A clinical psychologist investigated the efficacy of two different intensive psychotherapeutic approaches for individuals diagnosed with Borderline Personality Disorder (BPD): Schema Therapy (ST) and Dialectical Behaviour Therapy (DBT). After a 12-month treatment cycle, patients' clinical outcomes were classified as either achieving 'Full Remission' or 'Partial/No Remission'. The psychologist wanted to determine whether there was a significant association between the type of therapy administered and the level of clinical remission achieved. The observed data is recorded in Table 1.
Calculate the chi-squared (χ2\chi^2χ2) value for this dataset by completing Table 2. Show your calculations and state your final χ2 \chi^2\,χ2 value to 2 decimal places.
| Therapy Type | Full Remission | Partial/No Remission |
|---|---|---|
| Schema Therapy (ST) | 32 | 18 |
| Dialectical Behaviour Therapy (DBT) | 18 | 22 |
| Therapy | Remission Level | Observed (OOO) | Expected (EEE) | O−EO-EO−E | (O−E)2(O-E)^2(O−E)2 | (O−E)2/E(O-E)^2/E(O−E)2/E |
|---|---|---|---|---|---|---|
| ST | Full | 32 | 27.8 | |||
| Partial/No | 18 | 22.2 | ||||
| DBT | Full | 18 | 22.2 | |||
| Partial/No | 22 | 17.8 | ||||
| χ2\chi^2χ2 = |
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