chi- squared

Test of Association: Chi-Squared

Introduction to Chi-Squared Test

• The Chi-Squared test is an inferential test used for:
  • Determining differences
  • Assessing associations in categorical data.
• Key feature:
  • Data is not listed separately; instead, frequency counts are provided.
  • Data is typically organized in a contingency table (most commonly a 2x2 table).
  • Larger tables can also be utilized (e.g., 3x2, 3x3) where:
  • The first number indicates the number of rows.
  • The second number indicates the number of columns.
• Data independence:
  • Each data item corresponds to a unique individual (e.g., one person per cell).

Worked Example: Cognitive Development Study

• Aim:
  • To investigate if there is a difference in the ability to decentre between 5-year-olds and 8-year-olds.
• Hypotheses:
  • Alternative Hypothesis (Directional, one-tailed): More 8-year-olds than 5-year-olds can select a photograph that represents a perspective different from their own.
  • Null Hypothesis: There is no difference in the ability to decentre between 5-year-olds and 8-year-olds.
• Method:
  • Two independent groups of children are assessed:
  • Group 1: 5 years old
  • Group 2: 8 years old
  • Each group is given the Three Mountains Task.

Creating a Contingency Table

• Step 1: Construct a 2x2 contingency table based on the observed frequencies from the task:
  

  	Could Decentre	Could Not Decentre	Totals
  5-year-olds	6 (Cell A)	27 (Cell C)	33
  8-year-olds	28 (Cell B)	9 (Cell D)	37
  Totals	34	36	70

• Step 2: Calculate expected frequencies for each cell:
• Expected frequency formula:
  $E = \frac{(\text{Row Total} \times \text{Column Total})}{\text{Grand Total}}$