Valid Application:

• If there are only two cells, expected frequency in each cell should be 5 or more ❌
  This is a valid condition for applying χ², not a restriction.

• Samples of at least 50 observations must be drawn randomly from the population ❌
  Random sampling and adequate sample size are requirements, not conditions for non-application.

• Data should be expressed in original units rather than ratio or percentage ❌
  Chi-square is applied to frequency data, not ratios or percentages—this is again a valid condition.

One of the key limitations/conditions for applying the χ² (chi-square) test is related to expected frequencies:

• When the number of cells is more than two, not more than 20% of the cells should have expected frequencies less than 5.

• If more than 20% of the cells have expected frequencies below 5, the chi-square test should NOT be applied, as the approximation becomes unreliable.

Hence, this condition represents a situation where χ² should not be used.