Is random sampling and random assignment the same? What are they?

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No, they are two different things.
Random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population. Each member of the population has an equal chance of being selected.
Random assignment is a way of placing participants into treatment and control groups using randomization. With random assignment, every member has a known or equal chance of being placed in a control or treatment group. Random assignment helps you ensure that all groups are comparable at the beginning: any differences between them are due to the treatment rather than sampling or selection bias.