A clinical psychologist investigated the success of two different therapy programmes for anxiety: Cognitive Behavioural Therapy (CBT) and Stress Inoculation Training (SIT). After a 10-week course, patients' anxiety reduction was classified as either 'Substantial Improvement' or 'Minimal Improvement'. The psychologist wanted to see if there was a significant association between the type of therapy received and the level of improvement. The results are shown in Table 1.

Calculate the chi-squared ( $χ2\chi^2$ ) value for this data by completing Table 2. Show your calculations and state your final $\chi^2\,$ value to 2 decimal places.

Table 1: Observed frequency of patient improvement by therapy type

Therapy Type	Substantial Improvement	Minimal Improvement
CBT	30	10
SIT	20	15

Table 2: Chi-squared calculation template

Therapy	Improvement	Observed ( $O$ )	Expected ( $E$ )	$O-E)^2$
CBT	Substantial	30	26.7
	Minimal	10	13.3
SIT	Substantial	20	23.3
	Minimal	15	11.7
				$χ2\chi^2$ =

Calculate the chi-squared ( $χ2\chi^2$ ) value for this data by completing Table 2. Show your calculations and state your final $\chi^2\,$ value to 2 decimal places.

Table 1: Observed frequency of patient improvement by therapy type

Therapy Type	Substantial Improvement	Minimal Improvement
CBT	30	10
SIT	20	15

Table 2: Chi-squared calculation template

Therapy	Improvement	Observed ( $O$ )	Expected ( $E$ )	$O-E)^2$
CBT	Substantial	30	26.7
	Minimal	10	13.3
SIT	Substantial	20	23.3
	Minimal	15	11.7
				$χ2\chi^2$ =

Research methods and skills

Question 20

Table 1: Observed frequency of patient improvement by therapy type

Table 2: Chi-squared calculation template

Markscheme

Research methods and skills

Question 20

Table 1: Observed frequency of patient improvement by therapy type

Table 2: Chi-squared calculation template

Markscheme

Research methods and skills

Question 20

Table 1: Observed frequency of patient improvement by therapy type

Table 2: Chi-squared calculation template

Research methods and skills Questions

Research methods and skills

Question 20

Table 1: Observed frequency of patient improvement by therapy type

Table 2: Chi-squared calculation template

Research methods and skills Questions