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,
	2019			2018			2019			2018
Basic and Diluted:
Net income attributable to UHS	$	97,190		$	171,746		$	569,678		$	621,630
Less: Net income attributable to unvested restricted share grants		(243	)		(317	)		(1,414	)		(813	)
Net income attributable to UHS – basic and diluted	$	96,947		$	171,429		$	568,264		$	620,817

Weighted average number of common shares - basic		87,952			92,849			89,288			93,639
Net effect of dilutive stock options and grants based on the treasury stock method		403			481			231			459
Weighted average number of common shares and equivalents - diluted		88,355			93,330			89,519			94,098
Earnings per basic share attributable to UHS:	$	1.10		$	1.85		$	6.36		$	6.63
Earnings per diluted share attributable to UHS:	$	1.10		$	1.84		$	6.35		$	6.60

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 4.3 million for the three months ended September 30, 2019 and 6.6 million for the nine months ended September 30, 2019. The excluded weighted-average stock options totaled 7.3 million for the three months ended September 30, 2018 and 8.2 million for the nine months ended September 30, 2018. All classes of our common stock have the same dividend rights.

The decrease in our basic and diluted weighted number of common shares outstanding for the three and nine months ended September 30, 2019, as compared to the comparable prior year three and nine months, was due primarily to the impact of shares repurchased by us since January 1, 2018.

During the three-month periods ended September 30, 2019 and 2018, pre-tax compensation cost of $14.9 million and $14.2 million, respectively, was recognized related to outstanding stock options. During the nine-month periods ended September 30, 2019 and 2018, pre-tax compensation costs of $45.4 million and $46.7 million, respectively, was recognized related to outstanding stock options. In addition, during the three-month periods ended September 30, 2019 and 2018, pre-tax compensation cost of approximately $2.3 million and $1.4 million (net of cancellations), respectively, was recognized related to restricted stock. During the nine-month periods ended September 30, 2019 and 2018, pre-tax compensation costs of approximately $6.0 million and $3.1 million (net of cancellations), respectively, was recognized related to restricted stock. As of September 30, 2019 there was approximately $140.6 million of unrecognized compensation cost related to unvested options and restricted stock which is expected to be recognized over the remaining weighted average vesting period of 2.7 years. There were 2,456,015 stock options granted during the first nine months of 2019 with a weighted-average grant date fair value of $30.40 per share. There were 145,076 shares of restricted shares granted during the first nine months of 2019 with a weighted-average grant date fair value of $133.98 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 $52.2 million and $50.6 million during the nine-month periods ended September 30, 2019 and 2018, respectively.