 145 | 26 | 23 | 4 | 4 | 3 | 4 | 209 |
Symmetric Measures | |||||
Value | Asymptotic Standardized Error^{a} | Approximate T^{b} | Approximate Significance | ||
Measure of Agreement | Kappa | ,051 | ,022 | 2,418 | ,016 |
N of Valid Cases | 209 | ||||
a. Not assuming the null hypothesis. | |||||
b. Using the asymptotic standard error assuming the null hypothesis. | |||||
Unweighted Kappa is poor, but significant 0.051.
Kappa with Quadratic Weighting based on atatched webpage is 0.1852.
Weighted kappa are meaningful only if the categories are ordinal and if the weightings ascribed to the categories faithfully reflect the reality of the situation.
Whereas unweighted kappa does not distinguish among degrees of disagreement, weighted kappa incorporates the magnitude of each disagreement and provides partial credit for disagreements when agreement is not complete.
SRH1 * SRH1R Crosstabulation | |||||||
Count | |||||||
SRH1R | Total | ||||||
1 | 2 | 3 | 4 | 5 | |||
SRH1 | 1 | 8 | 11 | 2 | 0 | 0 | 21 |
2 | 3 | 40 | 9 | 0 | 0 | 52 | |
3 | 1 | 8 | 33 | 15 | 1 | 58 | |
4 | 0 | 1 | 8 | 31 | 9 | 49 | |
5 | 0 | 0 | 0 | 12 | 17 | 29 | |
Total | 12 | 60 | 52 | 58 | 27 | 209 |
Symmetric Measures | |||||
Value | Asymptotic Standardized Error^{a} | Approximate T^{b} | Approximate Significance | ||
Measure of Agreement | Kappa | ,503 | ,043 | 13,679 | ,000 |
N of Valid Cases | 209 | ||||
a. Not assuming the null hypothesis. | |||||
b. Using the asymptotic standard error assuming the null hypothesis. | |||||
Unweighted Kappa is moderate, and strongly significant.
Kappa with Quadratic Weighting is 0.8338, which is very good.
Value of K | Strength of agreement |
< 0.20 | Poor |
0.21 – 0.40 | Fair |
0.41 – 0.60 | Moderate |
0.61 – 0.80 | Good |
0.81 – 1.00 | Very good |