Color Rendering Index is a subjective measurement of how well a lamp source renders colors. A measurement of the degree of color- shift an object undergoes when illuminated by a light source when compared to a reference source of comparable color temperature. Incandescent light is assumed to have a CRI of around 100 so it will render all colors correctly. MH only has a CRI of about 70, so only 70% of colors will be rendered correctly. HPS has a CRI of 22.
Color Temperature is not how hot the lamp is. Color temperature is the relative whiteness of a piece of tungsten steel heated to that temperature in degrees Kelvin. HPS has a warm (red) color temperature of around 2700K as compared to MH at 4200K, which has a cool (blue) color temperature.
What is important to remember about these two terms is that CRI readings, of two sources, can only be compared if their color temperature is equal. You cannot compare the CRI of HPS (CRI=22) vs. Metal Halide (CRI=70) because the color temperatures are dif erent (2200K vs. 4500K).
Lumen is a measurement of light output. It refers to the amount of light emitted by one candle that falls on one square foot of surface located at a distance of one foot from the candle. Traditionally, lumens have been the benchmark of a lamps ability to grow plants; meaning the brighter the lamp the better the plant. However, studies have shown that a broader color spectrum lamp will perform much better than a lamp with high lumen output, especially when it comes to plant growth.