informed customers that if the sales clerk did not ask them, they would get a lottery ticket for free.
From Campbell’s perspective, four threats to the level of certainty (internal validity) in this example observational study could interact with selection and undermine causal inference regarding the intervention and the observed outcomes (Shadish et al., 2002):
Selection × history interaction—Some other event unrelated to the treatment could occur during the lottery game that would affect sales. Control stores could be disproportionately affected by nearby highway construction, for example, resulting in a decrease in customer traffic.
Selection × maturation interaction—Sales in treatment stores could be growing at a faster rate than sales in control stores even in the absence of the treatment.
Selection × instrumentation interaction—The nature of the measurement of lottery ticket sales in the treatment stores could change during the game in the treatment but not the control group. For example, stores in the treatment group could switch disproportionately from manual reporting of sales to more complete computer recording of sales.
Selection × statistical regression interaction—Stores having unusually low sales in the previous lottery game could self-select to be in the treatment group. Sales could return to normal levels even in the absence of the intervention.
Reynolds and West (1987) matched treatment and control stores on sales in the prior game and on ZIP code (a proxy for neighborhood socioeconomic status). As shown in Figure E-2, they implemented the basic observational study design and then added several design features to address possible threats to the certainty of the causal relationship (internal validity). Panel (a) displays the results of the basic design, showing no difference in sales in the prior game (game 10, no program intervention in both stores, i.e., baseline) but greater sales in the treatment stores during the campaign (game 11) compared with matched control stores with no program intervention. Panel (b) displays the results from a set of nonequivalent dependent measures, sales categories that would be expected to be affected by other general factors that affect sales but not by the intervention. The increase in sales of lottery tickets was greater than the increase for other sales categories. Panel (c) displays the results from a short time series of observations in which the sales campaign was implemented in the treatment stores in week 4 of the game. The results show that both the treatment and control stores experienced similar levels of sales each week prior to the intervention, but that the treatment stores sold far more tickets each week following the initiation of the campaign at the beginning of week 5 (i.e., “program started” in Figure E-2). Taken together, the pattern of results presented by the basic design and the additional design elements provided strong support for the effectiveness of the sales campaign.