The answer to this is that FDR's programs were somewhat effective in responding to problems of the Depression but that they were not able to end the Depression. The Depression only ended when the US started to get geared up to participate in WWII.
For example, the unemployment rate in 1940, when the US was not yet involved in the war, was still much higher than it had been in 1929. Since one of the major goals of the New Deal was to get people back to work, this is not a sign that the New Deal was effective.
However, it does seem likely that the Depression would have been worse had it not been for the New Deal. Unemployment rates in 1940 were not as low as in 1929, for example, but they were much lower than the rates were in 1933, when FDR became president.
It is also probably worth noting that FDR's programs had the effect of giving people more hope. The programs led them to feel that the government was actually going to help them. This was surely also an important way in which these programs were effective.