It started out with a phone call, as so many things do.

Hey, he said, or something to that effect. You know, I bet its cheaper to shop for groceries in New York City than it is here. I work at the Voice of America, he continued, and I have been following the grocery ads in the New York papers and there's a big difference. I don't mean a small difference, a big deference.

He gave some examples and they sound intriguing: orange juice 50 cents less or half a gallon, coffee a dollar a pound less.

We don't usually respond to calls with such activity, but the idea seemed worth pursuing.

Jim Rowe of our staff had just transferred to our New York office and was living on the upper West Side. We decided to take a semi-scientific look to see if the thesis would prove true.

Using the Labor Department's market basket list as a guide, the two of us drew up a list of 46 items that no bachelor's kitchen should be without.

We set a day for shopping. We really didn't buy all the items, merely priced them from the shelves. We chose A&P markets in each city-the one at 48th and Yuma Streets. NW in Spring Valley here and the one at 68th and Broadway in Manhattan.

In some instances, we used house brands (A&P or Ann Page) and in others we relied on nationally known names. Sizes proved difficult to match in some instances and when there was multiple-article pricing (4 for $1, for example) we had to project the unit cost through arithmetic.

There were few dramatic differences in the prices of items and the overall total was remarkably similar.

So caller, wherever you are, the thesis didn't prove true. According to our semi-scientific, one-shot sample, the total for New York City was $71.85, for Washington, $71.55. CAPTION: Illustration, no caption, By Ken Burgess-The Washington Post; Chart, SHOPPING LIST.