Basic earnings per share are based on the weighted average number of common shares outstanding during the period. Diluted earnings per share are based on the weighted average number of common shares outstanding during the period adjusted to give effect to common stock equivalents.

The following table sets forth the computation of basic and diluted earnings per share for the periods indicated (in thousands, except per share data):

	Three months ended September 30,						Nine months ended September 30,
	2022			2021			2022			2021
Basic and Diluted:
Net income attributable to UHS	$	182,814		$	218,351		$	500,789		$	752,466
Less: Net income attributable to unvested restricted share grants		(179	)		(396	)		(592	)		(1,609	)
Net income attributable to UHS – basic and diluted	$	182,635		$	217,955		$	500,197		$	750,857

Weighted average number of common shares - basic		72,595			82,262			73,769			83,756
Net effect of dilutive stock options and grants based on the treasury stock method		465			1,411			743			1,275
Weighted average number of common shares and equivalents - diluted		73,060			83,673			74,512			85,031
Earnings per basic share attributable to UHS:	$	2.52		$	2.65		$	6.78		$	8.96
Earnings per diluted share attributable to UHS:	$	2.50		$	2.60		$	6.71		$	8.83

The “Net effect of dilutive stock options and grants based on the treasury stock method”, for all periods presented above, excludes certain outstanding stock options applicable to each period since the effect would have been anti-dilutive. The excluded weighted-average stock options totaled 6.7 million for the three months ended September 30, 2022 and 6.0 million for the nine months ended September 30, 2022. The excluded weighted-average stock options totaled 4.1 million for the three months ended September 30, 2021 and 4.3 million for the nine months ended September 30, 2021. All classes of our common stock have the same dividend rights.

During the three-month periods ended September 30, 2022 and 2021, pre-tax compensation costs of $15.8 million and $14.6 million, respectively, was recognized related to outstanding stock options. During the nine-month periods ended September 30, 2022 and 2021, pre-tax compensation costs of $48.6 million and $44.8 million, respectively, was recognized related to outstanding stock options. In addition, during the three-month periods ended September 30, 2022 and 2021, pre-tax compensation cost of approximately $4.9 million and $3.5 million, respectively, was recognized related to restricted stock awards, restricted stock units and performance based restricted stock units. During the nine-month periods ended September 30, 2022 and 2021, pre-tax compensation cost of approximately $13.0 million and $9.6 million, respectively, was recognized related to restricted stock awards, restricted stock units and performance based restricted stock units. As of September 30, 2022 there was approximately $170.0 million of unrecognized compensation cost related to unvested options, restricted stock awards, restricted stock units and performance based restricted stock units which is expected to be recognized over the remaining weighted average vesting period of 2.8 years. There were 1,828,573 stock options granted during the first nine months of 2022 with a weighted-average grant date fair value of $45.63 per option. There were an aggregate of 250,089 restricted units granted during the first nine months of 2022, including 73,782 performance based restricted stock units, with a weighted-average grant date fair value of $142.70 per share.

The expense associated with stock-based compensation arrangements is a non-cash charge. In the Condensed Consolidated Statements of Cash Flows, stock-based compensation expense is an adjustment to reconcile net income to cash provided by operating activities and aggregated to $62.7 million and $55.5 million during the nine-month periods ended September 30, 2022 and 2021.