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 June 30,						Six months ended June 30,
	2020			2019			2020			2019
Basic and Diluted:
Net income attributable to UHS	$	251,929		$	238,320		$	393,966		$	472,488
Less: Net income attributable to unvested restricted share grants		(824	)		(656	)		(1,197	)		(1,171	)
Net income attributable to UHS – basic and diluted	$	251,105		$	237,664		$	392,769		$	471,317

Weighted average number of common shares - basic		84,632			89,136			85,422			89,956
Net effect of dilutive stock options and grants based on the treasury stock method		427			99			335			145
Weighted average number of common shares and equivalents - diluted		85,059			89,235			85,757			90,101
Earnings per basic share attributable to UHS:	$	2.97		$	2.67		$	4.60		$	5.24
Earnings per diluted share attributable to UHS:	$	2.95		$	2.66		$	4.58		$	5.23

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 7.1 million for the three months ended June 30, 2020 and 6.5 million for the six months ended June 30, 2020. The excluded weighted-average stock options totaled 8.5 million for the three months ended June 30, 2019 and 7.8 million for the six months ended June 30, 2019. 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 six months ended June 30, 2020, as compared to the comparable prior year three and six months, was due primarily to the impact of shares repurchased by us since January 1, 2019.

During the three-month periods ended June 30, 2020 and 2019, pre-tax compensation cost of $13.2 million and $14.7 million, respectively, was recognized related to outstanding stock options. During the six-month periods ended June 30, 2020 and 2019, pre-tax compensation costs of $28.6 million and $30.5 million, respectively, was recognized related to outstanding stock options. In addition, during the three-month periods ended June 30, 2020 and 2019, pre-tax compensation cost of approximately $2.4 million and $2.1 million (net of cancellations), respectively, was recognized related to restricted stock. During the six-months periods ended June 30, 2020 and 2019, pre-tax compensation costs of approximately $4.7 million and $3.7 million (net of cancellations), respectively, was recognized related to restricted stock. As of June 30, 2020 there was approximately $128.1 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 2.6 years. There were 2,545,966 stock options granted during the first six months of 2020 with a weighted-average grant date fair value of $14.25 per share. There were 125,467 shares of restricted shares granted during the first six months of 2020 with a weighted-average grant date fair value of $68.06 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 $34.0 million and $34.7 million during the six month periods ended June 30, 2020 and 2019, respectively.