In scientific research, we make a hypothesis, such as "Vitamin K causes childhood leukaemia."
You work out your sample size (how many people are needed) to prove this statement to, say, 95% confidence. www.surveysystem.com/sscalc.htm
You then look at your different groups, say, children given Vit K and children not given Vit K. Is there any increased risk of childhood cancer in the vitamin K group?
You show no increased risk of leukaemia and report as,
"there is no convincing evidence that neonatal vitamin K administration, irrespective of the route by which it is given, influences the risk of children developing leukaemia or any other cancer."
"The observation of an increased risk of childhood leukaemia and cancer associated with intramuscular vitamin K is not confirmed by this independent population based study."
"The alleged association between intramuscular vitamin K prophylaxis to newborn infants and childhood cancer could not be verified"
"We found no association between exposure to vitamin K and an increased risk of any childhood cancer or of all childhood cancers combined, although a slightly increased risk could not be ruled out. " [because the sample sizes were not sufficient to demonstrate a tiny increase given the very low incidence of childhood cancer with 48 cases in a group of 54,795 children)
"We conclude that whilst the broad nature of the diagnostic groups and the poor quality of some of the vitamin K data mean that small effects cannot be entirely ruled out, our analysis provides no convincing evidence that intramuscular vitamin K is associated with childhood leukaemia."
"Earlier concern regarding a possible causal association between parenteral vitamin K and childhood cancer has not been substantiated. "
"This population based study adds substantial evidence that there is no association between parenteral vitamin K and childhood cancer."
No sensible person would read this as anything other as what is means - there is no evidence of any risk of childhood leukaemia with Vitamin K.