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I want to plot data with very small differences. I can't see the differences in my plot:

enter image description here

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Please post code, not (just) images. And take a look at PlotRange. – Yves Klett Jun 10 '14 at 16:27
data = {4.60001, 4.60002, 4.60003, 4.60004}

ListPlot[data, Joined -> True, AxesOrigin -> {1, 1}]

enter image description here

ListPlot[data, Joined -> True]

enter image description here

Your definition of AxesOrigin was the evildoer

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Your Data are plotting just fine;

sdata = {4.67884, 4.67874, 4.67862, 4.67850, 4.67843, 4.67845, 4.67856, 4.67872, 4.67885};

Compare the two plots p1 and p2;

p1 = ListLinePlot[sdata, AxesLabel -> {"a", "b"}, AxesOrigin -> {1, 1}];
p2 = ListLinePlot[sdata, AxesLabel -> {"a", "b"}, AxesOrigin -> Automatic];
GraphicsRow[{p1, p2}, ImageSize -> 600]

enter image description here

You simply messing with AxesOrigin

I suspect the help Files Axes Origin and Axis will support you;

AxesOrigin is an option for graphics functions that specifies where any axes drawn should cross.

Axis is a symbol that represents the axis for purposes of alignment and positioning.

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That's a duplicate of my answer given hours ago :) – eldo Jun 10 '14 at 18:32

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