The new compromise natural gas pricing legislation approved yesterday by a House-Senate conference committee is expected to prove a major step in ending the nation's longstanding problems involving supply shortages and crazy-quilt pricing.

While the proposal will raise prices visibly for gas-users outside the South Central gas-producing states, it also will make substantially more gas available in these regions, reducing overall energy costs as customers shift away from more expensive fuels, such as oil.

The proposal also is expected to reduce the nation's dependence on imported oil and natural gas. And, depending on the supply-and-demand pattern over the next several years, it could spur significant new efforts to locate and tap new gas reservoirs.

Perhaps the major element in the compromise is the end of the present "dual market" for natural gas, under which prices are controlled for gas sold across state lines, but left totally unregulated for that left in producing states.

The effect of this dual system has been to keep most of the natural gas discovered in recent years inside a handful of producing states, such as Texas and Louisiana, where prices are unregulated and sellers may charge whatever the market will bear.

By contrast, the rest of the country often has been plagued by shortages. For example, while customers in producing states enjoyed a surplus of gas two winters ago, gas users in Ohio were forced to buy from Canada, which has no price controls. The interstate market here dried up.

What the compromise bill would do is shift to a single nationwide market by gradually deregulating prices of newly discovered natural gas in most states and simultaneously imposing price ceilings on new gas sold within the state where it is produced.

The result would be a far more rational allocation of available gas supplies, both among industrial and residential users. And analysts say the steady revenues would help stem the shrinkage in gas supplies that experts say otherwise would occur if there were no legislation.

Analyses by Data Resources, Inc., the economic consulting firm, and by the staff of the House Commerce Energy Subcommittee, show the following impact of the natural gas-pricing compromise.

Prices of newly discovered natural gas will rise gradually, from the presents $1.52 per thousand cubic feet (outside the gas-producing states) to $3.72 by 1985. Gas from existing wells would be treated under a separate formula.

The subcommittee estimates that for a typical family of four, the increase represents about $165 in added gas bills between now and 1965 - or, about $20 a year. But the impact won't be spready evenly throughout the economy.

For residential customers in the interstate market, gas prices would virtually double from $2.50 a thousand cubic feet to about $4.80 im 1985. However, much of the increase would have come about anyway. Had present controls continued, prices would have jumped to $4.60.

gas producers will reap added revenues, ranging from $4 billion to $4.5 billion more than they would under Present law between now and 1985, as calculated by DRI, to $9 billion over the period as estimated by the subcommittee staff.

However, whether that constitutes a windfall or a setback will depend upon how heavy demand is over the next several years. If supplies prove inadequate over the short run, producers may actually receive less than they would have under the present system.

The main point about the compromises is that the pricing formula will guarantee the producers a predetermined level of revenues, thus providing a certainty that experts say will remove any doubts about whether to begin new exploration.

Present gas supply levels would be preserved, both by distributing available gas more evenly and by drawing in the added revenues needed to spur new drilling efforts.

The Data Resources estimates show the compromise would maintain supply levels for the nation as a whole at the present 17.5 trillion cubic feet through 1985 - possibly even boosting them to 18 trillion Cubic feet or more.

By comparison, DRI estimates that if the compromise had been rejected - or if President Carter's gas-pricing proposal had been adopted instead - gas supplies would have shrunk to 14 trillion cubic feet by 1985. The subcommittee's estimates also show probable shrinkage.

The compromise is expected to boost gas prices for industrial users even more rapidly than prices for residential users. However, industrial users will be hurt less, because they will be able to shift more easily to other forms of energy.